Question

A submarine operating underwater is to be modelled based on Reynold’s Number scaling. Derive the expression for prototype velocity, Vp as a function of model velocity, Vm. If we now wish to model a breakwater in a physical laboratory, we must base this on Froude Number scaling. For this second application, derive the expression for prototype velocity, Vp as a function of model velocity, Vm.

Answer 1

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when the friction force is dominating then Reynoold's Number model is applicable.When submarine is underneath the water,the Reynold's Model law will be applicable.

From Reynold Model law

(Re)m = (Re)p ( m = model and p = prototype)

{ Vm*Lm//NUm} = {Vp*Lp/NUp} (NU = kinematic viscosity = dynamic viscosity/fluid density)

Vp = {(Lm/Lp)*(NUp/NUm)} = (Lr/NUr) ( length ratio = Lr = Lm/Lp and NUr = NUm/NUp)

Vp = (Lr/NUr)

When gravity force is dominant then Froud Number Model law will be applicable.For breakwater condition,from the Froud Model Law

(Fr)m = (Fr)p

{Vm/(g*Lm)^0.50} = {Vp/(g*Lp)^0.50}

Vp = (Lp/Lm)^0.50 = (1/Lr)^0.50 ( length ratio = Lr = Lm/Lp )