WATER WHEELS AND TURBINES 495 
Ratio of Radius r, to Radius r,.—The ratio 7, +7 is also assumed, 
For outward flow 7,+7, varies from 0°7 to 0°85, and for inward flow 
een m 12 to 2. In parallel flow turbines take r,=7r,=7, the mean 
Result of Continuity of Flow.—Since the water completely fills the 
in flowing through them, it follows that v,A, = 
elocities of Whirl.—At entrance to wheel the velocity ‘of whirl is 
2 cos @,, and at exit v, cos 4. 
_ Work Imparted to Wheel. —It W = weight of water passing through 
the wheel per second, then by Art. 419, p. 482, the work imparted 
to the wheel per second is 
Ten cos, — Cy C089). 
| Efficiency.—The energy available per second is Wh, where h is the 
available head of water. Hence the efficiency is 
E= alc cos 0, — csv, cos 9). 
_ The efficiency varies from 75 to 85 per cent., and may be taken, 
_ when unknown, at 80 per cent. 
___ Velocity of Flow from Guide Passages (v,).—First assume that the 
s wad of whirl at exit v, cos 0, =0. 
The angle 9, is then 90°, and foc 
_ Work imparted to wheel per second = weit cos 4. 
. a vy A, % 
a Eificioncy E= 5 11 C08 0,= pst hairs . cos 4, cos py. 
E 
Hence » = za Ba jy -PR— Ks Aah 
z 
where K,= NES , “1 cos 4, cos py may be called the coefficient of velocity. 
2 
If instead of assuming that 6,=90° it be assumed that w= cy, then 
it may be left as an exercise to the student to show that 
E 
—A/gAi(%1 -3) 
K, q Z(B 00s 6 + cos dy A,)" 
