TABLE OF CONTENTS A gradually-varied flow profile or gradually-varied water surface profile is a line indicating the position of the water surface. It is a plot of the flow depth as a function of distance along the flow direction. A sound understanding of possible profiles under different flow situations is essential before we can obtain numerical solutions to gradually-varied flow problems. A qualitative investigation of Equation 4.7 will serve this purpose.
Consider a mild channel as shown in Figure 4.1. By definition, y n > y c. The channel bottom, the critical depth line, and the normal depth line divide the channel into three zones in the vertical dimension, namely M1, M2, and M3 (M stands for mild). The solid lines in the figure represent the shapes of the possible flow profiles in these three zones. Obviously, the normal depth line itself would represent the water surface if the flow in the channel were normal. In zone M1, the water surface is above the normal depth line. Therefore, in this zone y > y n and consequently S f < S 0. Also, y > y c and thus F r < 1.0 in zone M1. Therefore, both the numerator and the denominator of Equation 4.7 are positive quantities, and ( dy/dx) > 0. In other words, the flow depth must increase in the flow direction in zone M1. We can examine the zones M2 and M3 in a...
