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Question

The flow of glycerin (kinematic viscosity v=5×104m2/s) in an open channel is to be modeled in a laboratory flume using water (v=106m2/s) as the flowing fluid. If both gravity and viscosity are important, what should be the length scale (i.e ratio of prototype to model dimensions) for maintaining dynamic similarity?

A
1
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B
22
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C
63
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D
500
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Solution

The correct option is C 63
Equating Reynolds number and Froude number, we get
VrLrνr=VrLr
Lr=(νr)2/3
νr=νmνp=1065×104=2×103
Lr=(2×103)2/3
Lr=0.0159
But Lr=LmLp

LpLm=1Lr=10.0159=62.99=63

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