134 SLOWLY VARIED FLOW 



The relationship between the elevation of the water surface and the 

 discharge through the outlet may be represented by an equation of the 

 form 



= Bh"" [1101] 



or of the more general form 



o=fi{E) [1102] 



In these equations o is the outflow, or rate of discharge through the 

 outlet, jB is a constant which depends upon the size and hydraulic 

 properties of the outlet, h is the elevation of the water surface above the 

 zero-elevation of the outlet, and n is an exponent, ordinarily either 1/2, 

 for orifice-type outlets, or 3/2, for weir-type outlets. Often the rela- 

 tionship is not expressible by an empirical equation, and has to be 

 tabulated or plotted graphically, in which case the elevation of the 

 water surface E may be measured from any convenient datum. This 

 case is represented by equation (1102). For outlets of simple geomet- 

 rical shapes, the methods explained in elementary texts on hydraulics 

 will suffice for the determination of the relationship between the water- 

 surface 'level and the discharge, but for complicated or natural outlets, 

 one of the following methods may have to be used: (1) field measure- 

 ments of elevation and discharge, (2) model studies, (3) construction 

 of rating curves by the methods explained in Chapter VIII. 



The capacity-depth information for the pool, obtained by computa- 

 tion from survey data giving the areas at regular intervals of elevation, 

 is tabulated or plotted graphically. Vertical distances are preferably 

 measured from the same datum that was used in the outflow-depth 

 relationship. Thus 



S=f2{h) [1103] 



or 



S=fs{E) [1104] 



where 5 represents the total amount of water stored when the water 

 surface is at elevation E or is at a distance h above the zero elevation 

 of the outlet. It is usually possible to obtain an empirical equation 

 representing this relationship, but this is not necessary for the method 

 which is now to be explained. 



The inflow hydrograph is usually specified by giving values of the 

 inflow at regular intervals of time. The hydrograph may be long-time, 

 representing a continuous record of inflow, or it may only include one 

 flood. At any rate the given values follow each other at brief enough 

 intervals that the general shape of the sharpest flood peak is well defined. 

 The outflow hydrograph, which is the result desired, should preferably 

 be obtained in terms of values of the outflow at the same regular inter- 



