Fon a chosen Courant number C and number of linear reservoirs N, there is a unique dimensionless unit hydrograph based on the cascade of linear reservoirs.
The dimensionless unit hydrograph has dimensionless time t* as abscissa and dimensionless discharge Q* as ordinate.
The dimensionless time is t* = t / tr, in which tr is the duration of the unit hydrograph, in hours.
The dimensionless discharge is Q* = Q / Qm, in which Qm = 2.777778 (A / tr), is the maximum attainable discharge
(runoff concentration only), in m3/s.
In this formula, basin area A is in km2; unit hydrograph duration tr is in hours.
The dimensionless unit hydrograph is independent of unit hydrograph duration tr and reservoir storage constant K, and is dependent only on their ratio C = tr / K.
The dimensionless unit hydrograph is independent of the basin area A.