Define hydraulic slope

Hydraulic slope (hydraulic gradient, $S_w$) is the slope of the hydraulic grade line (HGL), which in an open channel coincides with the water surface. It is the fall of the water surface (piezometric head $z+y$) per unit length of the channel:

$$S_w=-\frac{d(z+y)}{dx}$$

For uniform flow the water surface is parallel to the bed, so $S_w=S_0$ (bed slope) and also equals the energy slope $S_f$. For non-uniform flow $S_w$ differs from both $S_0$ and $S_f$.

 EGL ------\
 HGL(WSL)    ------\      S_w = slope of water surface
 Bed             ------\  S_0 = slope of bed