Define hydraulic depth

Hydraulic depth ($D_h$ or $\bar{D}$) is the ratio of flow area to the top width of the water surface:

$$D_h=\frac{A}{T}$$

It is the depth of a rectangular channel having the same area and top width. For a rectangular channel $D_h=y$, for a triangular channel $D_h=y/2$, and for a trapezoidal channel $D_h=\dfrac{(b+zy)y}{b+2zy}$.

It is used in the Froude number, $Fr=\dfrac{V}{\sqrt{gD_h}}$, and in the critical-flow condition $\dfrac{Q^2T}{gA^3}=1$ for non-rectangular sections. Hydraulic depth should not be confused with hydraulic radius, $R=A/P$.