92 ANALYSIS OF FLOW PROBLEMS 



tations. Assume that the discharge for every possible pair of reser- 

 voir elevations is known, having been determined, say, by actual meas- 

 urements. It is desired to represent the information graphically in a 

 convenient form. Evidently the values of the discharge can be plotted 

 on a plane, at points whose coordinates represent the corresponding 

 water-surface elevations in the two reservoirs. A series of lines drawn 



Elev. A 



Fig. 803. Channel Connecting Two Reservoirs or Lakes. 



through points having the same discharge will facilitate interpolation 

 for intermediate discharges. Figure 804 shows a typical diagram of 

 this type. The water-surface elevations in the two reservoirs are 

 measured from a common datum, and the lowest elevation shown on the 

 diagram is the highest elevation of the bottom of the channel. When 

 the two elevations are the same, there is no flow, so that the line for 

 ^ = is a straight line extending upward from the origin at an angle 

 of 45° with the axes. Values of Q above this line represent flow from 

 reservoir A to reservoir B) values below the line represent flow in the 

 opposite direction. The diagram will not be symmetrical about the 

 line (2 = unless the channel is symmetrical about a section midway 

 between the two reservoirs. 



The areas shown separated by the dotted lines in Fig. 804 represent 

 different conditions of flow. Throughout areas I and IV the curves 

 for constant Q are straight lines perpendicular to the adjoining coor- 

 dinate axis. The discharge is independent of the water level in the 

 lower reservoir. This is the result when there is a control somewhere 

 between the two pools. For a channel with steep or adverse slope, the 

 control will be critical flow over the crest, and the water level in the 

 lower pool will not affect the discharge until the control is drowned 

 out. If the channel has a mild slope and is short, areas I and IV will 

 be comparatively small, and may not extend down to the origin, for 

 the critical flow section, which forms at the lower end, can be drowned 

 out by a relatively low water-surface elevation in the lower pool. (If 

 this is possible, a lower elevation should be chosen for the origin of coor- 

 dinates.) The control section will also be at the lower end for a 

 channel with horizontal bottom. A long channel with a mild slope will 

 have a friction control, the discharge not being affected by the water 



