The GATE Grind

GATE 2025 ME – Question 17

Fluid Mechanics · Dimensional analysis · 1 mark · Multiple choice

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$^{-1}$, the velocity (in m s$^{-1}$) of the prototype is

  1. 0.1
  2. 1
  3. 10
  4. 100

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Correct answer: (C) 10

Explanation

Equal Froude numbers mean $\frac{V}{\sqrt{gL}}$ is the same for the model and the prototype. So $V_p = V_m\sqrt{\frac{L_p}{L_m}} = 1 \times \sqrt{100} = 10$ m/s.