Define energy slope

Energy slope ($S_f$) is the rate of loss of total energy head per unit length of channel. It is the slope of the energy grade line (EGL).

$$S_f=-\frac{dH}{dx}=\frac{h_f}{L}$$

where $H=z+y+\dfrac{\alpha V^2}{2g}$ is the total head and $h_f$ is the friction head loss over length $L$. It is a positive number since energy falls in the flow direction.

   EGL  ------\
                 \----  slope S_f
   WSL  ---------\---   slope S_w
   Bed  -----------\--  slope S_0

For uniform flow, $S_f=S_w=S_0$ (all three lines are parallel). For non-uniform flow, $S_f\neq S_0$. In Manning's equation, $S$ is the energy slope: $S_f=\dfrac{n^2V^2}{R^{4/3}}$.