OVERSHOT WATER-WHEEL 427 



A preferable form of bucket is that indicated at P (Fig. 185). Here 

 the vanes, usually of metal, are made in a single piece, and have a con- 

 tinuous curvature throughout. 



Theory of Action. Let H be the total head available. A certain pro- 

 portion of this head must first be utilized in giving the supply water 

 sufficient velocity to carry it into the wheel buckets. If hi is this head, 

 the velocity will then be given by v = ^/^gh^ 



A small clearance must be allowed between the highest point of the 

 wheel and the bottom of the inlet channel, this clearance &i being usually 

 about 1 inch. 



A rather larger clearance S 2 must in general be allowed between the 

 lowest point of the wheel and the level in the tail-race, so as to prevent 

 submergence of the wheel buckets in time of flood. 



In general 8 2 is about 6 inches, but depends largely on the special 

 circumstances of the plant. 



Finally, a certain proportion h 2 of the head must be devoted to produc- 

 ing velocity of flow along the tail-race, so as to give a free discharge from 

 the wheel. 



The outer diameter of the wheel buckets is thus limited to H (lii -j- 



fo) - (Si + 82). 



Let R = outer radius of wheel. 



r = inner 



Then 2 R = H - (hi + h) - (^ + S 2 ). 



The depth of buckets depends on the diameter, breadth arid velocity of 

 wheel, and on the quantity of water to be utilized. 

 Let Q = quantity of water per second in cubic feet. 

 <o = angular velocity of wheel in radians per second. 

 b = breadth of wheel, 



and since the buckets are never completely filled with water, let x = frac- 

 tion of bucket volume occupied by water. Generally x lies between J and f . 

 Then we have, neglecting the volume occupied by the wheel vanes, 



Bucket volume passing ) co 



= TT (IP i 3 ) X jr X b cubic feet, 

 inlet per second 2 TT 



x (R* - r 2 ) co b 

 .-. Q i - cubic feet per second. 



w b x 

 giving r, and therefore R r, the depth of the buckets. 



To avoid excessive loss under low heads this should be as small as 

 practicable. 



