CHAPTER IV 



CRITERIA OF FLOW AND THE HYDRAULIC JUMP IN 

 CHANNELS OF NON-RECTANGULAR CROSS SECTION 



Critical depth. In Chapter II the critical depth was found to be that 

 depth of flow, in a rectangular channel with level bottom, at which the 

 rate of change of velocity head is just equal to the rate of change of 

 depth. (Though these two rates are numerically equal when the flow 

 is critical, it should be noted that they are opposite in sign.) For 

 channels of general prismatic shape, this fundamental definition still 

 applies, but a more convenient criterion is that which states that the 

 flow is critical when the velocity head is equal to one-half the average 

 depth. To prove this, let 



D = depth, measured from the bottom, and 



T = width of the section at the water surface, or top width. 



Then, since the flow is steady, 



A ^ A^ dA A" A 



But dA = TdD, by geometry, so that 



d\_ _ TV 

 dD~ ~ A 



At the condition of critical flow 



dD \2g ) dD V 



Eliminating dV/dD, we find that at the critical stage 



Yl^A^^ [401] 



2g 2T 2 



Two other definitions of critical flow are more significant, though not 

 so convenient for computations. The first states that for a given total 

 head above the bottom of the channel, the discharge is a maximum; the 

 second that for a given discharge, the total head above the bottom of 

 the channel is a minimum. These definitions may be proved simul- 



38 



