324 HYDEAULICS AND ITS APPLICATIONS 



The value of H, the uniform depth necessary to give this supply is 

 given by 



H = \/ fV* = A 8 / >OQ3 X 25 X 10,000 

 V fc 2 2 g i V 64-4 X 400 X "001 



= 3*08 feet. 



If at the upper end the depth of water is greater than this, say 4 feet, 

 we have (Case 1 (c) ) and everywhere h > H. The depth of water thus 

 increases down stream. 



Applying equation (10), we now have 



f h (at entrance to flume) = 4'0 ; li = 



* ( S ) -^ *' i^gW )- ^ * (1 ' 8) = 1 ' 280 (tables) 



4 - A, = - -001 (3,000) + ^ { 1-280 - 

 /. 7 - 1-315 = fo - 1-027 



.-. /i, - 1-027 4 (||) - 5-685 = y. 



If h = 6-70 y = 1-015 - 1-027 (1-017) = - '030 

 fo = 6-75 y = 1-065 - 1-027 (1'015) = + "022. 

 The correct value of h%, the depth in the forebay, is approximately 

 6*73 feet. The depth of the water in the flume at different points in 

 its length can be calculated in the same way, and the necessary 

 height of side ascertained. 



If, at the upper end, the depth of water is equal to H, this will 

 remain constant throughout, while if less than H and greater than 



H or -871 H, i.e., between 3'08 feet and 2*68 feet, we get Case 



J 



1 (b). The height will now decrease down stream until it reaches the 

 value >y/ 7- , after which a series of waves will be produced, and the 

 depth will, as explained in Case 1 (b), finally settle down to 3'08 feet. 



y 



The critical point is found by putting h* = ^J ~ H = 2*68 in 



equation (10). Let hi = 3'0 feet. 

 Then we have at the critical point 



