BACKWATER CURVES IN HORIZONTAL UNIFORM CHANNELS 83 



The slightly different result for the exponent b will require a different value 

 of the corresponding coefficient : 



1.78X10" ,^,^^^^^ 



Cb = z — = 40,100,000 



123-38 



In this particular problem, not one of the three empirical equations developed 

 gives results differing more than 2 per cent from the values to which they were 

 fitted. 



PROBLEM 



702. The backwater curve in a circular conduit 10 feet in diameter lies between 

 the depths of 2 and 6 feet. Determine appropriate values of the exponents and 

 coefficients in equations (704) and (705). Use n = 0.012. 



Backwater curves in horizontal uniform channels: integration. To 

 proceed, now, with the integration of the backwater curves in horizontal 

 channels, the differential equation takes the special form 



dy d /V\ 



S^= -^. = Sf + -[^J [706] 



in .which 



and 



so that 



dx dx 



dx \2gJ 



-Q^T dy _ -Q^dy 

 gA^ dx gCay°' dx 



dy Q^ Q^ dy 



dx ciy^ gCay'^ dx 

 Separating the variables 



\ Q. gCa / 



Integrating 



L<3(o + l) gCa(6 + 1 - a) Xi 



Equation (707) facilitates the computation of the cases of backwater 

 curves in uniform channels with horizontal grade line. 



PROBLEM 



703. Solve problem 604, taking into account the shape of the channel, a rec- 

 tangfular concrete flume 20 feet wide. 



