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:

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