GRADUALLY AND RAPIDLY VARIED OPEN CHANNEL FLOW

The depth of the open channel flow varies (either increases or decreases) in the flow direction depending upon the bottom slope and energy line slope. Physically, the difference between component of weight and shear forces in the direction of flow produces a change in fluid momentum. Thus, there is a change in velocity and consequently a change in depth. The shape of the surface can be calculated by solving the governing equation obtained form combination of Manning equation and energy equation. The result will be a nonlinear differential equation, which is beyond the scope of this syllabus. However, some physical interpretation of gradually varied flows can be made from the following equation;
                                                (8)
For , the factor becomes a non-zero quantity, which is essentially the gradually or rapidly varying flow. Now, the sign of i.e. whether the flow depth increases or decreases with distance along the channel depends on both numerator and denominator of Eq. (8). The sign of denominator depends on whether the flow is sub-critical or super-critical. In fact, for a given channel, there exists a "critical slope" and a corresponding critical depth that leads to under conditions of uniform flow.