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# Mulvaney Equation

The Mulvaney Equation was proposed by the Irish engineer Thomas James Mulvaney (1822-1892). The equation was first published in 1851. The model predicts the peak discharge $Q$ as a function of an empirical constant $C$, the average rainfall intensity of the catchment $I$ and the area of the catchment $A$:

$$Q [m^3/s] = C \left[\frac{1E+6}{1E+3*3.6E+3}\right] * I \left[\frac{mm}{hour}\right] * A [km^2]$$

The intensity being given in $mm/hour$ and the area in $km^2$, the constant $C$ accounts for the transformation of units from $mm/hour$ and $km^2$ to $m^3/s$. This equation is only valid for small catchments in which storage and losses are not significant! This rather the case in urban (small) catchments:

This equation in commonly used units reads:

$$Q_{peak} = 0.278 * C * I * A$$

where

$Q_{peak}$ = peak discharge in cubic meters per second

$I$ = Intensity of rainfall in mm/hour

$A$ = Area in square kilometers

$C$ is a runoff coefficient.