490 APPLIED MECHANICS 
the wheel is regulated by a sluice E, which has teeth on its upper face 
gearing with a pinion. F, which is secured to the shaft H. A worm K 
gears with a worm wheel L, which is fixed to the shaft H. The worm K 
is fixed to a shaft operated by a governor or by hand. 
The rim of the particular wheel illustrated runs at a high speed, over 
100 feet per second, and it is strengthened by steel hoops M shrunk on. — 
In some wheels of this type these steel hoops are made of much larger 
section than shown in Fig. 789, in order to increase the fly-wheel action, — 
preventing a too rapid change of speed with charge of load. 
Owing to the greater obliquity of the vanes at exit than at entrance, the — 
distance d between two consecutive vanes at exit is less than the distance © 
between them at entrance, and to prevent the choking of the passage by — 
the water the passage is widened transversely towards the circumference — 
of the wheel, as shown in the left-hand view in Fig. 789. oe 
In impulse wheels the water flows over the vanes under atmospheric 
pressure, and to ensure free access of air ventilating holes e are made — 
through the sides at the back of the vanes, as shown. 
426. Speed, Power, and Efficiency of Girard Impulse Wheel.— 
Referring to Fig. 790, 7; and ry are the inner and outer radii respec- — 
tively of the wheel. 
¢,=B,C, is the tan- 
gential velocity of the 
wheel at radius 7. 
Cy = BC, is the tan- 
gential velocity of the 
wheel at radius 79. 
Obviously ¢,/7, = 9/75. 
v,=B,V, is the ab- 
solute velocity of the 
water as it enters the 
wheel. t,=B,V, is 
the absolute velocity 
of the water as it 
leaves the wheel. pisos 
0, =angle CB, V,. 0, = angle C,BoVo. B,C, V,U, and B,CoV2U_ are 
the parallelograms of velocities at entrance and exit respectively. — 
u,=B,U, is the relative velocity at entrance, and B,U, is the direction 
of the tangent to the vane at entrance. %,=B,U, is the relative velo- — 
city at exit, and B,U, is the direction of the tangent to the vane at exit. 
, =angle C,B,U,. ¢,=the supplement of the angle C,B,U,. 
As the water in entering and passing through the wheel is under 
atmospheric pressure, the velocity v, depends only on the effective head — 
at B,, and is to be calculated from the formula »,= ,/2gH,, where — 
H, is the effective head. 
If W is the weight of water entering the wheel per second, then, neglect- : 
ing friction, the energy given to the wheel per second is 5,07 — 03). 
But by Art. 419, p. 482, the energy given to the wheel per second is ; 
Ww 
also equal to gia cos 4, — UxCq COs Oy), a 
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