Question

In the model of a highway bridge constructed to a scale of 1:25, the force of water on the pier was measured as 5 N. What is the force (approximate) on the prototype pier?

• A. 15.6 kN
• B. 25.3 kN
• C. 78 kN
• D. 90 kN

Answer 1

The correct option is C 78 kN

Froude model law will be applicable in this case.
$F{r}_m=\frac{V_m}{\sqrt{gLm}}=\frac{V_p}{\sqrt{g{L}_p}}=F{r}_{p}If{L}_r=\frac{L_m}{L_p}and{V}_r=\frac{V_m}{V_p}=\sqrt{L_r}\frac{(Force{)}_m}{(Force{)}_p}={\rho }_r{L}_r^2{V}_r^2\Rightarrow \frac{(Force{)}_m}{(Force{)}_p}={\rho }_r{L}_r^3[\because {\rho }_r=1]\Rightarrow \frac{5}{(Force{)}_p}={\left(\frac{1}{25}\right)}^3\Rightarrow (Force{)}_p=5\times {25}^3\Rightarrow (Force{)}_p=78.125kN$