GATE ME 2025 Set 1 — Question 17
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Fluid Mechanics → Dimensional Analysis & Similitude → Dimensionless Numbers
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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
Correct answer
(C) 10
Solution
For dynamic similarity in open channel flow (like scour at a bridge pier), the Froude number () must be the same for both the prototype and the model.The Froude number is defined as , where is the velocity, is the acceleration due to gravity, and is the characteristic length.Given:
Ratio of prototype length to model length:
Velocity of the model: m sFor Froude number similarity:
Since is the same for both prototype and model, we can write:
Substitute the given values:
m sTherefore, the velocity of the prototype is 10 m s.
Ratio of prototype length to model length:
Velocity of the model: m sFor Froude number similarity:
Since is the same for both prototype and model, we can write:
Substitute the given values:
m sTherefore, the velocity of the prototype is 10 m s.
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