The law in which models are based on Froude Number is called as Froude’s model law.

Whenever gravity forces are predominant over other forces for dynamic similarity, the Froude number for the model must be equal o Froude number for prototype.

(F_r)_prototype  =  (F_r)_model

V_p / √ g_p L_p = V_m / √ g_m L_p

It the place of model and prototype is same, then gm = gp

V_p / √ L_p = V_m / √ L_m

V_p / V_m x 1/ √ L_p / L_m  = 1

V_p / V_m  =  √ L_p / L_m

V_p / V_m  =  √L_r

V_r  =  √L_r

Time scale ratio

T_r  = T_p / T_m = (L/V)_p / (L/V)_m  =  L_p / L_m x V_m / V_p

= L_r 1/ √ L_r

T_r  =  √ L_r

Acceleration scale ratio

a_r  =  a_p / a_m  =  (V / T)_p / (V / T)_m  =  V_p / T_p x T_m / V_m

=  √ L_r x 1/ L_r

a_r  = 1

Discharge scale ratio

Q_r  =  Q_p / Q_m = (L^₃ / T)_p / (L³ / T)_m = (L_p / L_m)³ x (T_m / T_p)  = L_r³ . 1/ √L_r

Q_r  = L_r^5/2

Force scale ratio

F_r  = F_p / F_m  =  ρ_p L_p² V_p² / ρ_m L_m² V_m²

F_r  = ρ_p / ρ_m x (L_p / L_m)² x (V_p / V_m)²

If the fluid used in model and prototype is same, then

ρ_p / ρ_m  = 1

F_r = (L_p / L_m)² x (V_p / V_m)² = L_r² x (√ L_r)² = L_r² . L_r

F_r  = L_r³

Pressure scale ratio

P_r = P_p / P_m = ρ_p V_p² / ρ_m V_m²

P_r = V_p² / V_m² = V_p² / V_m² = ( V_p / V_m)²

P_r  =  L_r

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