## 3.6. Gradually Varied Flow

The governing equation derived from the energy conservation law for describing the gradually varied flow is given by:

$\frac{dh}{dx}=\frac{{S}_{0}-{S}_{f}}{1-{F}_{r}^{2}}=\frac{{S}_{0}-{S}_{f}}{1-\frac{T{Q}^{2}}{g{A}^{3}}}$

(3.150)

in which S

_{0}is the bottom slope of the channel, S_{f}is the friction or energy slope, F_{r}is the Froude number, dh/dx is the variation flow depth with respect to distance x, Q is the discharge (m^{3}/s), T is top width of the channel (m), and A is the water area (m^{2}).### 3.6.1. Classification of Gradually Varied Flow

To classify gradually varied flow, first it is necessary to classify the slope, which is based on the relative magnitude of normal depth and critical depth of flow. ...

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