STORAGE UNDER THE BACKWATER CURVE 145 



tributary flow changes very appreciably during the step. The remedy 

 is to make a new chart based upon a shorter length of step At. 



The submergence effect due to downstream backwater is not the only 

 effect that can be included by the method shown in Fig. 1104. Other 

 independent variables that affect the discharge-stage relation, such as 

 the number of gates open, may be treated in the same way. 



Storage under the backwater curve : superstorage. For extremely 

 long reservoirs in the valleys of rivers having mild slope, the assumption 

 of a level pool may be seriously in error, for the volume of water between 

 a horizontal plane through the water surface at the lower end of the pool, 

 and the actual water surface, which follows a backwater curve, may be 

 considerable. This part of the storage may be referred to as super- 

 storage. If the river valley is essentially uniform the volume of super- 

 storage is a function of the inflow, and may be evaluated by computing 

 backwater curves for various inflows in a typical section of the valley. 

 For valleys that are not uniform, the volume of superstorage is a func- 

 tion of both the inflow and the stage in the reservoir. A large amount of 

 data and many computations would have to be made before this func- 

 tional relationship could be summarized, but its effect can be included 

 in the routing, if deemed necessary, by a method similar to that of the 

 previous article. We assume that the stage-discharge relationship is 

 fixed, and not affected by any other variables. Therefore equation 

 (1108) applies, but (^i — ^Oi • At) and (^2 + ^02 ■ At) are functions of 

 the inflow as well as of the reservoir stage. The slide chart with the 

 transparent upper slide is drawn in exactly the same manner as that of 

 Fig. 1104, but the horizontal lines labeled " tributary flow " are now 

 labeled " inflow." This makes two " inflow " scales on the same chart. 

 The left-hand scale represents the average inflow during the step, while 

 the right-hand scale represents the inflow at the beginning or end of the 

 step. The rule must be read with point B in line with point A , but not 

 coincident with it unless the inflow remains constant during the step. 

 This slide-rule solution may be used whether the superstorage is or is 

 not a function of the stage. In the former case the collection, compu- 

 tation, and tabulation of the data is a formidable task. 



In sciectmg the length of step to be used in the routing computations, 

 two requirements must be complied with. First, the step must be short 

 enough so that the shape of inflow hydrograph is reproduced with satis- 

 factory accuracy. Second, the step must be long compared with the 

 time necessary for a wave to travel from the upper end of the pool to the 

 lower end. If both of the requirements cannot be met, the problem is 

 not of the type of slowly varied flow that can be treated as steady flow. 



