FLOW IN OPEN CHANNELS 



307 



Again, since 



clA Z ~ 2 C X P- A * 



*' V : = 2 "X* 



so that, neglecting the small increase in the wetted perimeter accompany- 

 ing an increase in depth, any small increase in the cross sectional area 

 produced by such a change in depth will be accompanied by 1*5 times 

 this proportional increase in the discharge. 



Again assuming A to be known and a small error to be made in the 

 estimated value of P, we have 



dP 



2Pf, 



dMg _ 1 dP_ 

 '"" (/ 2 P ' 



error leads to one-half the proportional error 



n 



the 



so that this 

 estimation of (J. 



Since these errors should be severally small and may all occur in tho 

 same direction, the total possible error will be equal to their sum. 

 Thus if the probable error in the estimation of i = p per cent. 



A = q per cent. 

 P / per cent. 



The possible area in the estimation of the discharge, assuming C to 

 have its correct value, will be given by 



( P + F , -- i 

 I 



1*5 q f per cent. 



ART. 88. GENERAL EQUATION OF FLOW TN AN OPEN CHANNEL. 



Consider a steady stream of cross-sectional area A , flowing over a bed 

 having an inclination to the 

 horizontal, where sin 6 = slope 



Let A B (Fig. 134) be any 

 stream tube, the vertical depths 

 of A and B below the surface 

 being y A and y R . FlG - 1: ^. 



Let A h B be the loss of head in this stream tube from A to B, due to 

 frictional resistances. 



x 2 



