From equation (7b), for a pipe of circular section and diameter d,
| W = 1⁄4π √ (gd5 (p02 − p12) / ζ lcτ), = .611 √ (d5 (p02 − p12) / ζ lτ). |
(13)
Approximately
W = (.6916p0 − .4438p1) (d5 / ζ lτ)1/2.
(13a)
§ 94. Application to the Case of Pneumatic Tubes for the Transmission of Messages.—In Paris, Berlin, London, and other towns, it has been found cheaper to transmit messages in pneumatic tubes than to telegraph by electricity. The tubes are laid underground with easy curves; the messages are made into a roll and placed in a light felt carrier, the resistance of which in the tubes in London is only 3⁄4 oz. A current of air forced into the tube or drawn through it propels the carrier. In most systems the current of air is steady and continuous, and the carriers are introduced or removed without materially altering the flow of air.
Time of Transit through the Tube.—Putting t for the time of transit from 0 to l,
t = ∫l0 dl/u,
From (4a) neglecting dH/H, and putting m = d/4,