t = .001412 ζ1/2 l3/2 (p03 − p13) / d1/2 (p02 − p12)3/2;

(15a)

which gives the time of transmission in terms of the initial and final pressures and the dimensions of the tube.

Mean Velocity of Transmission.—The mean velocity is l/t; or, for τ = 521°,

umean = 0.708 √ {d (p02 − p12)3/2 / ζ l (p03 − p13)}.

(16)

The following table gives some results:—

Absolute
Pressures in
℔ per sq. in.		 Mean Velocities for Tubes of a
length in feet.
p0 p1 1000 2000 3000 4000 5000
Vacuum
Working		 15 5 99.4 70.3 57.4 49.7 44.5
15 10 67.2 47.5 38.8 34.4 30.1
Pressure
Working		 20 15 57.2 40.5 33.0 28.6 25.6
25 15 74.6 52.7 43.1 37.3 33.3
30 15 84.7 60.0 49.0 42.4 37.9

Limiting Velocity in the Pipe when the Pressure at one End is diminished indefinitely.—If in the last equation there be put p1 = 0, then

u′mean = 0.708 √ (d / ζ l);