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e e e MEASUREMENT OF PEAK DISCHARGE BY THE SLOPE.AREA METHOD By Tafe Dalrymple and M. A. Ben!:>n Abstracf This chapter deacribes application of the Manning equation to measure peak discharge in open channels. Field and office procedures limited to this method are described. Selection of reaches and cross sections is detailed, discharge equations are given, and a complete facsimile example of computation of a slope..g,rea measurement is also given. Introduction A slope-area measurement is the most com- monly used form of indirect measurement. In the slope-area method, discharge is computed on the basis of a uniform-flow equatiol' involv- ing channel characteristics, water-surface pro- files, and a roughness or retardation coefficient. The drop in water-surface profile for a uniform reach of channel represents losses caused by bed roughness. In application of the slope-area method, any one of the well-known variations of the Chezy equation might well be used. The Geological Survey uses the Manning equation. This equa- tion was originally adopted because of its simplicity of application. The many years of experience in its use that have now been accu- mulated show that reliable results can be obtained from it. Basic Equations The Manning equation, written in terms of discharge, is Q= 1.486 AR'I3SI/' 11 ' where Q=discharge, A = cross-sectional area, R=hydraulic radius, S=friction slope, and n=roughness coefficient. The Manning equation was developed for conditions of uniform flow in which the water- surface profile and energy gradient are paral- lel to the streambed and the area, hydraulic radius, and depth remain constant throughout the reach. Lacking a better solution, it is assumed that the equation is also valid for nonuniform reaches that are invariably en- countered in natural channels, if the ener~ gradient is modified to reflect only the losses due to boundary friction. The energy equa- tion for a reach of nonuniform channel between sections 1 and 2 shown on figure 1 is (h+h,h=(h+h.),+(h,),_,+k(Ah,h." (2) where (1) h=elevation of the water surface at the respective sections above a common datum, h,=velocity head at the respective section=aV'/2g, h,= energy loss due to boundary fric- tion in the reach, 4h..= upstream velocity head minus the downstream velocity head, k(4h..) = energy loss due to aeeeleration or deceleration in a contracting or expanding reach, and k=a coefficient. 1