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In model similarity, if gravitational and inertia forces are the only important forces, then what is the discharge ratio (Note: Lr is the ratio of length dimension)?

In model similarity, if gravitational and inertia forces are the only important forces, then what is the discharge ratio (Note: Lr is the ratio of length dimension)? Correct Answer Lr <sup>5/2</sup>

Explanation

Given, if gravitational and inertia forces are the only important forces. So it corresponds to Froude Number.

In Froude Model law,

  • Scale ratio for velocity (Vr = Vm/Vp) = (Lr)0.5
  • Scale ratio for time, Tr = (Lr)0.5
  • Scale ratio for discharge, Qr = (Lr)2.5
  • Scale ratio for Force, Fr = (Lr)3
  • Scale ratio for Power, Pr = (Lr)3.5

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