MR. RENNIE ON THE FRICTION AND RESISTANCE OF FLUIDS. 439 
Table XI. 
Experiments on the Discharge of Water by Leaden Pipes of ^ an inch bore, 
] 5 feet long, but bent in the forms of from one to twenty-four right-angled 
elbows, each side being 6§ inches long. 
Height of the 
surface of the 
water above the 
centre of the 
orifice. 
One right angle 
8§ inches from 
the end of the 
pipe. 
Straight pipe 
15 feet long. 
Twenty-four 
right angles. 
Remarks. 
feet. 
4 
3 
2 
1 
seconds. 
180 
214 
246 
371 
seconds. 
143 
164 
208 
312 
seconds. 
393 
465 
584 
872 
In the first three experiments we have a 
diminution of expenditure in the ratio of 
2y to 1, and in the last experiment as 
3 to 1 nearly. 
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Conclusions. 
From the foregoing experiments with one rectangular pipe, it would be reasonable to conclude that 
the diminution of discharge would be as the number of right angles ; but comparing the expenditure by 
one right-angled pipe with the expenditure of a pipe with twenty-four right angles, the difference is 
only in the ratio of about two to one. 
General Remarks on the Expenditure of Horizontal and Bent Pipes. 
Formulae adapted to the different circumstances of the motion of water in 
pipes and conduits have been given by various authors. 
By some, the retardations were supposed to be in the inverse ratios of the 
squares of the lengths of the pipes ; and by others, to be represented by a certain 
portion of the altitude of the reservoir above the centre of the pipe, the resist- 
ance being directly as the length and circumference of the pipe, and inversely 
as the area of the section. 
M. Girard, in his beautiful experiments*, conceived the resistance to be com- 
pounded of the first and second powers of the velocity. So that, deducing the 
values from Dubuat’s experiments, and expressing the resistance due to cohe- 
sion by R.r U, R being the quantity to be obtained by experiment, and making 
MDCCCXXXI. 
* Memoires des Scavans Etrangers. 
3 L 
