Model: Discharge rate am=1.25$m^{3}/s$

Scale $\frac{Lm}{Lp}-\frac{1}{50}$ ie. scale ration, $L_{r}=\frac{L_{p}}{L_{m}}=50$

(i)Discharge rate in prototype QP

In cse of spillway for dynamic similarity the froude number for the model and prototype must be equal discharge scale ratio

$\frac{Qp}{Qm}=(\frac{L_{p}}{L_{m}})^{s/2}; \ \ \ QP=(\frac{Lp}{Lm})^{s/2}$.Qm

$Q_{p}=(50)^{5/2}\times 1.25=22.09=m^{3/s}$

ii) Scale ratio for time $T_{r}$

$T_{r}=\frac{T_{p}}{T_{m}}=\sqrt L^{r}$

$T_{p}$=12hrs

$T_{m=}\frac{T_{P}}{\sqrt L^{r}}=\frac{12}{\sqrt 50}$=1.697 hrs