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Reynold’s Model Law

The law in which models are based on Reyold’s Number is called as Reynold’s Model Law.

Whenever viscous forces predominate over inertia or other forces for dynamic similarity, the Reynold’s Number for the model mush be equal to the Reynold’s Number for the prototype.

(Re)prototype  =  (Re)mode

ρp Vp LP / μp  =  ρm Vm Lm / μm

ρp Vp LP / ρm Vm Lm  . 1/ μp / μm = 1

ρr Vr Lr / μr = 1

Where scale ratio are

ρr = ρp / ρ'  Vr  =  Vp / Vm

L =  Lp / Lm,  μr = μp / μm

Now, Time scale ratio

Tr = Lr / Vr

Velocity scale ratio

Vr  =  Vr / Lr

Acceleration scale ratio

ar  =  V

Force scale ratio

Fr  =  mr ar =  (ρr ArLr) ar

Fr =  (ρr L3r)ar           

Discharge scale ratio

Qr =  ρr Ar Vr

Q =  ρr Lr2 Vr

Reynold’s  Model Law is Applicable in Following Cases:

(i)    Flow in closed pipes, flow meter, fans etc.
(ii)    Flow around immersed bodies like aero plane, submarine etc.

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