In a downward sloped channel with subcritical flow, if the flow depth is greater than normal depth, what happens to the flow depth in the direction of flow?

In a downward sloped channel with subcritical flow, when the flow depth is greater than the normal depth, the behavior of the flow can be analyzed using the concepts of specific energy and energy grade line. In this situation, the normal depth represents the depth that would occur under uniform flow conditions for a specific discharge in a channel with a constant slope.

Since the flow is initially at a depth greater than normal and under subcritical conditions, it has a certain amount of specific energy associated with it. As the flow moves downstream through the channel, it will experience gravitational effects and, because of the downward slope, will lose energy. However, in subcritical flow, the flow also has the tendency to recover from disturbances by adjusting its depth toward normal depth.

Because the initial flow depth is above normal, the energy in the flow will cause it to gradually increase in cross-sectional area, resulting in an increase in flow depth downstream until it reaches normal depth. This behavior adheres to the principles of energy conservation and flow characteristics, where the flow depth adjusts to reduce the specific energy towards the equilibrium state of normal depth.

Thus, under these conditions, as the flow moves downstream, the flow depth will indeed increase in the direction of flow until it adjusts to the normal