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.

(R_e)_prototype  =  (R_e)_mode

ρ_p Vp L_P / μ_p  =  ρ_m V_m L_m / μ_m

ρ_p V_p L_P / ρ_m V_m L_m  . 1/ μ_p / μ_m = 1

ρ_r V_r L_r / μ_r = 1

Where scale ratio are

ρ_r = ρ_p / ρ'  V_r  =  V_p / V_m

L_r  =  L_p / L_m,  μ_r = μ_p / μ_m

Now, Time scale ratio

T_r = L_r / V_r

Velocity scale ratio

V_r  =  V_r / L_r

Acceleration scale ratio

a_r  =  V

Force scale ratio

F_r  =  m_r a_r =  (ρ_r A_rL_r) a_r

F_r =  (ρ_r L³_r)a_r           

Discharge scale ratio

Q_r =  ρ_r A_r V_r

Q_r  =  ρ_r L_r² V_r

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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