140 



SLOWLY VARIED FLOW 



venient method would probably be to construct two rules, one suited to 

 the reservoir as a whole, and the other for the bottom portion only. 



The slide rule should be planned so as to minimize the work of com- 

 putation. If the rule is correctly planned no computations of any kind, 

 other than setting and reading the rule, need to be made in the actual 

 routing. For example, if daily values of inflow are given corresponding 

 to gage readings made each d^-y at a certain time, say noon, averaging 



This Distance, to Scale, Equals the Value of S+ JjoAt for o= 75,000 c.f.s. 



Scale I- 



1 = 100,000 day sec- ft. 



Upper Slide 



/^2040 



,10| 50 55 



wu 



loolooo ^°o\ 



Average Inflow ^^^^ 



During Step, c.f.s. ^O^OS" 



Outflow at End of Step, in Thousands of Cubic Feet per Second 



60 65 70 71 72 73 74 



i— I 1 I ,1 , 1 , I , U 1, L, 



—J 



76 



'ili'ii' I'i'i 'i 



I' I' r 



55 60 65 70 71 72 73 74 



Outflow at Beginning of Step, in 1,000's of c.f.s. 



Lower Slide -^ 

 Distance Equal to S-hoa^t for o= 75,000 c.f.s. 



^—Distance Equal to t-At for t= 75,000 c.f.s. 



I'lG. 1102. Fiood-Routing blide Rule for Example 1101. 



Graduated in terms of outflow. The setting shown in this figure illustrates the condition of steady 

 flow, with inflow Eind outflow equal. 



computations may be eliminated by making the duration of a step run 

 from midnight to midnight. The inflow values taken at noon can then 

 represent the average inflow during the step. The outflow values sub- 

 sequently obtained are for midnight, not noon, a fact which should be 

 remembered if the inflow and outflow hydrographs are to be plotted on 

 the same diagram. 



If values of outflow are desired as a result of the routing computations, 

 the labor of converting values of water-surface elevation to outflow may 

 be eliminated by graduating the slide rule in terms of outflow instead 

 of elevation. This can be done, for (S — ^o ■ At) and {S -^ ^o • At) 

 are single-valued functions of the outflow, as well as of the elevation. 

 The computations for a slide rule to solve illustrative problem 1101 in 

 this way are shown in Table 1102, and the rule is shown in Fig. 1102. 

 If needed for some special purpose, a similar rule could be made which 

 would give successive values of the storage. 



After the scales have been graduated, a partial check on the plotting, 

 which will disclose certain common types of errors, is easily made. For 

 the rule shown in Fig. 1101, set equal values of the elevation, on the 

 upper and lower scales, opposite each other, and for the rule of Fig. 1102, 

 set equal values of the outflow opposite each other. This represents 

 the condition of steady flow with the inflow equal to the outflow, so that 



