438 MR. RENNIE ON THE FRICTION AND RESISTANCE OF FLUIDS. 
Table X. 
Experiments on Leaden Pipes with Flexures. 
The straight pipe of an inch bore, on which the preceding experiments 
were made, was carefully bent into one, two, and fourteen semicircular bends 
respectively, each of inches in the semidiameter, and two of ^th part of a 
circle of 3| inches radius. One end of the pipe was fixed in the wooden 
orifice as before, and the following are the results. 
Pipe 15 feet long, ^ inch bore, with one semicircular and two ^-circle bends. 
Constant height 
of the surface of 
the water above 
the centre of the 
orifice. 
Time in dis- 
charging one 
cubic foot by a 
pipe with three 
bends. 
Time discharg- 
ing one cubic 
foot by a 
straight pipe. 
Remarks. 
feet. 
4 
3 
2 
1 
seconds. 
147 
175 
213 
316 
seconds. 
143 
164 
208 
312 
The position of the bends, whether vertical 
or horizontal, at either extremity of the 
pipe, does not affect the result. 
xAAAA/W 
Pipe 15 feet long, \ inch bore, with 14 semicircular and two ^-circle bends. 
feet. 
4 
3 
2 
1 
seconds. 
162 
200 
247 
351 
seconds. 
143 
164 
208 
312 
The expenditure is diminished by the bends 
from -5- to 1, which represents the friction 
of the pipe. 
Results. 
1. That with one semicircular and two £ of a circle bends, as compared with a straight pipe of 
equal length and bore, the resistance varies from xVth to ^th part of the resistance of the straight 
pipe. 
2. That with fourteen semicircular and two quarter of a circle bends, the resistance varies from T ' 7 th 
to -^vth of the resistance of a straight pipe. 
3. That the increased number of bends does not increase the resistance in the ratio of the number 
of bends, but merely shows an increased resistance, as compared with the four bends, of T vtb to -rVth. 
