Related Resources: fluid flow
Velocity Escaping Compressed Air Equation and Calculator
Hydraulic & Pneumatics
Fluids Design and Engineering Data
Velocity of Escaping Compressed Air Equation and Calculator
If air, or gas, flows from one chamber to another, as from a chamber or tank through an orifice or nozzle into the open air, large changes in velocity may take place due to the difference in pressures. Since the change takes place almost instantly, little heat can escape from the fluid and the flow may be assumed to be adiabatic.
For a large container with a small orifice or hole from which the air escapes, the velocity of escape (theoretical) may be calculated from the formula:
where:
v_{2} = Velocity of escaping air in feet per second (ft/sec);
g = Acceleration due to gravity, 32.16 feet per second squared (32.16 ft/sec^{2});
k = 1.41 for adiabatic expansion or compression of air;
F = Temperature, degrees F;
p_{2} = Atmospheric pressure = 14.7 pounds per square inch (14.7 lbs/in^{2});
p_{1} = Pressure of air in container, pounds per square inch (psi).
In applying the above equation, when the ratio p_{2}/p_{1} approximately equals 0.53, under normal temperature conditions at sea level, the escape velocity v_{2} will be equal to the velocity of sound. Increasing the pressure p_{1} will not increase the velocity of escaping air beyond this limiting velocity unless a special converging diverging nozzle design is used rather than an orifice.
Pressure Above
Atmospheric Pressure 
Theoretical
Velocity, ft/sec 
Pressure Above
Atmospheric Pressure 
Theoretical
Velocity, ft/sec 

Atmospheres

Inches
Mercury 
psi


Atmospheres

Inches
Mercury 
psi


0.010

0.30

0.147

134

0.408

12.24

6.00

769

0.068

2.04

1.00

344

0.500

15.00

7.35

833

0.100

3.00

1.47

413

0.544

16.33

8.00

861

0.136

4.08

2.00

477

0.612

18.37

9.00

900

0.204

6.12

3.00

573

0.680

20.41

10.0

935

0.272

8.16

4.00

650

0.816

24.49

12.0

997

0.340

10.20

5.00

714

0.884

26.53

13.0

1025

The theoretical velocities in the preceding table must be reduced by multiplying by a “coefficient of discharge,” which varies with the orifice and the pressure. The following coefficients are used for orifices in thin plates and short tubes.
Type of Orifice

Pressure
Atmospheres Above Atmospheric Pressure 

0.01

0.1

0.5

1


Orifice in thin plate
Orifice in short tube 
0.65
0.83 
0.64
0.82 
0.57
0.71 
0.54
0.67 