NON-RECTANGULAR PRISMATIC CHANNELS 



43 



The hydraulic jump in non-rectangular prismatic channels. The 

 mathematical theory of the hydraulic jump in prismatic channels of 

 other than rectangular cross section is based upon the fundamental law 

 of conservation of linear momentum. In order that a stationary jump 

 may form, the flow must first be at less than critical stage. The relation 

 between the sequent depths cannot be expressed by a simple formula as 

 for rectangular sections, but may be determined by a graphical method. 

 Transpose the momentum equation to the following form : 





[402] 



in which wAiji and 'wA2y2 represent the total hydrostatic pressure on 

 cross sections before and after the jump, respectively. The other terms 



-4 — 



$3 



S2 



12 3 4 5 6 



Values of P+ Af, in Thousands of Pounds 



Fig. 403. P + M as a Function of the Discharge and the Depth of Flow, in a 

 Typical Trapezoidal Channel. 



represent the momentum passing the section per second. This equation 



expresses the equality, before and after the jump, of the function 



P + M, given by 



wOV 

 P + M = wAy + ^^- [403] 



Since for a given discharge P + -M is a function of the depth only, curves 

 representing values of the function for different constant values of Q 

 may be plotted against the depth. An example is shown in Fig. 403. 

 Depths before and after a jump are found at the two intersections of the 

 curve for the given discharge with a constant value of P + ikf . The 

 value of the depth at the point where the curve becomes parallel to the 

 depth axis is the critical depth for that discharge. If a large number 



