40 HYDRAULIC JUMP IN NON-RECTANGULAR CHANNELS 



within which the desired results may reasonably be expected to fall. 

 Next, the total head is computed for each of these depths, corresponding 

 to the given discharge and the geometrical properties of the cross section. 

 A curve is then plotted, using the depths as ordinates and the values of 

 total head as abscissas. Alternate depths are selected by inspection of 

 the curve, being the pairs of depths for which the total head is the same. 

 A number of such curves, plotted for different discharges, are shown in 

 Fig. 401. Alternate depths for discharges between those plotted may 

 be obtained by interpolation. When one complete Q-curve has been 

 plotted, others may be quickly added if advantage is taken of the fact 

 that horizontal distances from the Q = line are proportional to the 

 square of the value of Q. 



The computational procedure to be employed will depend upon the 

 circumstances. Thus, if only the critical depth is needed for one value 

 of discharge in a channel, the cut-and-try procedure based upon the 

 criterion 



2g 2 



will suffice, or tables may be used if these are available for the cross 

 section. If a number of alternate depths are to be computed in addi- 

 tion, computation of the critical 

 depth by the criterion may be omit- 

 ted, for the critical depth will be de- 

 termined by the minimum (total 

 head) point of the curve used to 

 determine the pairs of alternate 

 depths. 



When only a single depth, alter- 

 nate to a given depth, is needed, 

 the entire curve need not be com- 

 puted. The alternate depth may be 

 computed by a cut-and-try proce- 

 dure, or a small portion of the 

 curve may be computed. 

 Again, it may be necessary to compute a very large number of alter- 

 nate depths in a given channel. Selection of the values from the diagram 

 similar to Fig. 401 becomes burdensome, and it is desirable to prepare 

 another type of diagram from which the alternate depths may be read 

 directly. Such a diagram is shown in Fig. 402, which has been prepared 

 for the same data shown in Fig. 401. 



The variety of problems of this type that may arise is great. In 



12 3 4 5 



Di in Feet 



Fig. 402. Alternate Depths in a 

 Typical Trapezoidal Channel. 



