Machinery's Handbook, 31st Edition
2822 NOZZLES Flow rate faster than the speed of sound is possible with a converging-diverging nozzle. Analysis of this type of nozzle is beyond the scope of this text. Velocity of Escaping Compressed Air: 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:
k – 1 k ----------
p 2 p 1 ---
k k –1 ------ 53.3 459.7 F + ( ) 1 ⋅
⋅
=
2 g
–
v 2
In this formula, v 2 = velocity of escaping air in feet per second; g = acceleration due to gravity, 32.16 feet per second squared; k = 1.41 for adiabatic expansion or compression of air; F = temperature, degrees F; p 2 = atmospheric pressure = 14.7 pounds per square inch; and p 1 = pressure of air in container, pounds per square inch. In applying the preced- ing formula, 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. In- creasing 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. The accompanying Table 40 provides velocity of escaping air for various values of p 1 . These values were calculated from the preceding formula simplified by substituting the appropriate constants: v 2 108.58 459.7 F + ( ) 1 14.7 p 1 ----- 0.29 – = Table 40. Velocity of Escaping Air at 70-Degrees F Pressure Above Atmospheric Pressure Theoretical Pressure Above Atmospheric Pressure
Theoretical Velocity, Feet per Second
Velocity, Feet per Second
Atmo spheres 0.010 0.068 0.100
Inches Mercury
lbs per sq. in.
Atmo spheres 0.408 0.500 0.544
Inches Mercury
lbs per sq. in.
134 344 413 477 573 650 714
12.24 15.00 16.33 18.37 20.41 24.49 26.53
0.30 2.04 3.00 4.08
0.147 1.00 1.47 2.00 3.00 4.00 5.00
6.00 7.35 8.00 9.00
769 833 861 900 935 997
0.136 0.204 0.272 0.340
0.612 0.680 0.816 0.884
6.12 8.16 10.20
10.0 12.0 13.0
1025 The theoretical velocities in Table 40 must be reduced by multiplying by a “coefficient of discharge,” which varies with the orifice and the pressure. The coefficients in Table 41 are used for orifices in thin plates and short tubes. Table 41. Coefficients of Discharge
Pressures in Atmospheres Above Atmospheric Pressure 0.01 0.1 0.5 1
Type of Orifice
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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