Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Dimensional analysis – concepts of geometric dimensionless numbers
Question Statement:
A $1:25$ scale model of a spillway is tested in a hydraulic laboratory. If the discharge measured in the model is $0.16\text{ m}^3\text{/s}$, the corresponding prototype discharge in $\text{m}^3\text{/s}$ governed by Froude model law is ________ (answer in integer).
Answer Key:
500
Step-by-Step Solution & Explanation
According to Froude similitude law:
$\text{Discharge ratio } Q_r = L_r^{5/2}$
Given length scale ratio $L_r = 25$:
$Q_r = 25^{5/2} = (\sqrt{25})^5 = 5^5 = 3125$
Therefore, prototype discharge $Q_p$:
$Q_p = Q_m \times Q_r = 0.16 \times 3125 = 500\text{ m}^3\text{/s}$