FLOW IN OPEN CHANNELS 



301 



Whatever the slope of the sides, the trapezium of best shape will be 

 that in which the sides are made tangent to the circle of radius = d 

 having its centre in the surface, and as may be readily shown, all such 



channels have the same hydraulic mean depth =-5. It follows then 



a 



that the velocity of flow when the channel is full will be independent of 

 the slope of the sides, and will depend solely on the gradient of the bed. 

 The discharge of any two trapezoidal channels of the best form and of 

 the same gradient and depths, will, when running full, be proportional 

 to their respective mean widths. 



The following table indicates how the top and bottom widths for a 

 section of this type, vary with the slope of the sides : 



Circular Section. Fig. 130. 

 Let d = diameter of circle. 

 = angle at centre subtended by wetted perimeter. 



Then 



A = 



For maximum velocity 



; P = 





" 



J. Suppose d fixed. 



*($)_ 



dS 



.'. = tan 

 .-. 6 = 257J. 



