302 



For maximum discharge 



HYDRAULICS AND ITS APPLICATIONS 

 A 9 



d 



3D 

 L T~/\~ 



6 (Id 



.-. 3 (1 cos 6) = 6 sin 

 .-. -26 30 cos 6 -f- sin = 0. 



The value of B which satisfies this equation is 308, so that a circular 

 conduit will give its maximum discharge when the depth of water is 

 about '95 of the diameter, the discharge then being about 5 per cent, 

 greater than when completely full. 



The discharge corresponding to any depth of water is given by 



= C 



sin 



when = 180 = 



Q = -_' d 2 \/i. cub. ft. per sec. 



The semi-circular section when running full has a hydraulic mean 

 depth of -, and since this is greater than that 



of any other form of channel of the same area, 

 this section is well fitted for an open channel. 



Where a polygonal channel is used, the 

 hydraulic mean depth is greatest when the sides 

 and bottom of the channel are designed so as to 

 be tangent to a circle having its centre in the 

 water line. The trapezoidal section and rect- 

 angular section of greatest flow, are particular 

 cases of this. Where vertical sides are to be used the most suitable 

 form of bottom consists of a circular arc, concave upwards. 



Channel of Constant Mean Velocity. Where the depth of water in a 

 channel may vary within wide limits, it is in general desirable to design 

 this so that the velocity of flow may be as nearly as possible independent 

 of the depth. Otherwise, in an open canal, the velocity may become so 

 great as to damage the sides and bottom by scouring (Art. 97), while in 

 a sewer, with low heads, the velocity may become insufficient to produce 



FIG. 130. 



