Understanding basic principles o ow calculations

 V alve size often is described by the

nominal size of the end connec-

tions, but a more important

measure is the ow that the valve can

provide. And determining ow through

a valve can be simple. Using the princi-

ples of ow calculations, some basic

formulas, and the effects of specic

gravity and temperature, ow can be

estimated well enough to select a valve

size easily and without complicated

calculations

Flow calculation principlesThe principles of ow calculations are

illustrated by the common orice ow 

meter (see Figure 1). We need to know 

only the size and shape of the orice,

the diameter of the pipe and the uid

density. With that information, we can

calculate the ow rate for any value of 

pressure drop across the orice (the

difference between inlet and outlet

pressures).

For a valve, we also need to know the

pressure drop and the uid density. But in addi-

tion to the dimensions of pipe diameter and

orice size, we need to know all the valve passage

dimensions and all the changes in size and direc-

tion of ow through the valve.

However, rather than doing complex calcula-

tions, we use the valve ow coefcient, which

combines the effects of all the ow restrictions in

the valve into a single number (see Figure 2).

 Valve manufacturers determine the valve ow 

coefcient by testing the valve with water at

several ow rates, using a standard test method2 

developed by the Instrument Society of America

for control valves and now used widely for all

 valves.

 John Baxter and Ulrich Koch Swagelok Company 

Flow tests are done in a straight piping system

of the same size as the valve, so that the effects

of ttings and piping size changes are not

included (see Figure 3).

Liquid owSince liquids are

i n c o m p r e s s i b l e

uids, their ow 

rate depends only 

on the difference

 between the inlet

and outlet pres-

sures (∆p, pressure

drop). The ow is

www.digitalrefning.com/article/1000088  March 2008 

1

Figure 1

Figure 2

Equation 1

 

the same whether the system pressure is low or

high, so long as the difference between the inlet

and outlet pressures is the same. Equation 1

shows the relationship.

The water ow graphs show water ow as a

function of pressure drop for a range of  C  v  

 values.

2 March 2008  www.digitalrefning.com/article/1000088 

Gas owGas ow calculations are

slightly more complex

 because gases are

compressible uids whose

density changes with pres-

sure. In addition, there

are two conditions that

must be considered: low 

pressure drop ow and

high pressure drop ow.

Equation 2 applies when

the low pressure drop ow 

outlet pressure ( p2) is

greater than one half of 

the inlet pressure ( p1):

The low pressure drop air ow graphs show 

low pressure drop air ow for a valve with a C  v  

of 1.0, given as a function of inlet pressure ( p1)

for a range of pressure drop (∆p) values.

 When outlet pressure ( p2) is less than half of 

inlet pressure ( p1), high pressure drop, any 

further decrease in outlet pressure does not

increase the ow because the gas has reached

sonic velocity at the orice and it cannot break 

that “sound barrier”.

Equation 3 for high pressure drop ow is

simpler because it depends only on inlet pres-

sure and temperature, valve ow coefcient and

specic gravity of the gas:

Figure 3

The basic orifce meter illustrates the dier-ence between high and low pressure drop owconditions.

In low pressure drop ow, when outlet pres-sure (  p

2 ) is greater than hal o inlet pressure

(  p1 ), outlet pressure restricts ow through the

orifce: as outlet pressure decreases, owincreases and so does the velocity o the gasleaving the orifce.

When outlet pressure decreases to hal o inlet pressure, the gas leaves the orifce at thevelocity o sound. The gas cannot exceed thevelocity o sound, so this becomes the maxi-mum ow rate. The maximum ow rate is alsoknown as choked ow or critical ow.

Any urther decrease in outlet pressure doesnot increase ow, even i the outlet pressureis reduced to zero. Consequently, high pres-sure drop ow only depends on inlet pressureand not outlet pressure.

Low and high pressure drop gas ow

 

The high-pressure drop air

ow graphs show high pres-

sure drop air ow as a function

of inlet pressure for a range of 

ow coefcients.

Eects o specifc gravity The ow equations include the

 variables liquid specic gravity 

(G  f ) and gas specic gravity 

(G g), which are the density of 

the uid compared to the

density of water (for liquids)

or air (for gases).

However, specic gravity is

not accounted for in the

graphs, so a correction factor

must be applied, which

includes the square root of G.

Taking the square root reduces

the effect and brings the value

much closer to that of water or

air, 1.0.

For example, the specic

gravity of sulphuric acid is

80% higher than that of water,

 yet it changes ow by just 34%.

The specic gravity of ether is

26% lower than that of water,

 yet it changes ow by only 

14%.

Figure 4 shows how taking

the square root of specic

gravity diminishes the signi-

cance on liquid ow. Only if 

the specic gravity of the liquid

is very low or very high will

the ow change by more than

10% from that of water.

The effect of specic gravity 

on gases is similar. For

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3

Low pressure drop air ow graphs

Flow tet are

doe a traght

ppg ytem of 

the ame ze a

the valve

 

example, the specic gravity of 

hydrogen is 93% lower than

that of air, but it changes ow 

 by just 74%. Carbon dioxide

has a specic gravity 53%

higher than that of air, yet it

changes ow by only 24%. Only 

gases with very low or very high

specic gravity change the ow 

 by more than 10% from that of 

air.

Figure 5 shows how the effect

of specic gravity on gas ow is

reduced by use of the square

root.

Eects o temperatureTemperature usually is ignored

in liquid ow calculations

 because its effect is too small.

Temperature has a greater

effect on gas ow calculations,

 because gas volume expands

 with higher temperature and

contracts with lower tempera-

ture. But similar to specic

gravity, temperature affects

ow by only a square root

factor. For systems that operate

 between -40°F (-40°C) and

+212°F (+100°C), the correc-

tion factor is only +12 to -11%.

Figure 6 shows the effect of 

temperature on volumetric ow 

over a broad range of tempera-

tures. The plus or minus 10%

range covers the usual operat-

ing temperatures of most

common applications.

Temperature

uually gored

lqud ow

calculato

becaue t effect

too mall

High pressure drop air ow graphs

4 March 2008  www.digitalrefning.com/article/1000088 

 

Cited reerences

1 ISA S75.01, Flow Equations or Sizing Control

Valves, Standards and Recommended Practices or 

Instrumentation and Control, 10th ed, Vol 2, 1989.

2 ISA S75.02, Control Valve Capacity Test Procedure,

Standards and Recommended Practices or 

Instrumentation and Control, 10th ed, Vol 2, 1989.

Other reerences

1 Driskell L, Control Valve Selection and Sizing, ISA,

1983.

2 Hutchinson J W, ISA Handbook of Control Valves,

2nd ed, ISA, 1976.

3 Chemical Engineers’ Handbook , 4th ed, Perry R H,

Chilton C H, Kirkpatrick S D, Ed, McGraw-Hill, New

 York.

4 Instrument Engineers’ Handbook , revised ed,

Lipták B G, Venczel K, Ed, Chilton, Radnor, PA.

5 Piping Handbook , 5th ed, King R C, Ed, McGraw-Hill, New York.

6 Standard Handbook for Mechanical Engineers, 7th ed,

Baumeister T, Marks L S, Ed, McGraw-Hill, New York.

Figure 4

Figure 5 Figure 6

www.digitalrefning.com/article/1000088  March 2008  5

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