PONCELET WHEEL 437 



.-. With a = 15, the maximum theoretical efficiency is "93. 

 Again (Fig. 192), 



u sin /3 = v sin (/3 a) 



.*. ^ cos a sin fi = v sin (/? a) 



a 



.'. cot 13 tan a = - 



tO 



.'. tan ft = 2 tan a 



If a = 15, tan /? = '5358 



.-. ft = 28-2. 



Actually, because of hydraulic losses caused by relative motion of the 

 mass of water in the buckets, and which are proportional to v r 2 , it is found 

 advisable to diminish the relative velocity slightly by giving the vanes a 

 velocity varying from *5 to *6 v. Under these circumstances the 

 maximum working efficiency is obtained. 



The construction of the wheel is substantially as shown (Fig. 193). 

 The buckets are open both at their inner and outer circumferences, and 

 to prevent water at impact from flowing into the inner part of the wheel, 



v 2 

 the depth of buckets should be not less than h -\- -^- , where h = 



thickness of stream. In practice h should not exceed 9 inches. 



u sin a 



But P ' = gin08-.) 



/. taking a = 15, /? = 30 (approx.), we have v r = u = '55 v (approx.), 

 and taking v 2 = 2 g H, where H is the supply head, we have 



? ;2 



Depth of buckets = '3^ + h 



* 9 

 = -3 H + h. 



TT 



In practice the depth is usually taken as -^ + h. 



The spacing varies so as to give about forty- eight buckets in the 

 circumference, the maximum spacing being about 16 inches. The most 

 suitable arc of water contact is about 30. Since at all points of this arc 

 the direction of the approach stream should make an angle fi with the 

 tangent to the circumference, the approach channel is not straight but 

 has a bed curved so as to fulfil this condition. 



To draw this curve, let K and M (Fig. 193) be the extremities of the 

 arc of contact, and from K and M draw K and M perpendicular to 

 the required directions of the stream, i.e., making an angle a with the 

 normals at K and M, and intersecting in 0. Then an approach bed, 



