Rational and empirical flood equations

Rational method

$$Q_p = \frac{C\,i\,A}{360}\quad(\text{A in ha, i in mm/h, Q in m}^3/\text{s})\qquad\text{or}\qquad Q_p=0.278\,C\,i\,A\ (A\text{ in km}^2)$$

i = intensity for duration $t_c$ and return period T; C = runoff coefficient.

• Limitations: only small catchments (up to about 50 km²); uniform rainfall and constant C assumed; gives only the peak; ignores storage and antecedent moisture; needs IDF curves.
• Appropriate use: design of urban drainage, culverts, small bridges, storm sewers and spillways of small catchments.

Empirical methods

Based on regional observations, the flood is a function of catchment area (and sometimes return period):

1. Dickens (north India): $Q = C_D\,A^{3/4}$ (A in km²; $C_D$ = 11 – 14 for the plains of north India, 14 – 28 for the hilly regions of north India, and 22 – 28 for central India).
2. Ryves (south India): $Q = C_R\,A^{2/3}$ ($C_R$ = 6.8 – 10.1 depending on distance from the coast).
3. Inglis (Maharashtra, ghat areas): $Q = \dfrac{124A}{\sqrt{A+10.4}}$
4. Fuller (USA): $Q_T = C_f\,A^{0.8}(1+0.8\log T)$
5. Nepal (WECS/DHM method): $Q_2 = 1.8767\,(A_{<3000}+1)^{0.8783}$ and $Q_{100}=14.63\,(A_{<3000}+1)^{0.7342}$, where $A_{<3000}$ is the catchment area below 3000 m elevation (km²), used for rivers without records.

• Limitations: valid only for the region and range of area where the constants were derived; they ignore rainfall intensity, slope, shape and land use of the particular catchment; the constants are subjective; the return period is not known (except Fuller and WECS).
• Appropriate use: quick, approximate estimates for preliminary design or for checking other methods, mainly in ungauged basins; not for final design of major structures.

Final design of large projects should use flood-frequency analysis (Gumbel, log-Pearson) or the unit hydrograph method with the observed data.