138 SLOWLY VARIED FLOW 



points are plotted to scale, but the intermediate divisions between them are 

 spaced equidistant. The rule as shown is set for the step during which the 

 average inflow is 305,000 c.f.s., for the left end of the upper slide is set opposite 

 305,000 in the left scale of the lower slide. Opposite 840, the reservoir elevation 

 at the beginning of the step, the elevation at the end of the step, 86L7, is read 

 on the upper slide. It is obvious that the slide rule solves equation 1108 auto- 

 matically. The complete routing computations made with the aid of the rule 

 are shown in column (10). The maximum stage reached is 902.4. The routing 

 computations have not been carried beyond 16 days. The flood of this example 

 is chosen to be large enough to cause the water to rise above the spillway level, 

 a circumstance which would not be permitted in the design of an effective flood 

 control reservoir. 



Notes on construction of flood-routing slide rules. There is a tempta- 

 tion, where the graduations are not uniform, to attempt curvilinear 

 interpolation of the intermediate points. The writers have found this 

 to be inadvisable, for straight-line interpolation of the intermediate 

 points is much easier, and almost invariably gives more accurate results. 

 If greater accuracy is desired than can be obtained with straight-line 

 interpolation, more points should be computed. Essentially, the two 

 scales with non-uniform graduations are made up of the sum (or dif- 

 ference) of two variables, one, the storage, and the other, a constant 

 times the discharge. At elevations where either of these is changing 

 rapidly, computed values should theoretically be more closely spaced. 

 Usually both will change rapidly near the origin, but since even fairly 

 large percentage errors at low stages have inappreciable effect after 

 high stages are reached, it is seldom necessary to compute intermediate 

 values for the low stages. Immediately above a spillway crest, how- 

 ever, the discharge will vary considerably for a small difference in water- 

 surface elevation, and since the stage is high, it is desirable to compute 

 values at close intervals for plotting the scales. In the example shown 

 in Table 1101, two-foot intervals were used above the spillway crest, 

 while 20-foot intervals were used below. 



Another effect, besides that just mentioned, must be taken into 

 account if greater accuracy is desired for the lower stages. Referring 

 to Table 1101 and Fig. 1101, it is seen that the " elevation at beginning 

 of step " scale has some negative values corresponding to the lower 

 elevations. This happens when ^o • At is larger than S, and it may 

 give rise to inconsistent results in the routing at low stages. The 

 negative values can be eliminated, if it is deemed advisable, by using a 

 smaller value of At. 



It should seldom, if ever, be necessary to obtain precise results for the 

 low stages in a large reservoir. If it were necessary, the most con- 



