PROBLEMS 23 



When the flow is from left to right, as shown in Figs. 201, 202, and 

 203, it is impossible for the depth to increase in the absence of friction or 

 impact, except by means of some such agency as those illustrated. If 

 the channel is of uniform width, with level bottom, open at the top, and 

 frictionless, it is impossible for the depth of flow to increase except by a 

 form of impact which will be discussed in the next chapter. A limited 

 amount of variation is possible, however, in the immediate vicinity of 

 the critical depth. 



Flow at velocities higher than the critical is said to be rapid flow, 

 shooting flow, or super-critical flow, while flow at velocities lower than 

 the critical is said to be tranquil flow, streaming flow, or sub-critical 

 flow. This criterion of flow, which, as we have seen, is based on a 

 balance of the velocity head and the static head, was discovered by 

 Belanger, and is often referred to as Belanger's critical flow. It should 

 not be confused with other criteria of flow such as Reynolds', which is 

 used to distinguish between turbulent and viscous flow. 



PROBLEMS 



20L What changes would result in Fig, 201 if Q was kept the same but D\ made 

 smaller? Larger? 



202. Find the equation of the curve EFGH in Fig. 201. 



203. Prove that the value of Dc in equation (207) is always between the values 

 of Di and Di. 



204. Make a graph of equation (207). Use values of Di/Dc as ordinates, and 

 values of Di/Dc as abscissas. For comparison, plot the rectangular hyperbola 

 DiDi = Dc^ on the same graph. 



