Hydronic System Design with the Bell & Gossett® System Syzer®

TECHNICAL MANUAL

TEH-908A

Hydronic System Design

with the Bell & Gossett

System Syzer

TABLE OF CONTENTS

Introduction ......................................................................................................................................................................................... 1

Determining required ﬂow rate .....................................................................................................................................................1

System pressure drop ....................................................................................................................................................................2

Velocity and friction head loss limits ..............................................................................................................................................2

System piping arrangements ........................................................................................................................................................2

Design example: Series Loop System .................................................................................................................................................2

Design example: Two-Pipe System ......................................................................................................................................................3

Application of pump curve data ..........................................................................................................................................................4

Speciﬁc g ravity ...............................................................................................................................................................................4

Water ho rsepower .......................................................................................................................................................................... 4

Effect of volume ﬂow changes .......................................................................................................................................................5

Calculating system pressure drop .......................................................................................................................................................5

Piping pressure drop .....................................................................................................................................................................5

Fitting and valve pressure drop .....................................................................................................................................................5

Pressure drop of other system components ..................................................................................................................................6

Control valve pressure drop: control valve types ...........................................................................................................................6

Procedures for calculating circuit pressure drop ............................................................................................................................8

The design process: Example: Two circuit series loop .........................................................................................................................8

Pump selection using the system curve ..............................................................................................................................................9

The Bell & Gossett System Syzer

.......................................................................................................................................................10

Scale 1: Load, ﬂow and delta T relationship .................................................................................................................................10

Scale 2: Flow, head loss, and pipe size relationship....................................................................................................................11

Scale 3: Flow velocity ..................................................................................................................................................................12

Scale 4: Circuit pressure drop .....................................................................................................................................................12

Scale 5: Determining unknown pressure drops, system curves, and control valve Cv ................................................................13

Design example: Pumps in parallel using the System Syzer ............................................................................................................13

Design example: Three zone, two pipe system .................................................................................................................................14

Pump selection using Bell & Gossett ESP PLUS ...............................................................................................................................18

System design using ESP PLUS System Syzer ® ................................................................................................................................21

Advanced circuit analysis ...................................................................................................................................................................22

Circuit ﬂow coefﬁcient ..................................................................................................................................................................22

Equivalent Cv of components in series ........................................................................................................................................22

Control valve authority .................................................................................................................................................................22

Equivalent Cv of components in parallel .....................................................................................................................................23

Appendix ...........................................................................................................................................................................................25

NOTE:

Pump curves and other product data in this bulletin are for illustration only. See Bell & Gossett product literature for more

detailed, up to date information. Other training publications as well as the Bell & Gossett design tools described in this

booklet including the System Syzer, analog and digital versions, and ESP Plus are all available from your local Bell & Gossett

representative. Visit www.bellgossett.com for more information or contact your Bell & Gossett representative.

Introduction

Hydronic heating or cooling systems use water as the

means for carrying heat from one point to another. They are

becoming more complex as they grow in capacity, and as

control methods become more sophisticated. Small systems

may still use a single pump, but it now serves several different

temperature zones: low temperature radiant systems, higher

temperature supplemental heat or domestic water zones.

Large systems may use pumps in parallel, serving many

buildings. Flow may be controlled by automatic temperature

control valves and variable speed drives to reduce the amount

of energy used by the pump. As a result, pressures and ﬂows

are constantly changing to meet the current need for heat

transfer.

All of these improvements and reﬁnements depend upon

the design of the pumping and piping system. It is still vitally

important to design the piping system, size the piping, and

determine the actual system pressure drop in order to select a

pump for lowest overall life-cycle cost, and take full advantage

of modern energy saving techniques.

Determining the ﬂow rate

Flow in a hydronic system is used to carry heat, so an accurate

heat load calculation is the foundation for any system design.

The following formula is often used to determine required

ﬂow in hydronic systems:

GPM =

Heat Load

500 Δt

Where:

gpm is the volume ﬂow rate, gallons/minute

Heat load is in BTU/Hr, or BTUH

Δt = Temperature difference between supply and return, ºF

500 is the constant for standard water properties at 60 ºF;

Density, 8.33 lbs. per gal.

Speciﬁc heat, 1 BTU/lb ºF

The complete calculation is then:

BTU

GPM =

8.33

lb.

x 1

BTU

x 60

min

x ΔtºF

gal lbºf hr

Where 8.33 x 60 x 1 ≈ 500

Both the speciﬁc heat and density in the formula are

referenced to 60ºF water. Since 60°F water is too cool for

typical heating systems and too warm for typical cooling

systems, it may seem that ﬂow should be calculated by taking

into account the following changes:

1. Speciﬁc heat and density changes caused by water

temperature changes.

2. Volume ﬂow changes between supply and return

pipes due to temperature differences between

them.

Mr. Gil Carlson, the Director of Technical Services for Bell &

Gossett, discussed these issues in an article published in

HPAC Magazine in February, 1968 entitled “How to Save

Pumping Power in Hydronic System Design”. His basic

analysis was updated and extended for this book.

We can evaluate the effect of these changes in physical

properties on heat conveyance of water by determining the

net change in heat conveyance as system temperature rises.

The formula for determining system ﬂow rate assumes a mass

ﬂow rate of 500 lbs. per hour for each gpm which means

that at a 20º Δt, 1 gpm will convey 10,000 BTUH (500 x 20)

referenced to 60º water. Now determine what happens to

the heat conveyance of 1 gpm @ 20º Δt when the circulated

water has a system average temperature of 200º, (supply

temperature = 210 and return temperature = 190). Water at

200º has a density of 8.04 lb/gallon instead of 8.33 as at 60º,

however, the speciﬁc heat goes up to 1.003 from 1.0 as at

60º. The heat conveyance for 1 gpm at 20º Δt will then be:

8. 04 x 60 x 1.003 x 20 = 9,677 BTUH

The net effect is therefore not signiﬁcant in itself, but there

is another factor to be considered for a complete evaluation.

As water temperature rises, it becomes less viscous, and

therefore its pressure drop is reduced. At 200º, water pressure

drop, or “head loss”, is about 81% of water at 60º for typical

small hydronic systems. Figure 1 gives a graphical analysis

of the effect on system ﬂow. The “system curve” represents

the changes in system head loss as system ﬂow changes for

any ﬁxed piping system. It will be described more completely

later.

Flow increase resulting from operation at 200ºF rather than at 60ºF base

amounts to 10.5 percent.

Figure 1

Note that the ﬂow increase amounts to 10.5% in this

case. Multiply the heat conveyance just calculated by the

percentage of ﬂow increase:

1.105 X 9,677 = 10,693 BTUH

It is apparent that from the standpoint of heat conveyance, the

simple “round number” approach will result in design ﬂows

very close to the “temperature corrected” ﬂows, providing the

result from the “round number” approach is left uncorrected

from the original 60ºF. base for both heat conveyance and

piping pressure drop. The plus and minus factors very closely

100

10 20 30 40 50 60 70 80 90 100 110 120

PEERCENT OF HEAD

PERCENT OF FLOW

Actual system curve

Actual head, only 80%

of specified at specified

flow for 200ºF water

Actual Flow, 110.5%

of specified @ 100% head

Specified point:

100% head at 100% flow

offset one another. A similar analysis for chilled water systems

shows that increased viscosity at lower temperatures reduces

ﬂow compared to 60ºF water, but the changes are small.

Sometimes other ﬂuids are used to carry heat; for example,

water and glycol solutions. Their properties are likely to be

quite different from those of standard water, so the system

designer must account for them. The tools for doing that will

be described later.

System Pressure Drop

Water ﬂowing through piping encounters resistance due to

friction at the conﬁning walls of the piping. This resistance is

called the “pressure drop”, or “friction head loss” of the piping

system. Pumps are installed in a closed loop piping system in

order to apply work to the system ﬂuid to overcome friction

head loss and maintain ﬂow.

Pressure drop will, of course, vary with the condition of the

piping; the rougher or more corroded or scaled the piping,

the higher the pressure drop for a given pipe length and ﬂow.

Pressure drop tables are available for new, clean pipe as well

as for piping which has aged and offers more resistance to

ﬂow because of its relatively poor condition.

Piping in a closed system, with little or no make-up water, can

be considered to be clean pipe since it does not deteriorate or

scale with the passing years. Use of aged pipe pressure drops

will result in deceptively high calculated pressure drops which

in turn result in the selection of pumps which are oversized

for the system. The oversized pump will cause ﬂows much

greater than design requirements resulting in high water

velocities which in many cases become audible and result in

unhappy building tenants. On the other hand, piping in open

systems like cooling towers can experience aging. Higher

design velocity in these piping systems may retard scale

deposits. Any noise is unlikely to cause objections, although

the resulting higher pressure drops will increase pumping

costs.

Velocity and Friction Head Loss Limits

The selection of pipe sizes and pumping equipment also

involves economic factors. Pumps which are larger than

necessary result in higher initial costs and increased

operating costs, especially in larger horsepower ranges.

Pipe size is determined by the ﬂow rate required in

that portion of the system. The designer must give due

consideration to the effect of the pipe size on water velocity

and pressure drop. The water velocity should, of course,

be evaluated on the basis of both the lowest and highest

velocities which can be tolerated. Velocities must be high

enough to entrain any air and carry it to the air separator but

low enough to avoid the generation of ﬂow noise.

Tests have shown that minimum velocities of 1½ to 2 feet

per second must be maintained to entrain air bubbles;

particularly to drive them down vertical piping. Selecting a

pipe with a friction loss rate of 0.85 feet of head loss per 100

feet of length will insure adequate minimum velocity. The

maximum allowable velocity depends on pipe size. Small

diameter pipes up to 1½" can allow velocities up to 4 feet per

second. Higher velocities can be allowed in larger pipe sizes.

Where quiet operation is a design objective, sizing piping for

friction loss rate no greater than 4.5 feet of head loss per

100 feet of length will give good results.

Where noise is not an important consideration, higher

velocities may be used within the limits imposed by

economical pump selection. A prime consideration in any

case is entrained air, which can cause noise even at low

water velocities. System design for proper management of

entrained air can be accomplished as outlined in other Bell &

Gossett publications.

System Piping Arrangements

Prior to the determination of actual pipe size and pressure

drop determination, the designer must establish the piping

conﬁguration of the proposed system to deliver water to

the heat transfer units. Single pipe and two-pipe systems of

various kinds are available. Each has characteristics which

may make it more or less appropriate for the system being

designed. The ﬂow required to carry heat to or from each

terminal unit, and the pipe size to carry this ﬂow can be

determined next. The pressure drop can then be calculated

for the various pipe sizes and lengths in the circuit using tools

provided for this purpose. In addition to the piping, the circuit

will contain ﬁttings, heat transfer equipment, valves of various

types and the terminal units themselves; these will also offer

resistance to ﬂow so their pressure drops must be calculated

or estimated and added to that of the piping.

Design Example:

Series Loop Piping System

The simplest distribution piping arrangement is the series

loop, used primarily for residential, small apartment systems

and retroﬁts. In this system, the radiation is connected in

series and therefore, becomes a part of the piping main.

The basic advantage is economy as substantial savings in

piping materials and the cost of installing these materials are

affected. Figure 2 illustrates a one-pipe series loop system.

Series Loop System

Figure 2

Water temperature entering each unit depends upon how

much heat was extracted or added upstream. This makes it

impractical to install too many units in series since the water

temperature could become too high or too low for effective

heat transfer. The ﬂow through a single circuit system is

limited to the water carrying capacity of the tube size used in

the heating units. In residential systems, these units are often

¾" copper baseboard, but commercial systems may use 1"

or 1½" units. They may also use much higher pressure drop

units like convectors or unit heaters. Another limit to circuit

Pump

Heating units

Boiler

Compression

Tank

length is the combined pressure drop of all the components.

Too many components in series would require very high

pump head. Control of heat transfer by modifying the ﬂow is

limited since a reduction at one device reduces ﬂow through

all of the terminals in that circuit.

When the system ﬂow requirements exceed the capacity

of a single circuit, two or more circuits may be taken off a

distribution or “trunk” main. A return trunk main is used to

pick up the various circuits and return them to the boiler.

Three Circuit Series Loop System

Figure 3

This is a three circuit series loop system. Assuming the use

of ¾" copper tube convector baseboard, each circuit must

be limited to the ﬂow this size tube can handle within

practical limits of pressure drop and velocity; about 4 gpm.

The minimum ﬂow rate and supply temperature leaving

the boiler must be great enough to supply all three zones

simultaneously. At a 20° Δt, that means:

• Circuit #1 is getting 40,000 BTUH

• Circuit #2 is getting 40,000 BTUH

• Circuit #3 is getting 30,000 BTUH

The supply trunk, A-B, must carry 11 gpm, section B-C must

carry 8 gpm, and so on.

The system pressure drop is determined by that of the highest

pressure drop circuit. Circuit #2 is the longest as measured

from the boiler supply, through the circuit and back to the

boiler return. A pump must be able to provide the sum of all

three circuit ﬂow rates, 11 gpm at the head determined by the

longest, or highest pressure drop circuit.

Design Example:

Two-Pipe Systems

In a two-pipe system, the heat transfer terminals are in

parallel. The difference in pressure from the supply main at

the pump discharge to the return main at the pump suction

allows the use of higher pressure drop coils. All of the devices

see the same supply temperature, and “zoning”, is easy and

effective since the ﬂow through one circuit can be changed

without a substantial effect on the other zones. A “zone” is a

room or a collection of rooms which are sufﬁciently similar

in terms of heat transfer requirements that they could be

controlled by a single control device, e.g., a thermostat. In

an apartment building, each apartment will probably be a

separate zone. Larger, multiple zone systems, will beneﬁt in

piping cost savings from a careful analysis of pressure drop.

Figure 4 shows a two-pipe, direct return system on the left.

The ﬁrst circuit to get water is the ﬁrst to return it. Since the

farthest unit has the longest pipe run, it probably determines

the pump head required, assuming that all the terminals have

roughly equal pressure drop. A reverse return system, shown

on the right will equalize the piping length, so all terminals

see the same pressure difference from supply to return.

Direct Return and Reverse Return Two-Pipe

Pumping Systems

Figure 4

Figure 5 is a piping layout for a 12-apartment, zone controlled

heating system. The system layout is based on overhead

supply, with four supply risers dropping down from the

supply main. Each supply riser feeds three apartments, with

series loop connected baseboard controlled by a zone valve

in each apartment. Return risers drop down from each group

of three apartments and are picked up by the basement

return main. Both the mains and the risers are hooked up in

reverse return. Apartments are all the same size; the four top

apartments each have a heat loss of 40,000 BTUH while the

other apartments are 34,000 BTUH each.

Circuit #1

4 gpm

100 ft.

Circuit #2

4 gpm

120 ft.

Circuit #1

3 gpm

90 ft.

Boiler Boiler

Figure 5

Figure 6 shows only the top ﬂoor circuit which will be used to

determine the system pressure drop, and therefore, the pump

head requirement. The ﬂow in each pipe section is shown and

the lengths are determined from the plan.

Figure 6

The trunk main, A to B, is sized to carry full system ﬂow, but

ﬂow in the supply main becomes smaller as each radiation

zone gets its share of the ﬂow, while the ﬂow in the return

main gets larger. An experienced designer would probably

select a 2½" or possibly a 2" pipe for section A-B. The smaller

pipe would have the greater friction loss rate over the length

of A to B. The product of length and friction rate yields the

total head loss in that pipe. Section B-C carries 22.4 gpm but

is very short. Section C-D carries only 11.2 gpm but is much

longer, and contains more ﬁttings. Theoretically, each section

of pipe must be evaluated in terms of the ﬂow it must carry, a

pipe size must be chosen, friction loss rate determined, then

multiplied by length to get the total head loss in that section.

After that, the sum of head loss in all sections has to be added

to the head loss of the boiler and the ﬁttings before the pump

can be selected. In practice, the process can be simpliﬁed by

applying some judgment. For example, an average ﬂow rate,

or most important ﬂow rate could be applied to a long pipe

section to reduce the number of calculations, rules of thumb

might be applied to account for ﬁttings, etc. Later in this book,

we’ll see that the Bell & Gossett System Syzer

is invaluable in

this process.

Application of Pump Curve Data

Centrifugal pump performance curves are developed by test

with 85ºF water and usually relate ﬂow in gpm to foot head.

In terms of relating pumping capacity, the term “foot head”

indicates that the pump is applying one foot-pound of energy

to each pound of liquid being pumped. The curve can be used

for water at any temperature, since “foot pounds per pound”

is an energy statement based on a speciﬁc weight to energy

relationship that remains the same regardless of temperature

or ﬂuid density.

Speciﬁc Gravity

Standard water, with a speciﬁc gravity of 1.0 supports a water

column of 2.3 ft. for each PSI, or 0.43 psi per foot of water

column. The ﬂuid column required for any other speciﬁc

gravity is derived by the formula:

Fluid column in feet = 2.3

For a ﬂuid of lower density, speciﬁc gravity of 0.6:

Fluid column in feet = 2.3/0.6

= 3.85 feet

Water Horsepower

Bell & Gossett Series 1531 Pump Curve

Figure 7

A pump curve indicates the pump will deliver 400 gpm at

30 ft. head. This means the pump will add 30 ft-lbs energy

to every pound of liquid when 400 gpm are circulating. If

the liquid is water at 8.3 lbs/gal, the weight of the circulated

water would be 3,320 lb /min. At 30 ft-lb per lb this would be

30 x 3,320 or 99,600 ft-lb/min energy input to the pumped

water. Dividing by 33,000 ft-lb/min per HP indicates the

pump is applying about three water horsepower, “WHP”.

44.8 GPM

44.8

GPM

22.4 GPM

11.2 GPM

11.2

GPM

22.4 GPM

11.2 GPM

4.0 GPM

7.6 GPM

COPPER TUBE

Head,

ft-lb x

Flow,

gal

x Speciﬁc gravity

WHP =

lb min

33,000 ft-lb x 1 gal

min 8.34 lb

WHP =

Head (ft) x Flow (gpm) x SG

3960

WHP =

30 x 400 x 1

3960

WHP = 3.03 hp

The WHP used by a pump is very important because it relates

the system head and ﬂow to the pump’s power requirement.

WHP represents the “transport energy” required to move

water against the system’s resistance. No practical machine

can be 100% efﬁcient, so the actual horsepower input to the

pump will always be greater then the WHP. The efﬁciency of

the pump and the WHP combine to determine the actual

amount of power required by the pump in the given system.

This factor is called brake horsepower, or “BHP”. If the pump is

80% efﬁcient at 400 gpm and 30 feet of head, it would use a

little less than 4 hp.

BHP =

BHP

Pump efﬁciency

BHP = 30 x 400 x 1

3960 x .08

BHP = 3.79 HP

Since 4 HP motors are not standard, this power would

probably be provided by a motor rated to provide 5 HP, but

actually delivering only 3.79 HP to the pump. These values

are displayed in Figure 7, which is a screen taken from Bell &

Gossett’s ESP Plus. This useful computer application will be

described in more detail later. The electrical energy used by

the pump, and therefore the building owner’s cost to operate

that pump, make BHP a very important factor in selecting and

evaluating pump performance.

Assuming that gauges were placed on the suction and

discharge openings of the pump and that these gauges were

calibrated in PSI, what would the differential readings be?

Since we have added 30 ft-lbs of energy per pound, each

pound is equivalent to 30 feet of the pumped liquid. In this

case, water is being pumped with a weight of 0.43 PSI per ft.,

so the gauges would read a differential of 30 ft. x 0.43 PSI or

12.9 PSI differential.

The speciﬁc gravity of the pumped ﬂuid affects the required

water horsepower to raise the energy level of the pumped

ﬂuid. Suppose the ﬂuid being pumped had a speciﬁc gravity

of 0.6, or 0.6 times the density of standard water. This ﬂuid

would have a weight of 0.26 psi per ft. The gauge differential

would be 30 ft. x .26 or 7.8 PSI.

Thus, the gauge differential, regardless of speciﬁc gravity,

will always read the energy level in terms of feet of the ﬂuid

being pumped. In the case of the gauge differential with

water, the head can be determined by using the differential

of 12.9 PSI and multiplying this by 2.31 feet per PSI, which

gives 30 feet of head. Reference to the pump curve would

indicate a ﬂow of 400 gpm.

The ﬂuid with a speciﬁc gravity of 0.6 would require a column

3.85 ft. high to exert a pressure of 1 PSI. The gauge reading

differential for this ﬂuid was 7.8 PSI; multiplying by 3.85 ft.

per PSI gives 30 ft. as the pump head.

Therefore the pump curve can be applied to liquids of any

speciﬁc gravity without correction. The changes in speciﬁc

gravity of water due to temperature have no affect on the

pump curve. Even though these curves are established

by test with 85º water, they may be used for water of any

temperature.

Effect of Volume Flow Changes

Water expands when it’s heated, contracts when it cools, so

volume ﬂow, in ft

/min changes a little bit due to temperature

differences. Warmer water in the supply will ﬂow a little

bit faster than the return water. These differences are small

enough to ignore without introducing any appreciable error.

But the mass ﬂow rate, lb/min remains a constant because

water is essentially incompressible. At steady state conditions,

that is, the average water temperature in the system is not

changing; the mass ﬂow rate must be the same in the supply

and return mains regardless of the difference in temperature

between them. In other words, the heat input at one point in

the system must be equal to the heat rejected at some

other point.

Calculating system pressure drop

Piping Pressure Drop

Pressure drop in straight runs of piping could be calculated by

reference to charts which state these losses in terms of feet of

60 °F water head per hundred feet of piping. An example is

included in the appendix.

The Darcy-Weisbach relationship is the basis for

determining friction head loss in pipes:

Friction head loss = f

L V

D 2g

Where:

Friction head loss is in units of feet of head, or foot-pounds of

work lost to friction/pound of ﬂuid

f is the friction factor, which relates variables such as

Reynolds number, relative roughness of the pipe, and

ﬂow regime, e.g. laminar, transition, or turbulent ﬂow.

L is the pipe length in feet

D is the pipe diameter in feet

V is the average ﬂow velocity in the pipe in feet per

second

g is the gravitational constant, 32.2 feet per second

The rate of friction head loss used to be stated in terms of

“milinches” per foot of pipe. A milinch is 1/1000 of an inch;

therefore, one foot of head is equivalent to 12,000 milinches.

This term was used because it was convenient to work with

when dealing with small increments of head loss. Most

designers today use units of feet of head loss per 100 feet of

system length. Design ﬂow rate, pipe size, and pipe type will

determine the friction loss rate.

()

(

)

Fitting and Valve Pressure Drop

Pressure drop for various ﬁttings and standard valves is

sometimes stated as some multiple of the velocity head:

Fitting head loss = k x

Where

k is the head loss coefﬁcient for the type of ﬁtting

V is the average velocity of ﬂow through the ﬁtting

g is the gravitational constant

It is possible to save time-consuming calculations for

determining ﬁtting pressure drops by establishing a table

which reads directly in equivalent feet of piping for all ﬁttings.

The variation in equivalent length due to velocity differences

is not of great magnitude in the ﬂow ranges encountered in

hydronic design work. A table of ﬁtting equivalent length

is included in the appendix. In determining the length of

pipe and the pipe size attributable to a given ﬁtting, the

downstream pipe size is used and the ﬁtting pressure drop is

established as the number of feet of that pipe size multiplied

by the friction loss rate. Figure 8 illustrates how the pipe size

is determined. For example, if the ﬂow pattern is from C to B,

the pipe size of F would be used in assigning pressure drop

for the branch ﬂow of the tee.

Where ﬂow enters a tee at C and splits to both A and B, the

pressure drop of the circuit ﬂowing from C to B would involve

the tee branch loss based on pipe size F. The circuit ﬂowing

from C to A would include the tee branch loss based on pipe

size J.

Flow Path Pipe Size Applying to Equivalent Length

A to B F

A to C H

C to B F

D to E G

Figure 8

Pressure Drop of Other System Components

A piping circuit has, in addition to the pipe and ﬁttings,

components such as heat exchangers, boilers, or other units

which have a substantial pressure drop. The pressure drop

of these components is usually stated by the component

manufacturer in either tabular form at various ﬂow conditions

or as pressure drop curves on a chart. Figure 10 is such a chart

showing the pressure drop characteristics for Bell & Gossett

Circuit Setter Balancing Valves. Circuit Setters are used to

prevent unwanted excess ﬂow in the branch of the system

where it’s installed. The round dial sets, and indicates the

valve opening.

Bell & Gossett Circuit Setter

Figure 9

As an example of the use of this chart, assume that a circuit

branch has a Circuit Setter Valve in it set at “0”. The valve

presents little resistance to ﬂow, so a given pressure difference

on the vertical axis results in a large ﬂow rate represented

on the horizontal axis by gpm 1. As the valve is set more

nearly closed, the ﬂow rate at the given differential pressure

would be reduced shown as gpm 2 and then gpm 3. All

components in the system: pipes, elbows, heat exchangers,

demonstrate a similar relationship between ﬂow rate and

head loss or pressure drop. The Circuit Setter is unlike those

other components in that it can change the relationship as it

is manually set from wide open to dead shut.

Control Valve Pressure Drop

Pressure drop data for control valves is often given in terms

of a “Cv” rating for the valve. The Cv for any given valve is the

ﬂow in gallons per minute that would cause a 1 psi pressure

drop to appear across the valve. For example, a valve with a

Cv rating of 10 would have 1 psi pressure drop when 10 gpm

ﬂow occurred through the valve.

Flow Rate vs Pressure Drop

Figure 10

In the Circuit Setter, each manual dial setting establishes a

unique Cv. If the horizontal dashed line represents 1 psi or

2.31 feet of head loss for standard water, then gpm1 is the

Cv for the fully open Circuit Setter, gpm2 and gpm3 are the

lower Cv’s as the valve is closed. If the valve is shut dead tight,

the Cv is 0.

System control valves react in exactly this way, but they

operate automatically in response to a thermostat and

temperature control system.

Headloss Feet

Pressure Drop

PSID

Flow Rate

GPM

gpm 1gpm 2gpm 3

Valve Set

Fully Open

Valve Set

Midway Open

Valve Set

Almost

Closed

DBA

The pressure drop of the valve will vary as the square of the

ﬂow difference. Since the valve pressure drop is 1 PSI at its

Cv ﬂow rating, the formula is:

GPM

Δp

The ﬂow and pressure drop relationship can be

established for any condition using the Cv.

To illustrate, assume a valve with a Cv of 10 will be used to

control a ﬂow of 30 gpm, what will the pressure drop through

the valve be at this ﬂow?

Valve pressure drop (psi) =

GPM

Valve pressure drop (psi) = (30/10)

= 9 psi

To determine the pressure drop in terms of feet of water head,

multiply by 2.3 assuming standard water.

9 x 2.3 = 20.7 Ft.

Control Valve Types

Control valves are used to modulate the system water

temperature or to control the quantity of water ﬂowing

through the system heat exchangers. The valves are furnished

in two general types, two-way or three-way, depending on the

number of ports in the valve.

Two-way valves are often used as two-position valves, either

open or closed. A commonly used illustration is the zone

valve, operated by a thermostat, which opens the valve on a

call for heat and closes it when the heat demand is satisﬁed.

Double and Single Seated Control Valves

Figure 11

The double-seated valve has no hydraulic forces acting on

the valve stem, as water ﬂowing through the ports tends

to open one disc and close the other. The single-seated

valve must operate against the hydraulic force of the water

entering the port as the valve moves toward the closed

position. The double-seated valve is not used for tight shut-off

requirements as the common shaft connecting the two discs

expands and contracts with temperature changes, making it

difﬁcult to close both ports simultaneously. Therefore, either

valve may be used for modulating type operation but for two-

position, (on-off) the single-seated valve is used.

For two-position operation, the valves are usually line-sized

and are selected for low pressure drop. Modulating valves,

on the other hand, should be selected for high initial (wide

open) pressure drops as this enhances control operation by

keeping the pressure drop increase ratio at a minimum as the

valve modulates to close-off. The topic of “valve authority” is

discussed later in this book. Other Bell & Gossett publications

explain valve selection in detail.

Three-way valves are furnished in two basic types. The mixing

type has two inlet ports and the third, or common port is the

outlet. The diverting type makes the common port the inlet

and the other two ports are outlets as shown in Figure 12.

Three-Way Mixing and Diverting Valves

Figure 12

Severe valve chatter may result if the common port of a

mixing valve is used as an inlet with the other two ports as

outlets as in a diverting valve. As the valve disc approaches

either seat, the velocity pressure will tend to over-ride the

operator and slam the valve shut. The velocity pressure is now

gone and the valve motor will then open the valve again. This

occurs rapidly, with severe chattering as a result.

The same thing happens with a diverting valve if an attempt

is made to use it as a mixing valve. This would require the A

and the B ports to be inlets, with the AB port as the outlet. The

velocity pressure would act to over-ride the operator as either

disc approached its port, resulting in valve slam or chatter.

The application and sizing of three-way valves is covered in

other Bell & Gossett publications. A general statement on

valve selection can be made without going into the actual

procedures. Three-way valves applied in the equipment room

for temperature modulation or system change from heating

to cooling should be selected for low pressure drops, if

possible under ten feet, in order to minimize required

pump head.

It is important from the standpoint of ﬂow stability in a system

using three-way valves to control coil ﬂow, to select the valves

for a substantial portion of the available pump head. As in

two-way valves used for this purpose, the pressure drop across

the valve increases as the valve closes down. This causes an

increase in ﬂow through the valve, making it necessary to

close off still further to compensate for the increase in ﬂow. If

the valve is selected for a low pressure drop, the pressure drop

ratio necessary to throttle to a given ﬂow will be very large

and the valve will have to “ride” its seat to achieve control.

Therefore, it is good practice to select the valve for high initial

pressure drops, on the order of three times the coil pressure

drop at design ﬂow, if possible. Due to the fall off of coil

pressure drop with reduced ﬂow, coils used with three-way

valve control should be selected for low design pressure

drop. This decreases the effect on circuit pressure drop as the

control valve goes to bypass. Typical three-way valve and coil

installations are shown in Figure 13. The bypass pipe around

the coil must have a Circuit Setter in order to equalize the

√

[

]

resistance of the paths through the coil and bypass. Without

the Circuit Setter, the pump ﬂow would increase whenever

ﬂow shifted to the bypass.

Circuit Setters in Diverting and Mixing Valve Applications

Figure 13

Procedures for Calculating Circuit Pressure Drop

Total Equivalent Length Method for Fitting Pressure Drop.

Calculating the actual pressure drop for each ﬁtting can be a

time-consuming and therefore, expensive procedure. In an

effort to reduce design time, an alternate method was devised

in which it is assumed that the ﬁttings and other system

components are equal to 50% of the circuit length. This 50%

is added to the circuit length and the total is considered to

be the Total Equivalent Length, TEL, of the circuit. Practical

experience has shown that this method leads to sufﬁciently

accurate results for systems up to about 400,000 BTUH. Larger

systems would warrant a more detailed analysis since savings

in pipe size or pumps may result. Short circuits with more

than the average member of ﬁttings should also be carefully

evaluated, since the 50% allowance may not be sufﬁcient to

cover the actual ﬁtting losses. Simple logic and experience

will indicate when a pipe sizing check using actual pressure

drop data for each ﬁtting is required.

Keep in mind that the “50% method” is for ﬁttings and

conventional baseboard radiation only. In the event that

there are high pressure drop devices such as fan coil units

in the circuit, the pressure drop of these devices should be

considered separately.

When the system consists of a single circuit, the pump must

provide the needed ﬂow and overcome the piping pressure

drop at this ﬂow. Larger systems require more circuits to keep

the pressure drop and pipe size down. The pump on multi-

circuit systems must be capable of meeting the pressure

drop of the highest pressure drop circuit, which is usually the

longest circuit. The pump also must furnish the ﬂow required

by all circuits.

The circuits with lower pressure drops will tend to short circuit

the high pressure drop circuit and must be brought up to the

pressure drop level of this circuit by the use of balance valves

or by reduction of pipe size to achieve the desired pressure

drop.

Flow in a pumped system will apportion itself among the

various circuits so that the pressure drops between the pump

and the individual circuits are just equal. The designer should

therefore endeavor, by judicious pipe sizing to keep circuit

pressure drops as close as possible, even though design ﬂows

may vary considerably. This will make the eventual balancing

requirements simpler.

The Design Process

It’s important to follow a coherent process of making

calculations, then making choices based on those calculations

in an orderly manner. Though this is not the only way to

do it, the Bell & Gossett design process makes sure all

the important details are covered. The most economical

combination of pump size and piping size within good

design parameters should be selected.

1. Calculate heat loss and select terminal units

2. Make piping layout to scale

3. Calculate required water ﬂow to carry the load

4. Size the piping

5. Select the pump

6. Select the boiler and other accessories

This method permits very quick pump selection and pipe

sizing for smaller systems. Larger systems should be

evaluated using more sophisticated procedures.

DESIGN EXAMPLE NO. 1

A two-circuit series loop system utilizing ¾" copper convector

baseboard is shown in Figure 14. The Six Step Method will be

used for designing the system at a 20º Δt.

Two Circuit Series Loop System

Figure 14

STEP 1 RADIATION REQUIRED

Calculate the heat loss in terms of BTUH for each room. Find

the output per lineal foot of baseboard at the desired mean

water temperature from the manufacturer’s catalog then

divide room heat loss by this ﬁgure to determine the lineal

feet of radiation required in each room

STEP 2 LAYOUT THE PIPING

Make a scale drawing of the piping system. Because the

radiation is in series, the ﬂow in each circuit should not

exceed the carrying capacity imposed by the pipe size of the

radiation. See Step 3 for ﬂow rate calculation.

Nomogram A (in the Appendix) indicates that a 1" pipe could

carry the ﬂow if a single circuit were used, but the proposed

baseboard units are constructed with ¾" copper which is

limited to about 4 gpm, so the system must be split into

two circuits of about 40,000 BTUH each which allows ¾"

baseboard to be used.

STEP 3 CALCULATE REQUIRED WATER FLOW

The total load is 76,000 BTUH. Required ﬂow is therefore:

Flow =

Heat Load

500 Δt

Flow =

76,000

= 7.6 gpm

500 x 20

Circuit 1 will need about 3.6 gpm, circuit 2 about 4.0 gpm

Circuit #1

35,500 BTUH

111 Ft.

Circuit #2

40,500 BTUH

134 Ft.

Mixing Valve

Diverting Valve

Circuit

Setters

Boiler

Circulator

Air Vent

STEP 4 SIZE PIPING

The trunk main must be 1”, each circuit will be ¾".

STEP 5 SELECT PUMP

A “Booster” pump is a small in-line circulator often used

for systems like this. It’s a simple pump whose selection

requires little more than knowing the system head and ﬂow.

System ﬂow is 7.6 gpm. System head loss could be estimated

by assuming that the friction head loss everywhere in the

system is near the upper limit of head loss, say 4.0 feet of

head loss per 100 feet of length. The measured length of the

longer circuit is 134 feet, a 50% allowance for ﬁttings would

add 67 more feet for a Total Equivalent Length (TEL) of about

200 feet. Pump head would then be estimated as:

Pump head =

4.0 feet of head loss

200 feet of TEL

100 feet of length

= 8 feet of head

If the head loss of other components like the boiler is low,

it may be assumed that this estimate of pump head will be

adequate. If higher pressure drop components are included

in the system, then the published data for their head loss at

the design ﬂow must also be included.

Plot the system head and ﬂow, the “design point”, on a chart

showing the performance of all sizes of booster pumps to

select the speciﬁc pump required. A more detailed discussion

follows.

STEP 6 SELECT THE BOILER

Select a boiler with a net rating equal to or slightly greater

than the 76,000 BTUH total heat loss. A discussion of required

air management and other equipment can be found in other

Bell & Gossett publications.

Pump Selection: the System Curve

In many cases, available pumps do not exactly ﬁt the system

requirements. In most cases, designers choose the next

larger size pump. While such a selection may cause no actual

problems, using the next smaller pump can save money, if an

analysis of the problem indicates that this can be done.

The analysis consists of plotting a “system curve”, which shows

system ﬂow versus system pressure drop, on the proposed

pump curves. This analysis will determine how any given

pump will perform in the system because a given pump in

a system must operate at the ﬂow rate determined by the

intersection of the two curves. This is a consequence of the

principle of conservation of energy. The system curve shows

the relationship between ﬂow and pressure drop in a given

piping system. The pressure drop varies in a direct ratio with

the square of the ﬂow change ratio. As an example, if the ﬂow

in a piping system should double, the pressure drop would

increase by a factor of four.

This simple relationship allows us to construct a curve which

can be superimposed on a pump performance curve. The

intersection of the two curves deﬁnes the ﬂow, or the point

of operation for the pump in the system. To illustrate this

method we will assume a pump is needed for a system

requiring a ﬂow of 30 gpm at a pressure drop of 20 ft.

The pump curves in Figure 15 show that this design point

falls between a PL-36 and a PL-55 pump. There is no point of

intersection at exactly 30 gpm. Which pump should be used?

Using the design condition as a starting point, we can

construct a system curve which will indicate the ﬂows which

either pump would produce.

Figure 15 shows the design point – 30 gpm @ 20 ft. We will

determine several points, beginning with 50% ﬂow, or 15

gpm. The system pressure drop at 15 gpm will then be the

square of the ﬂow ratio; that is the square of 0.50 which is

0.25 of the design pressure drop. 25% of 20 = 5 ft. Several

other points could be determined in similar fashion.

Assumed Ratio to Ratio to Design Head at

Flow Design Design Head New

gpm Flow Head Feet Flow

0 0 0 20 0

15 0.50 0.25 20 5.0

20 0.66 0.43 20 8.6

25 0.83 0.69 20 13.8

30 Design 1.00 1.00 20 Design 20

35 1.17 1.37 20 27.4

Plot these points on the curve as in Figure 15 and connect

them with a smooth line. This is the system curve. The line

intersects the PL-55 curve at 33 gpm and the PL-36 at 27 gpm.

We can now calculate the effect of either pump on system

operation.

System Curve Method for Pump Selection

Figure 15

If the system uses a 20º temperature drop, the lower ﬂow

of 27 gpm will increase the design temperature drop. The

relationship between ﬂow and temperature drop is an inverse

one; if we double the ﬂow we halve the temperature drop and

vice-versa. We can therefore, set up a proportion to calculate

the effect of reducing ﬂow:

30 gpm

= 22º

27 gpm 20 Δt

From this, we can determine that the system will operate at

a 22º design temperature drop instead of 20º, if we use the

smaller pump. This is negligible since heat output in units

like baseboards or convectors is not greatly affected by small

changes in ﬂow. Output is strongly affected by changes in

average water temperature so the lower ﬂow rate could

be easily compensated for by slightly raising the system

operating temperature if necessary.

The effect of using the PL-55 pump at 33 gpm can be

calculated in the same way. The larger pump provides 33

gpm, so the temperature change at the boiler would be about

18ºF.

It is probable that the smaller pump is the better selection

since it probably has a lower initial cost. It also has a smaller

motor, thus reducing operating costs at least a little bit.

The Bell & Gossett System Syzer

Determining the required operating head and ﬂow for small

hydronic systems is relatively simple. However, an engineer

must consult several different design tables, charts, and

formulae to establish ﬂow requirements, pipe size, pipe

pressure drops, water velocities, pumping heads, system

curves, control valve Cv ratings, etc. The B&G System Syzer

Calculator consolidates all necessary design information in a

simple, easy to use circular slide rule.

The System Syzer

Calculator is useful both in ﬁnal design

work and in preliminary system planning. Proposed pump

and pipe sizes can be quickly roughed out for estimating

purposes.

System Syzer

Scales 1-3

Figure 16

System Syzer

Scales 4-5

Figure 17

The System Syzer

Calculator has ﬁve scales sequenced

in the same way in which they would typically be used in

designing a hydronic system. The following discussion gives

the reference base of the various scales and illustrates their

uses with design examples. It’s best to obtain a System Syzer

calculator from your Bell & Gossett representative and use it to

work through these examples.

Scale #1 – Load-Flow Relationships

Scale #1 is stated in terms of temperature difference, MBH

and gpm. These terms are deﬁned as follows:

A. Temperature difference is the temperature drop (heating)

or temperature rise (cooling) taken by the water as it

transports heat through the system.

PL-55

PL-36

PL-45

PL-50

PL-30

10 20 30 40 50 60 700

140

130

120

110

100

01234

0246810 12 14 16

Bell & Gossett

Series PL Circulator

B. MBH is the heating or cooling load in Btu per hour where

1 MBH = 1000 Btu per hour; 10 MBH= 10,000 Btu per

hour; 1000 MBH = 1,000,000 Btu per hour or 1M.

C. gpm is the circulation rate in gallons per minute required

to convey the design heat load at design temperature

difference.

Flow rate in gpm, temperature difference in degrees F and

MBH load are related by the following formula:

Flow =

Heat Load

500 Δt

Scale #1 uses a specic heat equal to one and

water density at 8

⁄

lbs. per gallon (60ºF conditions). Changes

in these properties and their effect on heat transfer have

already been discussed.

Example #1: Determine required ow rate for a load of

150,000 Btu per hour at a temperature drop of 30º.

Set the 150 MBH capacity in the large window under the 30º

design Δt. Read gpm ﬂow rate in the small window opposite

the arrow: 10 gpm.

Example #2: Determine required ow rate for a cooling load

of 20 tons at a 10º temperature rise. At 12,000 Btuh per ton,

a 20 ton load is equivalent to 240,000 Btu per hour or

240 MBH.

Set 240 MBH opposite 10º temperature difference and read

48 gpm on the gpm scale.

Design Temperature Difference: For many years hot water

systems have been designed for a 20º temperature drop. This

has been done because at a 20º temperature drop, each gpm

circulated conveys about 10,000 Btu/hr. This allows simple

determination of ﬂow rates by use of the following formula:

GPM =

Heat Load

10,000

A 20º temperature drop in typical terminal units also provides

a great deal of “forgiveness”; 100% of design ﬂow is not

necessarily required to get a very high percentage of design

heat transfer. While the 20º design temperature drop is still

useful for small hydronic system, it is not necessarily best for

a larger engineered system. Higher temperature drops permit

lower ﬂow rates, smaller pipe and pump sizes and in general

return economic beneﬁts.

Scale #1 of the System Syzer

Calculator will assist the

hydronic designer in establishing minimum ﬂow – maximum

temperature difference system design through the various

design approaches now available. These include primary-

secondary pumping, coil re-circuiting, terminal unit ﬂow

evaluation, etc. Because of the simplicity of determining ﬂow

rates for various temperature differences, the System Syzer

Calculator will aid greatly in the design of higher temperature

difference systems.

Example #3: Determine primary to secondary ow rate for

a secondary zone using a heat injection pump as illustrated

in Figure 18. Negligible pressure drop in a pipe which is

common to two pumping circuits makes the two pumps

operate independently of one another. Details of primary-

secondary pumping are available in other Bell & Gossett

publications.

Figure 18

The radiant panel in the secondary zone requires 10 gpm

of 110º water at a 10º Δt to provide the zone requirements

of 50,000 Btu/Hr. Water at 200F is available at the primary

supply pipe. At design load conditions, the required quantity

of 200º water must ﬂow from point A to point B. An equal

quantity of 100º water must ﬂow from point C to point D. The

temperature difference between point A and point D of 100º

(200º-100º) and the 50,000 Btuh required for the secondary

zone determine the ﬂow required from the primary to the

secondary circuit.

On scale # 1 of the System Syzer Calculator, set the 100º

temperature difference opposite 50 MBH. Read the required

primary to secondary ﬂow rate: 1.0 gpm. The heat injection

pump should be sized to deliver 1.0 gpm against a head

determined by circuit A-B-C-D.

Example #4: There are many ways to use primary-secondary

pumping principles. In the next example, a one-pipe primary

loop supplies hot water to an independent secondary zone

through a small control valve. Determine the temperature

drop in the primary main of a one-pipe primary system with

a circulation rate of 50 gpm, after supplying 50,000 Btuh to a

secondary zone as illustrated in Figure 19.

Figure 19

As in the preceding example, the ﬂow from A to B is 1.0 gpm.

Since the total primary ﬂow is 50 gpm, a ﬂow of 50 minus 1.0

or 49 gpm of 200º water will ﬂow from point A to D. At point

D, 1.0 gpm of 100º water will blend with the 49 gpm of 200º

Radiant Panel

50,000 Btu/Hr

110F 100F

Primary Supply

200F

Primary Return

BC and AD are the low pressure drop

“common” pipes that allow

the pumps to operate independently

Circuit Setter

Secondary Panel

50,000 Btu/Hr

110F 100F

Primary Supply 50 gpm 200F

Circuit Setter

Control Valve

water to give 50 gpm, but at a reduced temperature. What is

the temperature downstream of point D?

Set 50 gpm in the small window of scale #1. Directly opposite

50 MBH read the temperature difference: 2º. Therefore, the

temperature beyond point D is 200º minus 2º = 198º.

Scale #2 – Flow-Pressure Drop Relationships and

Pipe Sizing

Scale #2 relates gpm ow rate to friction loss rate for both type

“L” copper tubing and for Schedule 40 steel pipe. Friction loss

is stated in terms of milinches per foot and in feet per 100

feet of pipe. Either milinches per foot or feet per 100 feet are

valid expressions of pipe friction loss. Deﬁning these terms:

A. Milinch means 1/1000 of an inch or 1/12,000 of a foot of

pressure energy head.

B. Feet per 100 feet expresses the rate of pipe friction loss as

foot head of energy loss per I 00 feet of pipe.

The pipe friction loss data used as a basis for construction

of scale #2 are The Hydraulic Institute Values, The ASHRAE-

Giesecke Chart Values and The ASHRAE Uniﬁed Pressure

Drop Chart data. Both the Hydraulic Institute values and

The ASHRAE Uniﬁed Pipe Pressure Drop data are based on

Moody’s pipe pressure drop correlation. Though established

by an entirely different experimental approach, the Giesecke

Chart values closely approximate Moody’s correlation-

generally accepted as most valid. Friction loss indicated for

type “L” copper tubing has been derived from the ASHRAE

Handbook.

Scale #2 is based on a water temperature of 60º. When used

for hot water design with temperatures in the area of 200º

piping pressure drop is over-stated on the order of 10% since

pressure drop decreases slightly as water temperature is

increased. However, the difference is not sufﬁcient to warrant

correction.

The normally used range of pipe friction loss rates is indicated

by a white wedge shape band on scale #2. Experience

indicates that the optimum friction loss range is from 100 to

500 milinches per foot or from approximately 0.85 foot to 4

.5 feet per 100 feet of piping.

Example #1: Determine pipe size for 70 gpm ow rate. Set

the rule so that 70 gpm appears in the “white” or optimum

design range on the rule. It is apparent that either 2½" or 3”

pipe can be used. Setting the arrow to 2½" pipe size in the

iron pipe window, a pipe friction loss rate of 3.6' per 100'

appears opposite 70 gpm. A simultaneous reading on scale

#3 establishes that at 70 gpm a water velocity will be 4.5' per

second.

Setting the rule to 3" pipe illustrates that at 70 gpm ﬂow

rate a pipe friction loss rate of 1.2' per 100' will occur. A

simultaneous reading on scale #3 indicates a water velocity of

3.0' per second.

Setting the rule to any pipe size then provides a complete

ﬂow-pressure drop-velocity relationship for that particular

pipe size. In the example, either 2½" or 3" piping, could be

used for the ﬂow rate of 70 gpm, depending on circuit needs,

available pumping head, etc. In many cases, the hydronic

system designer may also wish to evaluate water velocity as

this affects pipe sizing.

Scale #3 – Water Velocity

Scale #3 establishes water velocity in feet per second for

any given ﬂow rate through the particular pipe size. Water

velocity in the hydronic system should be high enough to

carry entrained air in the water stream-yet not high enough to

cause noise. Water velocity should be above 1½ to 2 feet per

second in order to carry entrained air along with the ﬂowing

water to the point of air separation (Rolairtrol, EAS, etc.) where

the air can then be separated from the water and directed to

the compression tank or vented from the system. See other

Bell & Gossett publications for details about air management

in hydronic systems.

Piping noise considerations establish the upper velocity

limitations. For piping 2" and under a maximum velocity of

4 feet per second is recommended. Note that in smaller pipe

sizes, this velocity limitation permits the use of friction loss

rates higher than 4 feet per hundred foot.

Velocities in excess of 4 feet per second are often used on

piping larger than 2 inch. It seems apparent that water

velocity noise is caused by entrained system air, sharp

pressure drops, turbulence, or a combination of these which

in turn cause ﬂow separation, cavitation and consequent

noise in the piping system.

It is generally accepted that if proper air management is

provided to eliminate air and reduce turbulence in the

system, the maximum ﬂow rate can be established by the

piping friction loss rate; at 4 feet per 100 foot. This permits

the use of velocities higher than 4 feet per second in pipe

sizes 2" and larger.

Example #1: A supply main in an apartment building has a

design ﬂow rate of 1600 gpm. Select the proper pipe size.

Setting Scale #2 at 8" pipe shows that at 1600 gpm, the pipe

friction loss is 3.8 feet per hundred feet. Scale #3 shows that a

water velocity in excess of 10 feet per second will result.

Setting the rule at 10" pipe illustrates a pressure drop of

1.2 feet per 100 foot and a water velocity of 6.5 feet per

second, less likely to cause noise. Because the main must

run adjacent to living quarters, a critical location concerning

possible noise generation, the 10" pipe would be preferred.

Scale #4 – Circuit Piping Pressure Drop

Scale #4 provides a simple method of determining required

pump head from the equivalent circuit piping length and the

resistance per unit length. To use Scale #4, it is rst necessary

to establish the total equivalent length (TEL) of the piping

circuit. As all ﬁttings have a greater resistance to ﬂow than

a straight length of pipe, this must be taken into account.

TEL is a summation of the straight lengths of pipe plus the

equivalent length of valves ﬁttings, etc.

In preliminary pipe and pump sizing, it is common practice

to consider the resistance of ﬁttings in a circuit to be a

percentage of the straight length of pipe (usually 50%). In

making a more accurate pressure drop calculation, the actual

resistance of each ﬁtting should be considered. The table on

the back of the System Syzer Calculator envelope indicates

the equivalent length of most commonly used ﬁttings. Recent

research has shown that these equivalent lengths tend to

overstate the ﬁtting head loss by some amount depending on

type of ﬁtting and ﬁtting size. Therefore, use of these values

builds in a small safety factor.

Example #1: A circuit owing 200 gpm is sized at 4" providing

a friction loss of 2.3 feet per l00 feet. The circuit has a TEL of

130 feet. What is the total circuit pressure drop?

Set 130 foot pipe length opposite 2.3 feet per 100 feet and

read 3 feet as the total circuit pressure drop.

In some instances, the system designer may wish to make

a preliminary pump selection and proportion its available

head over the longest circuit in the system to determine the

average resistance rate on which the piping should be sized.

Example #2: A designer is evaluating a pump with an

available head of 50 feet at the design ﬂow . The longest

circuit in the system has a TEL of 1500 feet. At what average

friction loss rate should the piping be sized?

Set 50 foot head opposite the arrow. At the TEL of 1500 feet,

a resistance of 3.3 feet per 100 feet is indicated.

Scale #5 – Determining Unknown Pressure Drops,

System Curves and Control Valve Cv ratings.

Scale #5 is based on the relationship which exists between

ﬂow and system resistance where the head varies

approximately as the square of the ow. Scale #5 can be

used in several ways: to determine an unknown pressure

drop from a known pressure drop, to establish system curve

relationships , to select control valves to their Cv ratings, and

to convert between pressure gauge readings in psi and head

loss values in feet of head.

To determine unknown pressure drop from a known pressure

drop condition, set the known pressure drop opposite the

known ﬂow and read the unknown pressure drop opposite

the design ﬂow.

Example #1: From manufacturer’s data, a chiller has a

pressure drop of 12 feet at 100 gpm. Determine pressure

drop at a ﬂow of 150 gpm.

Set 100 gpm in the window of scale #5 immediately below

12 feet of head. Read the unknown pressure drop at

150 gpm: 27 feet.

Scale #5 of the System Syzer

Calculator can also be used to

select control valves by their Cv rating .

Example #2: In the example of Figure 19, a control valve was

used to supply zero to 2.9 gpm from the primary circuit to

the secondary circuit in order to maintain circuit temperature.

Control valves must be selected for adequate pressure drop

in order to insure proper operation. They are usually selected

by their Cv rating. Control valve selection is discussed in detail

in other Bell & Gossett publications. In Figure 20, a control

valve for use with a secondary zone is to be selected for a 3 psi

differential at 2.9 gpm. Determine the required control valve

Cv rating.

Figure 20

On scale 5, set 2.9 gpm directly opposite 3 psi. Read the

required valve Cv rating at 1 psi: approximately 1.7. If a

control valve with a Cv of approximately 1.7 can be installed,

then with the control valve open and the secondary pump

on, the pressure drop across the Circuit Setter balance valve

should be adjusted to 3 psi. This will set the ﬂow into the

secondary zone to the design point of 2.9 gpm.

To plot a system curve, set the known (calculated) head loss

opposite the known (design) ﬂow. Read the required head

for several other ﬂow rates. These points determine a system

curve. Plot the system curve on a pump curve. The intersection

of the system curve with the pump curve determines the

actual pump operating point (on open systems, adjust the

system curve in accordance with the total static head).

Example #3: Your analysis of a closed loop piping system

indicates that a 200 gpm ﬂow rate results in 30 feet of head

loss. Calculate the resistance at several other ﬂow rates plot

a system curve on the pump curves illustrated below and

determine their actual operating points.

Set 200 gpm in the window below 30 foot head. Read the

resultant head at 100, 150, 250 and 300 gpm. These points

establish the system curve for this “friction only” system.

Pressure gauges

Circuit Setter

Control

Valve

Figure 21

Operation of the pump in the piping circuit described by

the system curve must be at the intersection of the pump

curve and the system curve. This is because of the ﬁrst law of

thermodynamics – energy in must equal energy out. Energy

put into the water by the pump must exactly match the

energy lost by the water as it ﬂows through the piping system.

The point of intersection is the only point that can meet this

basic engineering law. The speciﬁc points of operation for the

two pumps illustrated are 180 and 225 gpm.

Pumps in parallel

The application of pumps in parallel always requires a system

curve – pump curve analysis. When two identical pumps

are placed in parallel, each pump operates at the same

differential head and each supplies ½ the total system ﬂow.

Parallel Pumps

Figure 22

A parallel pump curve can be developed by doubling the

ﬂows at any constant head for the single pump curve.

Parallel Pumps Curve

Figure 23

The system curve for any piping circuit must be plotted on

the developed parallel pump curve. With both the pumps

in operation, the system ﬂow and head will be at point A.

However, each pump will operate at point B. This is because

each pump supplies half the total ﬂow and consumes half the

power requirement.

System Curve Plotted on Parallel Pumps Curve

Figure 24

When only one pump is operating, the point of operation is at

C. The operating point shifts to the right on the pump curve,

which means that the single pump can provide more than

50% of design ﬂow. This means that a single pump operating

alone will draw more power than when operating in parallel:

It is important that each pump be supplied with a motor large

enough to operate at point C.

Note that simply adding a second pump without changing

the existing system will increase the ﬂow, but will not double

it because the system curve was unchanged.

Two - Pipe System Design Example

A three zone heating system using air handling coils will be

used to illustrate the procedure to be followed in sizing a

typical two-pipe system, calculating its pressure drop, and

selecting a pump. In order to clearly understand this process,

it’s best to obtain a System Syzer

from your local Bell &

Gossett representative while you work through this example.

The system is illustrated in Figure 25. The water is heated by

means of a heat exchanger. Heat exchangers are discussed in

more detail later. The system is equipped with a Rolairtrol air

separator and vent. The pump is base mounted, end suction,

equipped with a Triple Duty Valve at the discharge and a

Suction Diffuser at the suction. The system expansion tank is

located near the pump suction.

Two-Pipe Fan Coil System

Figure 25

The coil pressure drops at their design ﬂow rates are shown

on the drawing. Each air handler coil was selected to provide

design heat transfer at design delta tee. For example, in a

typical heating system the ﬂow rate for standard water at

20° Δt is easily found by dividing the heat load in BTUH

by 10,000.

Capacity in U.S. Gallons per Minute

50 100 150 200 250 300 350 400 450

Total Head in Feet

500 550 600

Single Pump Curve

Flow “A” Flow “A”

Note: Flow “A” is Doubled to

Obtain Parallel Pump Curve

Operational Curve

For Two Pumps

In Parallel

Capacity in U.S. Gallons per Minute

50 100 150 200 250 300 350 400 450

Total Head in Feet

500 550 600

Single Pump Curve

Point “A”

System Curve

Operational Curve

For Two Pumps

In Parallel

Point “B”

Point “C”

Capacity in U.S. Gallons per Minute

50 100 150 200 250 300 350 400 450

180

225

Total Head in Feet

Heating Load at

Zone 20° Δt Flow rate (gpm)

(BTUH)

1 800,000 80

2 1,100,000 110

3 900,000 90

280

But suppose it’s a typical chilled water system designed for a

12° Δt. The cooling loads would require greater ﬂow.

Heating Load at

Zone 12° Δt Flow rate (gpm)

(BTUH)

1 800,000 130

2 1,100,000 180

3 900,000 150

460

Scale #1 of the System Syzer

can easily be used to calculate

the design ﬂow rate for each zone. Line up the heat load in

MBH in the white scale with the 12° Δt in the red scale to get

the chilled water ﬂow rates required.

Equipment Room Head Loss

The equipment room piping is common to all three zones.

The pressure drop between points A and B will be calculated

separately for each of the three zones in order to balance the

ﬂow. The greatest head loss zone will determine the pump

head required.

The total ﬂow rate of 280 gpm dictates the equipment room

pipe size and equipment selection since all of this equipment

must carry the total ﬂow. The system will use steel piping.

Scale #2 of the System Syzer can determine the pipe size.

Adjust the total ﬂow rate of 280 gpm within the white arc

in Scale #2 dened by the maximum and minimum friction

loss rates recommended for hydronic systems. Note that two

choices exist:

a. A 3" pipe would have a friction loss rate much greater than

the maximum allowable 4.5 feet head loss per 100 feet

of equivalent length. From Scale #3, the velocity would be

over 12 feet per second; much too high.

b. At 280 gpm, a 4" pipe would have a friction loss rate of

4.3 feet head loss per 100 feet of length, and a velocity of

about 7.0 f/s. This is within normal design limits.

c. A 5" pipe would have only 1.4 feet of head loss per 100

feet of length, so the total head loss in the equipment

room would be signiﬁcantly less. Low head loss in the

equipment room results in systems that are easier to

balance and easier to control at part load. However, the cost

of the 5" pipe and ﬁttings would be greater than the 4"

alternative, and 5" pipe may not be commonly available.

The equipment manufacturer‘s catalogs show the following

equipment data:

Heat exchanger 3 feet head loss at 200 gpm

Rolairtrol with strainer 4" Cv=135

5" Cv=215

Rolairtrol without 4" Cv=370

strainer 5" Cv=580

Triple Duty Valve Minimum of 3 feet of head

loss at 280 gpm to provide

accuracy as a ﬂow meter

4" Suction Diffuser 2.25 psi at 280 gpm

Note that the manufacturer’s friction loss data is given in

a variety of ways. Scale #5 of the System Syzer

can help in

reducing this data to consistent units which can be summed

to determine the total equipment room head loss.

Heat exchanger

Brazed plate heat exchangers

Figure 26

The heat exchangers in Figure 26 use very hot water directly

from the boiler, ﬂowing across one side of the corrugated

stainless steel plate then back to the boiler. Heat transfers

through the plate to the heating system water on the other

side of the plate which will be circulated through the system.

It is the pressure drop inside the heat exchanger that is of

concern in this example. The boiler water circulation must

be handled by a separate pumping system. Heat exchanger

data is provided in units of feet of head loss. These units are

preferred in order to simplify pump selection since pump

curves are usually stated in feet of head. The manufacturer

says the heat exchanger has 3 feet of head loss at 200 gpm. At

design ow of 280 gpm, the head loss will increase. Scale #5

can be used to calculate the actual head loss at design ﬂow.

On scale #5, align the given values of ow, 200 gpm in the

white scale and 3 foot head loss on the inner blue scale.

Without moving the scale, ﬁnd 280 gpm and read a bit less

than 6 feet head loss on the inner scale. Note that Scale #5

has both feet of head loss and psi pressure drop. Be sure to

use the right scale.

Rolairtrol air separator

Water carrying air bubbles enters through the tangential

nozzle at the top. Centrifugal acceleration separates air from

water, allowing the air to escape from the top, and the air-free

water to continue to circulate to the system from the other

nozzle. Rolairtrols are also available without the strainer.

Rolairtrol air separator

Figure 27

Rolairtrol data is given as a Cv. Remember that the Cv is the

ﬂow in gpm at 1 psi Δp. Scale #5 has a Cv index at 1 psi on

the outer blue scale or 2.31 feet of head on the inner scale.

To evaluate the head loss for the 4" Rolairtrol, rotate the scale

until the Cv index is at 135, then read 10 feet of head loss

opposite 280 gpm. The 5" Rolairtrol has a larger Cv, 215. At

280 gpm it has about 4 feet of head loss. Also notice that the

addition of a strainer in the Rolairtrol tends to reduce Cv, or

increase head loss. Unless there is an important reason to

include a strainer, it’s best to choose the Rolairtrol

without one.

Triple Duty

Valve

Triple Duty

Valve

Figure 28

As the name implies, the Triple Duty

Valve provides three

important functions at the pump discharge:

a. Isolation valve for pump service

b. Check valve, to prevent backward ﬂow

c. Balance valve, to eliminate the excess ﬂow which will be

caused by an oversized impeller

Angle pattern valves also act as an elbow at the pump

discharge, and all Triple Duty Valves are designed to serve as

rough ﬂow meters.

Details of Triple Duty Valve selection are covered in other Bell

& Gossett publications, but for this example, observe that the

fully open valve must have about 3 feet of head loss at full

ﬂow in order to measure ﬂow reasonably accurately.

Suction Diffuser

Figure 29

Suction diffusers provide proper entering conditions at the

pump in order to reduce wear and insure the pump performs

as designed. While they are not always required, they often

save equipment room space, especially with end-suction

pumps. The Suction Diffuser data is given as 2.25 psi at

design ow. Scale #5 can be used to convert to feet of head

by aligning any ﬂow rate line at 2.25 psi on the outer scale to

read the corresponding head loss of 5.2 feet of head loss.

Equipment room component head loss at design ﬂow:

Heat exchanger 6.0'

4" Rolairtrol w/o strainer 1.3'

3DS-4B Triple Duty Valve 5.0'

Suction Diffuser 5.2'

Total 17.5'

In addition to the equipment room components, the

equipment room portion of the system contains the following

piping and ﬁttings to the entrance of the tees at points A

and B:

9 – 90º Ells

1 - NPT Gate Valve

36' Piping

Piping Equivalent Lengths

Use the table on the System Syzer jacket to ﬁnd the equivalent

lengths.

Straight Pipe 36.0'

4" NPT Gate Valve 2.5'

9 -4" Ells 9 x 13 = 117.0

Total Equivalent Length= 156'

156' of 4'' Pipe @ 4.3' / 100 Ft. = 6.7 Ft.

Scale #4 of the System Syzer

can also be used in this

calculation.

Line up the TEL, 156 feet, with 4.3 Ft head loss per 100 feet

TEL, then read about 6.7 feet of total head loss in the window.

Equipment Room Pressure Drop B to A = 17.5' for all the

components PLUS 6.7' for the piping of 24.2 feet at

design ﬂow.

The rest of the system

The next step is to evaluate the pressure drop in each of the

three zones. One of those zones will have the highest pressure

drop at design ﬂow. Adding that zone pressure drop to the

equipment room pressure drop will determine the pump

head required. But if the pump provides enough differential

across points A-B to satisfy the highest pressure drop zone,

it will, by deﬁnition, provide too much across the other two,

and they will see excess ﬂow. In this example, Circuit Setter

balancing valves will be used to eliminate this excess ﬂow in

the lower-pressure-drop zones. Other devices for achieving

ﬂow balance certainly exist; their use is covered in other Bell

& Gossett publications.

Each zone has a modulating two-way valve on the coil return.

They are required in order to reduce coil ﬂow, and therefore

heat transfer, at part load conditions. These valves must be

selected to:

a. Operate properly in order to adjust the system performance

to part load conditions

b. Aid in balancing the individual circuits to one another.

It will be necessary to calculate the zone pressure drop exclusive

of the control valves in order to accomplish this.

The pressure drop calculation for each zone is as follows. Use

your System Syzer

to verify each of these calculations.

ZONE 1 - 80 gpm from A to B

Coil 3.0 Ft.

Piping 3" @ 1.6' / I00 ft. (A-C) 80 gpm

Straight Pipe 257'

Fittings - 3''

2 - Tees - Branch Flow @ 9 18'

5 - 90º Ells @ 4.0 20'

Total 295' @ 1.6' / 100' 4.7 Ft.

Piping 4" @ 1.7' / 100 ft. (C -B) 170 gpm

Straight Pipe 10'

2 Tees - Branch Flow @ 12.0 24'

34' @ 1.8' / 100 Ft. 0.6 Ft.

Balance Valve (2½" Circuit Setter set to 0) 2.2 Ft.

A Circuit Setter slide rule is available to determine the actual

head loss in the valve at each setting. Initially, all these

balancing valves will be set at the zero index mark to provide

minimal pressure drop. Later, after the differences in pressure

drop among all the zones are determined, we can set two of

these balancing valves to provide resistance in the zones that

need it to prevent excess ﬂow that would otherwise occur.

ZONE 1 - Pressure Drop (Less two-way valve) 10. 5 Ft.

ZONE 2 - 110 gpm from A to B

Coil 6.0 Ft.

Piping 4" @ 2.3' / 100 ft. (A-E) 200 G.PM

Straight Pipe 2'

2 Tees - Through Flow @ 5. 5 11'

13' @ 2.3' / 100 ft. 0.3 Ft.

Piping 3" @ 2. 8' /100 ft. (E-B) 110 gpm

Straight Pipe 149'

1 Tee - Through Flow @ 4.0 4'

1 Tee - Branch Flow @ 9.0 9'

4 - 90º Ells @ 4.0 16'

178' @ 2.8' /100 ft. = 5.0 Ft.

Balance Valve (2½" Circuit Setter set to 0) 4.0 Ft.

Zone 2 - Pressure drop (Less two-way valve) 15.3 Ft.

ZONE 3 - 90 gpm from A to B

Coil 5.0 Ft.

Piping 4" @ 2.2' / 100 ft. (A-E) 200 gpm

Straight Pipe 2.0'

1 Tee - Through Flow @ 5.5 5.5'

7.5' @ 2.3' / 100 ft. 0.2 Ft.

Piping 3" @ 2' / 100 ft. (E-C) 90 gpm

Straight Pipe 215'

2 Tees - Branch Flow @ 9.0 18'

5 - 90º Ells @ 4.0' 20'

253' @ 2.0' / 100 ft. 5.0 Ft.

Piping 4" @ 1.7' / 100 ft. (C-B) 170 gpm

Straight Pipe 10'

2 Tees - Branch Flow @ 12.0 24'

34’ @ 1.7' / 100 ft. 0.6 ft.

Balance Valve (2½" Circuit Setter set to 0) 2. 8 Ft.

Zone 3 pressure drop (Less two-way valve) 13.6 Ft.

Now that the pressure drop of each zone has been calculated,

the next step is to select the control valves for each zone. In

order to provide stable ﬂow conditions, and good control

at part load, the control valves should be selected for initial

pressure drops at least equal to the coil pressure drop if

possible in order to minimize distortion of the valve’s inherent

ﬂow-stem position characteristic. Select the control valve in

the circuit with the highest pressure drop ﬁrst. Then select

the other valves to help balance their circuit pressure drop

to the ﬁrst. The number and size of control valves available is

limited, so we should expect to ﬁnd we must compromise in

selecting the best size.

Zone 2 has the highest pressure drop, 15.3 Ft. with its coil

pressure drop of 6'. We’ll attempt to ﬁnd a valve with 12'

pressure drop at the required ow 110 gpm. Use scale #5

to calculate the desired Cv by aligning 12' and 110 gpm,

showing Cv=48.

Valves should generally not be sized for over 20' pressure

drop because of velocity and other problems. We will assume

the closest selection we can ﬁnd is a 3" valve with Cv = 44.

What’s the actual pressure drop?

Align the Cv index at 44, ﬁnd the design ﬂow of 110 gpm and

see the actual head loss of 14.5'.

The pressure drop of Zone 2, including the valve, will then be

the 15.3' previously calculated PLUS 14.5' for the valve, for a

total of 29.8'.

Zone 1 has a pressure drop, exclusive of its control valve,

of 10.5', which means that we must try to select a valve for

the difference between 10.5 and 29.8' in order to balance

it to Zone 2. This difference is 19.3', close to the allowable

20' maximum pressure drop. A valve which provides 20'

resistance at 80 gpm would require a Cv = 27. The closest

selection available is a 2½" valve, Cv = 29, which has

a pressure drop of 17.6' at 80 gpm. Adding this to ‘the

calculated 10.5' pressure drop for the zone yields 27.8’ total

pressure drop.

Zone 3 requires a valve with a pressure drop of 16.2' (29.8 -

13.6) to balance it to Zone 2. The control valve must therefore

provide 16.2' of pressure drop at 90 gpm, requiring a Cv of

34. The closest selection available is found to be a 2½" valve,

Cv = 36. The pressure drop of this valve at 90 gpm ﬂow is

14.4'.

The zone pressure drops, including control valves, are now as

follows:

Head Loss Head Loss Total Head

Coil, Pipe, Control Valve Loss (Feet)

Fittings

Zone 1 10.5' 17.6' 28.1'

Zone 2 15.3' 14.5' 29.8'

Zone 3 13.6' 14.4' 28.0'

In order to balance Zone 1 to Zone 2, the Circuit Setter in Zone

1 will have to be set to provide 1.7' of additional resistance,

or a total of 3.9' after including the 2.2' (when it’s set at zero)

resistance already included in the zone pressure drop.

Bell & Gossett tools and publications are available to show

exactly how to adjust the Circuit Setters. A 2½" Circuit Setter

adjusted to an index mark of 9 will provide the required 3.9'

head loss at the 80 gpm ﬂow.

Circuit Setter Slide Rule

Figure 30

Zone 3 requires 1.8' (29.8 - 28.0) to balance it to Zone 2.

Adding the 2.8' (when it’s set to zero) pressure drop already

included in the calculations requires a setting to provide 4.6'

total pressure drop. A 2½" Circuit Setter, when set at 8 will

provide this pressure drop at the 90 gpm zone ﬂow.

All three zones are now in balance at their respective design

ﬂows, with pressure drops corresponding to the Zone 2

pressure drop of 29.8'. Notice that the Circuit Setter in Zone 2

is still set “wide open”. There’s no point in adding resistance at

the balancing valve in Zone 2 because it’s already the highest

head loss zone. Remember, at the beginning of the process,

we didn’t know which of the zones would be the highest in

pressure drop, so we included a balancing valve in each zone.

The total system pressure drop is:

Equipment Room to A&B 24.2'

Zones, from A&B 29.8'

Total Pressure Drop 54.0'

A pump may now be selected for 280 gpm @ 54' head. In

this simple example, a constant rpm pump could be used.

As systems increase in size, and as energy costs increase,

variable speed pumps become more attractive. Those systems

would beneﬁt from the application of “automatic ﬂow

limiters”, and “pressure independent control valves”. These

more sophisticated valves automatically adapt to changes in

differential pressure as other control valves open and close,

and as the pump speed changes in response to those valves.

The design of variable speed systems is covered in other Bell

& Gossett publications.

Pump Selection

In the earlier example, booster pumps were used because

they are very simple, require few decisions, and illustrate the

basics very well. In larger systems, the designer must choose

among many larger pump types:

• In-line or base-mounted

• Single suction or double suction

• Close coupled or exibly coupled

It’s very common to use a base-mounted, ﬂexibly coupled,

end suction pump for an application like the one in this

example, but there may be good reasons to use a different

type. A discussion of the beneﬁts of other pump types can be

found in other Bell & Gossett publications.

ESP PLUS is a design tool available from your Bell &

Gossett representative. It helps guide you through the pump

selection process, assuming you have already completed the

system design, and you know the head and ﬂow required.

The next ﬁgure shows the ESP PLUS entering screen.

ESP Plus Opening Window

Figure 31

Enter the system head and ﬂow requirement and select the

Series 1510 end suction type pump, see Figure 32. The pump

discharge nozzle size is used to designate the pump size for

this type of pump. Letters following the nozzle size refer to

the largest impeller diameter and design modiﬁcations which

may have been applied to the original pump design.

Other types of pumps use different methods for

designating pump size.

Bell & Gossett Series 1510 End Suction Pump

Figure 32

ESP Plus Pump Summary

Figure 33

All of the pumps on this second screen are capable of

providing the system head and ﬂow. They are ranked in

order of increasing cost, so a simple analysis would choose

the 2½AB pump—the least expensive alternative. But note

the little thumb-nail sketch of the pump’s performance. It

shows that this 3500 rpm pump is operating at the extreme

right end of the smallest diameter impeller. That’s a very poor

selection, even though it’s the lowest cost pump. A detailed

explanation of why it’s such a poor choice is available in other

Bell & Gossett publications, but brieﬂy stated:

• The 2½" pump would require a high rpm motor, possibly

adding to procurement lead time, and maybe generating

noise at the high rpm.

• The smallest diameter impeller offers no room for

adjustment if the system’s head loss has been overstated.

“Trimming” an impeller is often a useful way to reduce

operating cost if the original selection is oversized for the

system. The minimum size impeller used in the 2½" AB

pump can’t be trimmed.

• Any pump which operates at the extreme end of its curve

will probably be less efﬁcient and will be more likely to

experience component failure compared to another pump

operating closer to the middle of its curve.

If this pump is such a poor choice, why did it appear on

the list?

Computer applications-as good as they are-can’t

replace the judgment of an experienced designer.

You must select the pump; and to help you do it, you

could re-rank the pumps in order of efﬁciency.

Re-Rank the Pump Candidates by Efﬁciency

Figure 34

The larger, and more expensive, 4GB pump is more efﬁcient,

and is operating closer to the middle of its curve, but it is

equipped with an 1150 rpm motor. That motor may take

longer to procure, may be more difﬁcult to replace in the

future. As an alternative, consider the smaller, less expensive

3BC. Its efﬁciency and point of operation are similar to the

4GB, but it uses a more readily available 1750 rpm motor. It

may be a better choice in terms of the total “life cycle cost”

of owning the pump. Clicking on the “Generate Curve”

button will provide a lot more information to help you make

decisions about the pump.

Series 1510 3BC Pump Curve

Figure 35

The actual pump curve for the Series 1510, 3BC 1750

rpm pump being evaluated is in Figure 35. Bell & Gossett

plots pump curves strictly in accordance with the Hydraulic

Institute/ANSI standards for pump testing. The coordinates

are ﬂow in gallons per minute versus head in feet. For a

pump, the vertical axis represents the amount of work the

pump applies to each pound of ﬂuid, foot-lbs work per

pound of ﬂuid. In a closed loop system, that work is used to

overcome the system friction loss, 54 feet, already calculated.

The largest impeller that Bell & Gossett will supply in this

pump has a diameter of 9.5". It’s also the most efﬁcient,

about 80%, at a ﬂow rate of about 500 gpm. Lines of constant

efﬁciency are usually plotted like the growth rings of a tree.

Note that this pump operating at the system design point,

280 gpm and 54 feet, would need only a 7.75" impeller. The

best efﬁciency that impeller is capable of achieving is 78%

at about 400 gpm. At the design point, efﬁciency is about

73.2%

For pumps like this, the designer must also select a motor.

The motor horsepower is calculated by the formula:

Brake Horsepower = GPM x Feet of Head x SG

3960 x η

pump

Where:

SG is the speciﬁc gravity of the ﬂuid. For standard water, SG=1

pump

is the efﬁciency of the pump at its operating point,

about 73.2%

Lines of constant horsepower--for this pump, 5, 7.5, 10,

and 15 HP-- are also drawn on the pump curve. These lines

represent all the combinations of head, ﬂow and efﬁciency

that would require that much horsepower. For the example

system, the point of operation lies just a bit above the

5 hp line:

BHP = 280 gpm x 54 feet x 1

3960 X 0.732

BHP=5.2 hp

If we had selected the “Select Motor Using Duty Point” option

shown on the initial ESP Plus screen, then ESP Plus would

have recommended a 7.5 HP motor, the smallest standard

size motor that could provide 5.2 hp without operating in the

service factor of the motor. On that initial screen we selected

the option, “Use Non-Overloading Motors”. The pump curve

illustrates the effect of that choice. If the ﬂow were to increase

above 280 gpm, the operating point would move to the right

on the impeller curve. The end of the impeller curve rises well

above the 5 HP line, but never above 7.5 hp.

Many designers choose to avoid relying on the service factor,

some motors don’t have one, and all designers should

hesitate to rely on the motor starter to prevent overload, so

they choose a larger, “non-overloading” motor. That’s the

choice we made in the initial ESP PLUS screen. This pump

would use a little more than 7 hp if it were to operate at the

far end of its curve. ESP PLUS would therefore recommend the

next size larger, and more expensive, 7.5 HP motor.

All of these, as well as many more details are provided by

ESP PLUS by clicking the “Pump Details” button.

Bell & Gossett Series 1510 3BC Operating Details

Figure 36

The System Curve

Earlier, we showed how the System Syzer

calculator can

be used to draw a system curve. ESP PLUS can do that with

the click of a button. On the ESP PLUS pump curve, click on

“Display System Curve”, then “Update Graph” to show the

pump and system curves together. The design point, 280

gpm and 54 feet of head, represent Q1 and h1. ESP Plus

generates a number of points and plots them on the

pump curve.

MBH/Flow/Δt relationship

ESP PLUS: Load, Flow and Delta Tee

Figure 39

In a previous design example, we used scale #1 to calculate

required ﬂow for 1,100,00 BTUH at 12°Δt. The digital screen

shows the same calculation. Though 60°F water is still the

default value, this version has a ﬂuids library with different

concentrations of propylene or ethylene glycol anti-freeze. It

also has an option to insert ﬂuid properties to deﬁne a

new ﬂuid.

Flow/Pressure drop/Pipe size/Velocity relationship

ESP PLUS: Flow, Pipe size, Friction Loss Rate

and Velocity

Figure 40

The 183 gpm calculated in the ﬁrst screen automatically

transfers to the next. A 4" pipe carrying 183 gpm would

have acceptable friction loss rate and velocity, just as we saw

with the plastic slide rule. For some ﬂow rates, more than

one pipe size will be acceptable in terms of friction loss rate

and velocity. An experienced designer will apply judgment

in choosing between these alternatives in order to improve

system balance, or reduce pump head requirements.

Other information like viscosity, Reynolds number, ﬂow

regime and Darcy-Weisbach friction factor are shown in case

a designer wants to make a more detailed analysis of the

piping system.

Pump and Closed System Curve

Figure 37

Pumps in parallel

The real value of applications like ESP PLUS comes in

evaluating alternatives, for example, using two smaller

pumps in parallel. Using the same design point, select two

parallel pumps in the initial ESP PLUS screen. Two smaller

close-coupled, end suction pumps would perform as shown in

Figure 38. Note that ESP PLUS constructs the composite curve

representing the combined effect of both pumps running,

Turning off either pump shifts the operating point well to the

right on the remaining pump curve, increasing power and

NPSHR. The two-way control valves close at part load, reducing

ﬂow, and increasing pump head, shifting the system curve

to the left. A parallel pump controller can sense any of these

effects, and automatically “destage” a pump at part load.

Since most hydronic systems operate at part load most of the

time, destaging can reduce energy costs signiﬁcantly.

Parallel Pumps

Figure 38

Digital ESP PLUS

Just as ESP PLUS simpliﬁed and made pump selections easier

and faster, the digital version of the System Syzer

calculator

expands the use of the original plastic System Syzer

slide

rule. The basic functions are identical:

Total Equivalent Length/Friction Loss Rate/ Total

Head LossESP PLUS: Total Equivalent length, Friction

Loss Rate and Total Head Loss

Figure 41

A 4" pipe carrying 183 gpm has a friction loss rate of 1.92 feet

of head loss per 100 feet of TEL. If the system is 1500 feet long.

The total head loss would be 28.8 feet.

Note: The System Syzer puts no limits on friction loss rate. The

designer must use judgment in selecting the pipe size for a

given value of ﬂow in order to maintain the friction loss rate

within the usual limits of 0.85 to 4.5 feet of head loss per

100 feet of equivalent length.

System Curve/Cv/PSI to Feet of head conversion

ESP PLUS: System Curve, Cv

Figure 42

Using the values of head and ﬂow developed in the

design analysis, the Cv and points on the system curve

can be calculated. Just as the plastic version allowed for

easy conversion between psi and feet of head using the

relationship of 2.31 feet of standard water equals 1 psi, the

digital version adjusts for changes in ﬂuid properties giving a

more accurate result with different ﬂuids.

√

[

Circuit Analysis

Flow Coefﬁcient, Cv

The Cv of any component is deﬁned as the ﬂow in gpm that

would pass through the component at a differential pressure

of one psi. Mathematically:

GPM

Δp

Control valves are often chosen by calculating the desired Cv,

but any component’s performance in the system could be

described by its Cv. For example, a coil or a pipe, or even an

entire ﬁxed piping system has a Cv; the ﬂow in gpm at one psi

differential. The Cv can be displayed on Flow vs Pressure Drop

coordinates. The system curve discussed earlier is an example.

Graphical Deﬁnition of Cv

Figure 43

This relationship is more useful than it may appear to be.

Components in series

Take a set of components in series. The ﬂow through all is the

same; the total pressure drop is the sum of the component

pressure drops. Each component pressure drop can be stated

in terms of its Cv:

Δp =

GPM

The total pressure drop through all components; a, b,

c, … is then:

Δp of the total =

GPM

The equivalent Cv of any number of things in series could be

written as:

Equivalent C

For two things with Cv1 and Cv2 in series:

Equivalent CV =

x C

+ C

This expression can be useful in describing why modulating

control valves must be selected for a substantial design

pressure drop.

]

[][] []

√

Pressure

Drop

1 psid

gpm

Flow

Cv = 50

Control Valve Authority

Suppose a control valve manufacturer has built a two-way

modulating valve with a linear “inherent characteristic”. That

means the relationship between percentage of valve stem

position and percentage of full ﬂow must be linear. The

manufacturer has controlled the shape of the valve plug and

seat in order to give the expected performance.

Linear Inherent Characteristic

Figure 44

He might have used a test stand like this to test the

completed valve.

Typical Valve Test

Figure 45

The water level in the tank remains at 2.3 feet to give a

constant one psi at the valve inlet. The pressure at the valve

outlet is 0 psi. The volume of water ﬂowing for one minute

can be weighed to determine the gpm. By means of this test,

he could verify the characteristic, measuring ﬂow at each

increment of valve stem position.

When the valve is installed in an actual system, there will be

some distortion of the inherent characteristic because of the

resistance of the other components which are in series with

the valve.

Equivalent CV =

x C

+ C

Assume that Cv1 represents all the ﬁxed components of

the branch; things like pipes, elbows, and the coil. These

components cannot change their Cv because thay cannot

change their cross sectional area available for ﬂow. Let Cv2

represent the Cv of the control valve. Unlike the other branch

components, the valve can change its ﬂow area and Cv. The

equivalent Cv of the branch is determined by both the ﬁxed

and the variable components, hence the distortion.

Other components in series with the valve were not present

during the test. Basic design data can be used to calculate

the equivalent Cv of the branch and show how low pressure

drop valves will result in greater distortion of the valve

characteristic.

Example:

Three different control valves will be used with a given coil to

show the effect of selecting a low, medium, or high pressure

drop valve.

If we consider just the two components, coil and valve, we can

calculate the equivalent Cv of the two things in series. Note

that the valve’s Cv changes as it closes from 100% to 0%, but

the coil Cv remains ﬁxed. The coil can’t change its Cv because

it can’t change the cross-sectional area available for ﬂow.

Flow in the coil-control valve combination does not change in

the linear manner we expected when we selected the linear

control valve.

Control valve pressure drop equal to coil pressure

drop. β = 0.5/1.0 = 0.5 (Curve B in Figure 46)

Valve Stem

Valve Cv Coil Cv Equivalent Cv

Flow

% %

0 0 30 0 0

10 3 30 2.98 14

20 6 30 5.88 28

30 9 30 8.62 41

40 12 30 11.14 53

50 15 30 13.41 64

60 18 30 15.43 74

70 21 30 17.20 82

80 24 30 18.74 89

90 27 30 20.07 95

100 30 30 21.00 100

Control valve pressure drop greater than coil pressure

drop. β = 0.9/1.0 = 0.9 (Curve C in Figure 46)

Valve Stem

Valve Cv Coil Cv Equivalent Cv

Flow

% %

0 0 30 0 0

10 1 30 0.99 10

20 2 30 1.99 21

30 3 30 2.98 31

40 4 30 3.96 42

50 5 30 4.93 52

60 6 30 5.88 62

70 7 30 6.81 72

80 8 30 7.72 81

90 9 30 8.62 91

100 10 30 9.48 100

√

Valve Stem

Position

Flow

100

10050

Flow

Valve Stem Position

Control valve pressure drop less than coil pressure

drop. β = 0.1/1.1 = 0.09 (Curve A in Figure 46)

Valve Stem Valve Cv Coil Cv Equivalent Cv Flow

% %

0 0 30 0 0

10 9 30 9.06 30

20 19 30 16.05 53

30 28 30 20.66 69

40 38 30 23.54 78

50 47 30 25.36 84

60 57 30 26.54 88

70 66 30 27.35 91

80 76 30 27.90 93

90 88 30 28.41 95

100 95 30 30.00 100

Effect of Branch Authority on Part Load Flow

Figure 46

The ratio of control valve pressure drop to branch pressure

drop is called the “branch authority”. The ﬁgure shows that

control valves selected for high pressure drop compared

to the pressure drop of the rest of the branch have better

authority, and less distortion of their inherent characteristic.

In the earlier design examples, control valves were selected

for appreciable pressure drop compared to the pressure drop

of the rest of the branch in order to minimize the distortion

of the valve’s inherent characteristic as well as to promote

“stable performance”. Let’s see the effect of valve authority

on the stability of the system. The thermostatic temperature

control in a heating system has detected a room temperature

much higher than the thermostat setting. It sends a signal to

the control valve telling it to go to 50% valve stem position,

expecting that the branch ﬂow will be reduced to 50% as

predicted by the inherent characteristic of the valve.

• Valve A, with poor authority, will allow much more than

50% ﬂow resulting in greater than required heat transfer

and rising temperatures in the room. In time, the room

will be so hot the temperature control system will have

to restrict the ﬂow severely. In effect, the valve tends to

operate more like an “ON/OFF”, or two position valve, rather

than a modulating valve as intended.

Flow Rate

50%

A Low Control Valve �p

B Medium Control Valve �p

C High Control Valve �p

D Inherent Characteristic

Valve Stem Position

1000

50%

>>50%

100

• Valve B, with better authority, will provide better control

since it is operating closer to the inherent characteristic.

• Valve C may have too much pressure drop leading to high

total branch pressure drop and possibly valve cavitation:

the formation and collapse of vapor bubbles in the liquid

stream. Cavitation can result in early valve failure.

• Valve D represents an authority of 1.0. This can be achieved

by using specially constructed pressure independent

control valves, which use a little regulator system to

maintain a ﬁxed pressure difference across the valve’s

control oriﬁce.

Components in parallel

Any number of components in parallel will have the same

inlet pressure and the same outlet pressure. The pressure

drop will be the same for all, but the total ﬂow will be

apportioned among them according to each branch’s Cv. The

branch with the largest Cv will get the greatest ﬂow, but the

total ﬂow through all branches will be the sum of all.

Flow

Total

= C

Δp + C

Δp + . . .

Equivalent C

= C

+ C

+ . . .

This explains the importance of achieving hydronic balance

among all the circuits of a multi-circuit system. Consider

the system in Figure 47. The design point A, is 1100 gpm at

50 feet of head. The impeller must be trimmed to 11.625"

diameter to meet this point. The system curve 0-A represents

the desired balanced system, each branch receiving

design ﬂow.

Pump Curve with Balanced and Unbalanced Systems

Figure 47

Now suppose that one or more of the circuits has a greater Cv,

or less resistance, at its design ﬂow rate. Each of them will see

a greater ﬂow than is required to provide design heat transfer.

System 0-B represents the unbalanced system. Even though

the impeller is the right diameter, the pump will provide

greater ﬂow, and use more horsepower than required, point

C. Point B shows the pump is oversized, providing more than

the total ﬂow required by all circuits. Each circuit will get more

ﬂow than it requires, operating costs will rise with no increase

in occupant comfort. Point D represents an impeller that’s

√

0.5

0.5 12

468102030406080100 200 300400 600 8001000 2000 3000 10000 40000 100000

Head Loss, ft/100 ft.

Volumetric Flow Rate, gpm

4FPS

3FPS

2FPS

1FPS

6FPS

8FPS

10FPS

15FPS

20FPS

1/2"

3/4"

1 1/2"

1 1/4"

2 1/2"

10"

12"

14"

16"

18"

20"

24"

Water 60ºF

Nominal Pipe Sizes

Schedule 40

Black Steel Pipe

too small in the unbalanced system. In this case, the pump

is still providing more than design ﬂow, and that ﬂow is not

proportionately divided among the branches.

In the design examples, Circuit Setter balancing valves

added just enough resistance in each of the lower pressure

drop circuits to make each branch Cv equal to that of the

highest pressure drop branch, the one used to select the

pump. Balance valves used in this way result in “proportional

balance” meaning that each branch will get its proper

proportion of the ﬂow from the pump. If the pump is selected

properly, each branch will get exactly what it needs for design

heat transfer. If the pump is over or under sized, each branch

will get more or less than it needs, but all will see the same

proportion of over or under ﬂow.

Appendix

A. Pipe Friction Loss Nomogram

Find the design ﬂow rate on the horizontal axis, proceed vertically to the intersection with the pipe size line. Read horizontally

to the left to ﬁnd friction head loss, ﬁnd velocity by interpolation between lines of constant velocity. Exampe: 70 gpm in a 2½"

Schedule 40 pipe will have a bit less than 4'/100 Ft. of length at a velocity of about 5 f/s.

90º El or Tee: Tee: Side Branch Flow 90º 45º

Valves

Nominal Flow Thru In or Out Miter Miter

Pipe

Size

Gate Globe Plug

Screw Cu or Weld Screw Cu or Weld Weld Weld All All All

½" 1 ½ 2 1 2½ ½ ½ 15 1

¾" 2 1 4 2 4 ¾ ½ 20 1½

1" 3 1½ 6 3 5 1 ¾ 25 2

1¼" 3½ 1¾ 7 3½ 6 1¼ 1 30 2½

1½" 4 2 8 4 7½ 1½ 1¼ 40 3

2" 5 2½ 10 5 10 2 1½ 50 4

2½" 6 3 12 6 12½ 2½ 2 80 5

3" 8 4 16 9 15 3 2½ 90 6

4" 5½ 12 20 4 3 110 8

5" 8 15 25 5 3½ 140 10

6" 9 18 30 6 4 170 12

8" 11 24 40 8 5 240 16

12" 18 36 60 12 8 320 24

* Applies to Side Branch Flow

TABLE 2 FITTING EQUIVALENT LENGTH TABLE

EXAMPLE 1:

1. Calculate friction loss from A to B given the following data:

a. Pipe Size is 3".

b. Flow is 130 GPM.

c. Measured length = 30'

d. Tee “A” is NPT with 3" run and 3"branch size.

2. Determine ﬁtting equivalent length:

a. From the Table, a threaded 3" tee with side branch has

an equivalent length = 16'.

b. The equivalent length of the tee at “B” is not included

for this section.

3. Determine the Total Equivalent Length, TEL:

a. TEL = 30 + 16 = 46'

4. Use scale #2 of the System Syze to determine the friction

loss rate in a 3" pipe at 130 gpm, then scale #4 to nd

total head loss:

a. Scale 2: 3.8 ft/100 feet length

b. Scale 4: 2.2 ft head loss

C. Equivalent length of ﬁttings

EXAMPLE 2:

1. Calculate friction head loss from B to D given:

a. Pipe Size is 3".

b. Flow is 120 GPM.

c. Measured length B to D is 40'

d. This section includes two 3" elbows and one 3" thru

ﬂow tee at point “B”.

2. Determine ﬁtting equivalent length:

a. Two 3" elbows @ 8 each = 16

b. One 3" ﬂow thru tee @ 4 = 4

3. Total Equivalent Length = 40' + 16' + 4' = 60'

4. Use scale 2 and 4 to determine the total head loss for

120 gpm in 3" pipe::

a. Scale 2: 3.3' ft/100 Ft.

b. Scale 4: 3.3'/100 Ft x 50' = 1.98 Feet

AIR EXCHANGER HEAT RUN

CIRCULATOR WITH

ISOLATION FLANGE

CIRCULATOR FITTING

AIR VENT HEAT EXCHANGER EXPANSION TANK

CONVENTIONAL

BOILER

RADIANT PANEL CIRCUIT SETTER

PRESSURE

GAUGE

TRIPLE DUTY

VALV E

ROLAIRTROL

DIVERTING

VALV E

MIXING

VALV E

HYDRONIC COMPONENTS LEGEND

Xylem Inc.

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Morton Grove, Illinois 60053

Phone: (847) 966-3700

Fax: (847) 965-8379

www.bellgossett.com

Bell & Gossett is a trademark of Xylem Inc. or one of its subsidiaries.

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