LEVEL-POOL ROUTING 143 



If water is withdrawn from the reservoir for irrigation or the genera- 

 tion of power, it may be withdrawn (1) at a constant rate, (2) at a 

 predictable variable rate, or (3) at an unpredictable variable rate. 

 In the first case, the discharge is still a single- valued function of the 

 reservoir stage, and the slide-rule method of the previous section may 

 be used without modification. If the amount of water withdrawn 

 follows some fixed pattern, such as full capacity during times of peak 

 load and half or three-quarters capacity at other times depending upon 

 whether the reservoir stage is above or below a certain elevation, a direct- 

 reading slide rule may be constructed. 



Let the discharge rate for power use be represented by Q. Then the 

 equation of continuity for a short step M becomes 



o^ -\- Oi 

 i- M = -^-^ — - ' M^- Q- M-\- ^S 



with A^ positive if the storage is increasing. The rate of discharge 

 through the natural outlets is represented by o, as before, with the sub- 



Value of Q-At 



(In terms of Q) 



Value of Sj+JjOz-At 



< Scale graduated in terms of E^ot Oj) 



(In terms of i) 



Value of Si-)4o,-At 



(Scale graduated in terms of Ex or o\) 



Fig. 1103. Slide Rule for Routing Inflow through a Reservoir when Part of the 

 Water is Discharged for Power, According to a Known Pattern, and Part Discharges 



Through Fixed Outlets. 



scripts 1 and 2 referring to rates at the beginning and end of the step. 

 Transposing, 



i' M^- (5i - Joi • M) = (52 + Jo2 ■ M) -\- Q- M [1109] 



The method of graduating the scales for direct solution of this equation 

 is shown in Fig. 1103. 



A less simple case occurs when the discharge from the fixed outlets is 

 affected by submergence, as from tidal waters or from backwater due to 

 a flood in a large downstream tributary. In order for the problem to be 

 solved, the value of the discharge for every possible combination of 

 values of reservoir stage and tributary flow must be known, and the 

 hydrograph of the tributary must be known, as well as the hydrograph 

 of the inflow into the reservoir. Let the flow in the tributary be repre- 

 sented by F. Then, as before 



* • A/ + {Si - \oi • AO = (52 -h J02 • AO 



