1919 .] 
Parry. -Power from Town Water-mains. 
381 
that is to say, the 2J power of the equivalent diameter is equal to the sum 
of the 2J power of diameters of the pipes to which it is the equivalent. 
Another question which presents itself is the equivalent length, where 
pipes of different diameters are connected in series. 
Let it be required to find a length l of a pipe of diameter d which 
shall deliver water at the same rate, and with the same loss of head in 
friction, as another pipe of length l x and diameter We have according 
to the usual convention h = lv 2 /C 2 r = l 1 v 1 2 /C 1 2 r 1 . Let the value of C be 
the same in both cases and we have l = l l v 1 2 r/v 2 r 1 . Substituting for v 
and v 1 their values in terms of the flow and the area—viz., Q/^d 2 and 
7T 
Q/ 4 di 2 —and for r and r l their values in terms of the diameters—viz., d/4 
and dj 4—we have l/l 1 — d 5 /dj 5 : i.e., the lengths are proportional to the 
fifth power of the diameter. 
The following are examples taken from actual practice. Referring to 
the case of Wellington, already cited, the diameter of pipe equivalent to 
the 24 in. and 20 in. mains in parallel is 2434 ft., and the equivalent length 
in 30 in. pipe is 53,400 ft., so that the 30 in. equivalent of the whole system 
is 53,400 + 25,400, or 78,800 ft. 
Another example from another town : Two pipes are run in parallel 
for a distance of 9,900 ft., the diameter of one being 18 in. and of the 
other 24 in. The two pipes are then united and joined into a single pipe 
3 ft. in diameter and 2,480 ft. long. The static head at the delivery end 
of the 3 ft. pipe is 246 ft. It is required to know approximately what is 
the maximum possible power which can be obtained at the end of the 3 ft. 
pipe. For simplicity and convenience it is desirable to reduce the system 
of pipes to one pipe of equivalent diameter and length. Take first the two 
pipes : we find the diameter of a single equivalent pipe to be, in accordance 
with the foregoing principles, 2*343 ft., and the length of a pipe of this 
diameter which is equivalent to a 3 ft. pipe to be 721 ft. ; so that the single 
equivalent of the system of pipes is a pipe 2*343 ft. in diameter and 
9,900 + 721 or 10,621 ft. long. 
In accordance with the principles already expounded, the maximum 
power, irrespective of good regulation or any other condition, is obtained 
when one-third of the static head is lost in friction in the pipes. The 
static head being 246 ft., the friction head is 82 ft. From the formula 
h = lv 2 /C 2 r we find the value of v to be 4*03 ft. per second where l — 10621, 
r = 2*343/4 = 0*586. The value of C is taken at a low value of 60 so as 
to take into account bends, joints, change in diameter, valves and screens, 
and deterioration of surface with age. The diameter of the equivalent 
single pipe being 2*343 ft., its area is 4*3 square feet, and the flow due to a 
velocity of 4*03 ft. per second 17*33 cubic feet per second ; the net head 
after deducting 82 ft. consumed in friction is 164 ft., and the power con¬ 
tained in the water is consequently 164 X 17*33 -y 8*8 = 323 h.p. 
The brake horse-power depends on the efficiency of the wheel, and taking 
70 per cent, as a fair efficiency for a wheel of this size we find the maximum 
brake horse-power to be 226. The figure of 323 h.p. must be regarded as 
a first approximation only in order to determine the order of magnitude, 
and is liable to modification upon detailing the length of straight pipe, the 
length of angle and number of bends, joints, &c., and it is quite possible 
that a much higher value of C may be justified ; but detailed calculation 
is hardly warranted, as the object is not to determine the amount of power 
to be actually utilized, but the maximum possible irrespective of other 
