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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

Correct answer: 10

Solution

The Froude number is a dimensionless parameter that relates the inertial forces to gravitational forces in fluid flow. Since the model length is scaled down by a factor of 100, to maintain dynamic similarity, the velocity of the prototype must be scaled by the square root of the length ratio, which is √100 = 10. Therefore, if the model velocity is 1 m/s, the prototype velocity must be 10 m/s.

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