ILLUSTRATIVE EXAMPLE 



137 



The greatest convenience of computation, however, is obtained by 

 constructing a special slide rule for solving equation (1108) directly. 

 This can best be described by mesuis of a numerical problem. 



Illustrative Example 1101 



The area-depth survey data for a large reservoir are shown in columi- " (1) 

 and (2) of Table 1101. Assuming that the reservoir has a fixed orifice-type t- 

 let, the discharge through which is given by the equation Oo = 5,650(£ — 680 \ 

 and an overflow spillway with discharge Ou, = 1,520(£ — 900)''^, route t. 

 flood inflow hydrograph shown in columns (8) and (9) of the table through th» 

 reservoir, starting with the reservoir empty, and carrying the routing past the 

 maximum stage in the reservoir. Construct a slide rule for step-by-step deter- 

 mination of the stages in the reservoir. 



Values of the storage capacity at diff^erent elevations are based upon the 

 elevation-area data of the first two columns of the table and are shown in column 

 (3) of the table, converted to c.f.s. days, a unit of volume also abbreviated as 



This distance, to scale, is the value of S+ijo-^t corresponding to ir=861.7 



Upper Slides 



680 720 

 I 1740760 780 



Reservoir Stage at End of Step 

 800 810 820 830 840 



|l ""l I ll 



ll,l,l| li l.| l ;i, ' | l |l|l)l.l|'<'f'i " .' U '| l |'l')i V) |li.i. l ii|,i, | ,|,;,;| J ,^ „ Nij.i, l \ h \\*.',l 



870 



780 



800 810 820 



830 



400,000 300,000 200,000 100,000 680 

 Average Inflow During ( 1 day) Step, c.f.s. 720 760 ''6S«"'°''' Stage at Beginning of Step 



Value of t'At for t= 305,000 c.f.s. 



-Lower Slide 

 Value of S-iio-U for £^=840 



All distances plotted to scale of •- 



■H = 100,000 c.f.s. days 



Fig. 1101. Slide Rule for the Reservoir of Illustrative Example 1101. 

 Graduated in terms of reservoir stage. 



d.s.f., and representing the volume of a cubic foot per second flowing for 24 

 hours. The values of outflow shown in column (4) include not only the discharge 

 through the orifice-type outlet, but also the discharge over the spillway crest 

 for elevations above 900. 



The time interval between the inflow values given in column (9) is one day, 

 frequent enough to define the inflow hydrograph and therefore frequent enough 

 to define the outflow hydrograph, which will be less sharply peaked than the 

 inflow hydrograph. The length of step At is accordingly chosen equal to 1 day. 

 The computations in columns (5), (6), and (7) then follow the formulas of their 

 headings. 



After the values in columns (6) and (7) have been obtained the " slide rule " 

 may be constructed. The divisions are marked in pencil upon two smooth, 

 straight strips of wood,* and are labeled as shown in Fig. 1101. The computed 



" Parting stop," purchasable at any lumber yard, is cheap and convenient. If 

 the rule is to be preserved or used for some time, a coat of clear linoleum lacquer, 

 applied after it has been graduated, is desirable. 



