Question

A river reach of 2.0 km long with maximum flood discharge of 10000 $m^3/s$ is to be physically modeled in the laboratory where maximum available discharge is $0.20m^3/s$. For a geometrically similar model based on equality of Froude number, the length of the river reach (m) in the model is

• A. 26.4
• B. 25.0
• C. 20.5
• D. 18.0

Answer 1

The correct option is A 26.4

According to Froude model law

$\frac{V_r}{\sqrt{L_r{g}_r}}=1$ $\because F_r=1$
$\therefore V_r=\sqrt{L_r}$
Now, we have

$\frac{Q_m}{Q_p}=L_r^2\times V_r$

$\Rightarrow \frac{Q_m}{Q_p}=L_r^2\times \sqrt{L_r}$
$\Rightarrow \frac{Q_m}{Q_p}=(L_r{)}^{5/2}$

$\Rightarrow \frac{0.20}{10000}=(\frac{L_m}{2\times 1000}{)}^{5/2}$

$L_m=26.4m$