—————————— lO 
GENERAL PRINCIPLES OF HYDRAULICS 
469 
The horse-power and the efficiency per cent. are shown plotted on a 
velocity base in Fig. 764. 
The maximum possible velocity is when the area through the nozzle 
is equal to the area through the 
44 vy yw 
_ pipe, then h -f. — - —- = —,and 
d 2g 2g 
this maximum velocity the horse- 
power is 10°17, and the efficiency 
_ 49 per cent. 
When the horse-power de- 
livered is a maximum, a,, the 
necessary area through thenozzle, 
G 0161 a. 
is a gil 
100 | Hoo 
60 SRN 0 § 
Boo Hg PEN To 
40 
er S420; 
WZ i 
Velocity U- (Feet: per Second.) 
Fia. 764, 
Case II. The pressure energy of the water is so great compared 
with the kinetic energy that the latter may be neglected, also the effect of 
variation in the level of the pipe may be neglected. 
Let p, and p denote the pressures in lbs. per square inch at points A, 
and A in the pipe at a distance / feet apart. Let H, = horse-power enter- 
ing the portion A,A of the pipe at A,, H=horse-power delivered at A, 
v=velocity of water ‘in feet per second, and d=diameter of pipe in 
feet. 
Loss of energy between A, and A per Ib. of water passing 
6 eeeen, | © iankeee 
and H = 
therefore p =p, — 
La thas 
144° d 2g" 
144prd*%7__— rd*v 
Al ‘ 
ES i Of: = ey 
4x 550 rete Eg ee 
To find when H is a maximum, 
dH _ 7d 
dv 4x 550 
2 
3uf+—- 3g 144p,, or when v= 
The maximum value of H is therefore = 0-483,/ 
(144p, — Buf - - . x) hence H is a maximum when 
24p,9d 
wfl © 
fl 
All the power is lost in friction in the pipe, and H=0, when 
4l v 72p,gd 
ws 997 Aah orv= “ae : 
The efficiency is T =l1- Hoge ; 
When H is a maximum, the efficiency is $. 
ExampLe.—Let p, = 1120 Ibs. per square inch, 7 = 1 mile = 5280 feet, 
d=0°5 foot, and f= 0°006, 
Hae 
4] y* 
cao ~uf At) = (57-58 —0-08750%). 
cess (14 ws 5) ww asin 
