4 GENERAL PRINCIPLES OF HYDRAULICS 467 
~§ In order that the water may flow from B towards D, it is evident 
if the pipe BD be closed the loss of head A between A and D 
that if 
must be greater than 40 feet. 
_ 10000Q? _ 7, — 8000Q? 
ha Torcrgs? ond 100- hm ta T5? 
where Q is the rate of flow through AD and DC when the pipe BD is 
closed. From these two equations, i =73 feet, nearly. Therefore if the 
_ pipe BD be open, water will flow from B towards D. 
Now let h,, h,, and h, be the losses of head between A and D, 
. B and D, and between D and C respectively, then 
_ 10000Q ya TOOUOs 
A 48? x 1:55’ pate ach 432 x 15’ 
8000Q2 
These equations are sufficient to determine Q, and Q,, but their 
solution is somewhat cumbersome, and it is really simpler and quicker 
to proceed by approximation, as follows :— 
hy, x 1-5 
=43,/"1 =1: 
| Qi = 48.4/-1 A = 1185 hy 
No x 15 
=4 =" 
Q 33500 O°555 hy, 
he x 1°75° 
=—4 cat’ Witla ee . 4 i] 5 
Q,=43,/ R000 71 88 wha 
Select values of h, (which must lie between 40 and 73) and 
calculate the values of Q;, Q,, and Q, from the equations just given, 
_ until values are obtained which make Q,+Q,=Q,. The work may 
be tabulated as follows :— 
: h,= 100 - hy, = 
4 
h, | 60 61 62 63 62°1 62°2 * 62°25 
hy 7746 | 7°810 | 7:874 T'937 7889 T'887 7890 
hg | 20 2h > | 23 23 221 22-2 22°25 
AVhy 4°472 | 4583 | 4690 | 4796 | 4-701 4°712 4-717 
hg | 40 | 89 38 37 37°9 37°8 37°75 
nJhs 6325 | 6°245.| 6164 | 6-083 6156 67148 6°144 
Q 9179 | 9°255 9°331 9-405 9°338 9°346 9°350 
Q. 2°482'| 2°544 2-603 2°662 2°609 2-615 2°618 
Q 12°321 | 12°165 | 12-007 | 11°850 | 11°992 | 11°976 | 11-969 
Q, +0 11°661 | 11-799 | 11-934 | 12-067 | 11-947 | 11°961 | 11°968 
The answers required, as found above, are Q, = 9°350, and Q, = 2°618. 
For practice, and to illustrate more fully the working of this example, 
the student would do well to find the answers directly by solving the 
- equations already given. 
- 409. Power Transmitted through a Pipe.—Case I. The pipe 
(Fig. 763) is provided with a nozzle at its delivery end, as for a Pelton 
wheel, and there is a valve by means of which the area through the nozzle 
. 
