Discussion of “The Backwater curve”

Abstract

Tho author's graphical construction is interesting. It has tho usual advantages of graphical methods, easy detection of gross errors and of situations where extra care is necessary to obtain accurate results. It also offers special advantages if curves must be computed for several different discharges or slopes. The special ease with which slope changes may be taken into account should make the method particularly useful for flow‐profile analyses.The author's method of integration by fitting a parabola through equidistant ordinates is not so appealing. The limits of integration in practical problems are seldom whole numbers, so that the equidistant ordinates would occur at values of the depth which would contain fractions and thus be awkward to compute. Moreover, the shape of the backwater curve is poorly approximated by parabolas, even of higher degree than the fourth. The writer's preference in integrating is to use a sufficiently large number of ordinates that the trapezoidal rule will yield accurate results. By plotting the curve to be integrated on coordinate paper (with as many points as seems desirable to establish the shape of the curve) and using a close spacing of ordinates, say Δy= 0.1, the successive ordinate values can be read off and added on a machine, the cumulative total being recorded at intervals as desired to obtain the integral curve. By this method, the shape of the backwater curve through the whole range is obtained with little. If any, more labor than for the computation of a single point by the integration formula.