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T’. Guerin on the delivery of water from conduit pipes. 191 
Art. XXI.—To ascertain the loss sustained in the delive 
of water from a conduit pipe, when it is tapped by a Branch 
at any portion of its length; by Tos, Guerin, Civil En- 
gineer, 
In water works for the supply of a city it happens sometimes 
that it is necessary to convey the water in a conduit pipe from 
a reservoir situated at a long distance; and before the conduit 
reaches the point of distribution it is tapped by a branch so as 
0 carry off a portion of the water for other special purposes, 
thereby interfering seriously with the proper supply for the 
city. 
On examining the action of the branch it is easy to perceive 
that it causes an increase in the flow from the reservoir; while 
at the same time, it causes a diminution in the delivery at the 
point of distribution in the city, and moreover, the quantity 
carried off by the branch must be composed of such increase 
and diminution. 
Thus, let A be a vertical section of a reser- 
voir supplied from a river, or some other 
great source, and let ANB be a conduit pipe 
leading water to the point of distribution at B. 
It is manifest that if the pipe were cut at the , 
point N, the delivery there would be greater than it had been 
at B before the pipe was cut, for the reason that a discha 
through a pipe varies very nearly as the square root of the 
length inversely; it follows then that the discharge from the 
reservoir would be increased by cutting the pipe at the point N. 
_ Again, if instead of cutting the pipe at N, n orifice were 
made in its side, such that the area of the orifice would be 
equal to the sectional area of the pipe, it is evident that almost 
as much water would flow through this orifice, as if the pipe 
were actually cut across at N (the only difference being the — 
amount arising from a change in the direction of the fluid); 
A 
at B will be a little diminished, and while the orifice at N in- 
creases, this delivery will continue to decrease until finally it 
