312 



HYDRAULICS AND ITS APPLICATIONS 



once the slope and physical condition of the bed is fixed, an investigation 

 of any particular case of flow must take into account both these factors. 



The surface curves corresponding to a few particular cases of flow will 

 now be investigated. 



First suppose ^ les,^ than unity, the state of affairs existing in a 



1 



f 



channel of slope less than ;-. 







The following may be taken as approximate values of / at such 

 velocities as are common in practice (Bazin), the foot being the unit of 

 length. 



so that for ^- to be less than unity, with a rubble masonry channel the 

 slope would not exceed "00825 feet per foot, or 1 in 310. 

 Case 1 (a). Let -^-< 1 and also /i 3 < ~H Z . 



J J 



Both numerator and denominator of the right-hand side of equation (6) 

 are now negative, so that -7 r is positive, i.e., the depth of water increases 

 down stream. 



V "2~7 



Also as h increases it finally reaches the critical value /y -. //. 



Here the denominator becomes equal 

 to zero, and in consequence the value 



of - becomes oo , or the surface 

 a I 



curve at this point becomes vertical 

 (Fig. 135), and the phenomenon 

 knpwn as the standing wave is 

 produced. 

 In the figure, suppose the dotted line S 8' to be drawn parallel to the 



FIG. 135. 



bed, to represent a depth A/ '*J. . II. If by means of a sluice we can 



