Question

In a laboratory experiment using a scaled down model to measure scour at a bridge pier, the Froude number is important. The ratio of the prototype length to the model length is 100. If the velocity of the model is 1 m/s, the velocity (in m/s) of the prototype is:

• A. 0.1
• B. 1
• C. 10
• D. 100

Hint:

When solving scale model problems involving the Froude number, remember that the Froude number is the same for both the model and the prototype, and use the scaling law to find the relationship between the velocities.

Answer 1

The Correct Option is C

The Froude number (\( Fr \)) is given by: \[ Fr = \frac{v}{\sqrt{gL}} \] where \(v\) is the velocity, \(g\) is the acceleration due to gravity, and \(L\) is the length. Since the Froude number is constant for both the model and the prototype, we can write: \[ \frac{v_m}{\sqrt{g L_m}} = \frac{v_p}{\sqrt{g L_p}} \] Where:
\( v_m = 1 \, {m/s} \) is the velocity of the model,
\( L_m = 1 \) is the length of the model,
\( L_p = 100 \) is the length of the prototype,
\( v_p \) is the velocity of the prototype.
Simplifying, we get: \[ \frac{v_p}{1} = \sqrt{100} \quad \Rightarrow \quad v_p = 10 \, {m/s} \] Thus, the correct answer is (C) 10.