# Page:EB1911 - Volume 14.djvu/80

68
[FLOW IN RIVERS
HYDRAULICS

Some later experiments on a very large scale, by E. Stoclcalper at the St Gotthard Tunnel, agree better with the value f=O'0028(I +3/rod). These pipes were probably less rough than Arson's. W'hen the variation of ressure is very small, it is no longer safe to neglect the variation of) level of the pipe. For that case we may neglect the work done by expansion, and then Zo-Zi'°Po/Go-P1/G1'ffvi/28) (l/m)=0, (10) precisely equivalent to the equation for the flow of water, zo and zi being the elevations of the two ends of the pipe above any datum, po and pi the pressures, G0 and Gi the densities, and 'U the mean velocity in the pipe. This equation may be used for the flow of coal gas. § 92. Distribution of Pressure in a Pipe in which Air is Flowing.-From equation (7a) it results that the pressure p, at l ft. from that end of the pipe where the pressure is po, is p=p0/{1 -§ 'lu0'/mgc-r }; (II) which is of the form 1>=~/(GH-12) for any given pipe with given end pressures. The curve of free surface level for the pipe is, therefore, a parabola with horizontal axis. Fig. loo shows calculated curves of pressure for two of Sabine's experiments, in one of which the pressure was greater than atmo-54- so 7 P . 3 +449 1, Hurt -io-0: 1:m;z9~1.s) A I I Q3-507 l' L J/

zo-oo

27-1.5. [1 za -as U C” 'Un (M-2.5)::,0 27 1-5 7-7

- .; - . 4 . | . - . N V J/ V o zna-sift. ~1-227Ft- sslo-.sF¢. sas-1-Ft. FIG. 100. spheric pressure, and in the other less than atmospheric pressure. The observed pressures are given in brackets and the calculated pressures without brackets. The pipe was the pneumatic tube between Fenchurch Street and the Central Station, 2818 yds. in length. The pressures are given in inches of mercury. Variation of Velocity in the Pipe.~Let po, ua be the pressure and velocity at a given section of the pipe; 17, u, the pressure and velocity at any other section. From equation (3a.) up = ci-W/Q =constant; so that, for any given uniform pipe, up=u0p0, u=4».f>», {1>; <12> which gives the velocity at any section in terms of the pressure, which has already been determined. Fig. IOI gives the velocity 4:-¢ C I 0 Vg/:w»""' |33:°”'7 284 .1 R, ,-nn |21

oe, zo-B 1

I nos Q 22 2 i, I I 1 1 |:

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