Slope area method of discharge

The slope-area method is an indirect method of finding discharge, mainly used for flood peaks when direct current-meter measurement is not possible. Discharge is computed from the water surface slope (from high flood marks) and the channel cross-sections, using Manning's equation.

Field work

1. Select a fairly straight, uniform reach (length $L$, about 75 m or more, fall ≥ 0.15 m).
2. After the flood, survey high water marks (silt lines, debris) at two (or more) sections 1 and 2.
3. Survey the cross-sections to get area $A$, wetted perimeter $P$ and hydraulic radius $R$ at each section.
4. Estimate Manning's $n$ from bed and bank conditions.

  Sec 1                   Sec 2
  ___ HFL ___  Dz (fall)
  |          ------____
  |  y1        L        ----___ HFL
  |____________________________y2_|
  =========== bed ============>

Computation

Energy equation between sections 1 and 2:

$$h_f = (Z_1 - Z_2) + \left(\frac{V_1^2}{2g} - \frac{V_2^2}{2g}\right) - h_e$$

where $Z$ = water surface elevation, $h_e$ = eddy loss $= K_e\left|\frac{V_1^2}{2g} - \frac{V_2^2}{2g}\right|$ ($K_e \approx 0$–0.1 for contracting, 0.3 for expanding reach).

Conveyance $K = \dfrac{1}{n}AR^{2/3}$ at each section; average $K = \sqrt{K_1K_2}$.

$$Q = K\sqrt{S_f}, \qquad S_f = \frac{h_f}{L}$$

Since $V$ depends on $Q$, solve by trial:

1. First take $h_f = Z_1 - Z_2$ (fall), find $S_f$ and $Q$.
2. Compute $V_1 = Q/A_1$, $V_2 = Q/A_2$; correct $h_f$ with the velocity head and eddy loss terms.
3. Repeat until $Q$ stops changing (usually 2–3 trials).

Limitations: accuracy depends on the choice of $n$ and on reliable flood marks; the reach must be free of backwater and sudden changes.