Principle and procedure of slope-area method

Principle

The slope-area method is an indirect method for estimating flood peak discharge in a stream reach from the high-water marks and the channel geometry, used when direct measurement is impossible. It assumes steady non-uniform flow in a reach and applies Manning's equation with the friction slope from the energy equation:

$$Q = K\sqrt{S_f},\qquad K = \frac{1}{n}AR^{2/3},\qquad S_f = \frac{h_f}{L}$$ $$h_f = (h_1-h_2) + \left(\frac{\alpha_1v_1^2}{2g}-\frac{\alpha_2v_2^2}{2g}\right) - h_e$$

where $h_e = k_e|\Delta(\alpha v^2/2g)|$ is the eddy loss, with $k_e=0.3$ for expansion and $0.1$ for contraction.

  E.G.L ----\_____
  W.S. -----\___   \__  h_f
  bed  ------------------
       [1]<--L-->[2]

Procedure

1. Select a straight reach with a fairly uniform cross-section and clear high-water marks (flood marks) on both banks.
2. Survey 2 to 3 cross-sections and the water-surface levels at each section; measure the reach length $L$.
3. Compute $A$, $P$ and $R=A/P$ for each section; choose Manning's $n$ from the bed material and vegetation.
4. Compute conveyance $K_1$, $K_2$ and $K_m=\sqrt{K_1K_2}$.
5. First trial: $Q=K_m\sqrt{(h_1-h_2)/L}$.
6. Compute $v_1=Q/A_1$, $v_2=Q/A_2$, velocity heads, $h_e$ and $h_f$.
7. Compute the new $Q=K_m\sqrt{h_f/L}$; repeat until $Q$ converges. This is the peak flood discharge.