Solution:

Given:

Scale ratio of length $L_r=40$

Velocity in model $V_m=2 m/s$

Discharge in model $Q_m=2.4m^{3}s$

Let $V_p$ and $Q_p$ be the velocity and discharge in prototype

Step No 1)

$\frac{V_p}{V_m}=\sqrt{L_r}$

=$\sqrt{40}$

$V_p=V_m \times \sqrt{40}$

=$2\times \sqrt{40}$

[$V_p=12.65m/s$]

Step 2)

$\frac{Q_p}{Q_m}=L_r^{2.5}$

=(40)$^{2.5}$

$Q_p=Q_m \times (40)^{2.5}$

=$2.5\times(40)^{2.5}$

[$Q_p=25298.2m^{3}/s]$