316 



HYDRAULICS AND ITS APPLICATIONS 



a flume ha r j a slight inclination delivers water to a penstock from 

 which one or .nore turbines or water wheels are fed. It then becomes 

 important that the proportions of the flume should be such as to prevent 

 the water level from falling below a certain minimum. This problem 

 will afterwards be considered in detail (p. 324). 

 Case 1 (c). 



[-*<! 



Let -! / ^ 



( h > If. 



Here the surface is everywhere above the line R R r (Fig. 138). Both 

 the numerator and denominator in the fraction. 

 - H 3 



(equation 6) are positive 



- 



, 3 



" 



2 i 



d h . ... 

 -7-r is positive. 



Down-stream then the depth increases, and 



- H 3 





ultimately 



tends to the limit unity, i.e., 



dh 



tends to the limit i, the slope of the 



bed. It follows that the down- 

 stream surface tends to become 

 horizontal. 



Up-stream h tends to the limit 



H, and ^-. to the limit zero, so 



FIG. 138. 



that the curve tends to become 

 asymptotic to the line R R'. 



This is the form of surface curve produced by a weir or dam in a 

 stream of small slope, and is of importance since the introduction of such 

 a dam causes what may be a serious raising of the backwater level for 

 some considerable distance up-stream. 



Next let -j be greater than unity, the state of affairs usually existing 



in artificial water supply channels. 

 Case 2 (a). 



Let 



h < II. 



