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:

Velocity of Escaping Compressed Air Equation and Calculator

where:

v2 = Velocity of escaping air in feet per second (ft/sec);
g = Acceleration due to gravity, 32.16 feet per second squared (32.16 ft/sec2);
k = 1.41 for adiabatic expansion or compression of air;
F = Temperature, degrees F;
p2 = Atmospheric pressure = 14.7 pounds per square inch (14.7 lbs/in2);
p1 = Pressure of air in container, pounds per square inch (psi).

In applying the above equation, when the ratio p2/p1 approximately equals 0.53, under normal temperature conditions at sea level, the escape velocity v2 will be equal to the velocity of sound. Increasing the pressure p1 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
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