At 1 : 50 scale model of a spillway is to be tested in the

At 1 : 50 scale model of a spillway is to be tested in the laboratory. The discharge in the prototype is 1000 M³ /s. The discharge to be maintained in the model test is

Froude’s law,

	V_m	=	V_p
	√g y_m	=	√g y_p

∴ V ∝ √y_m
i.e. V_r ∝ √L_r
Q_r = A_rV₂ = L_r² × √L_r
= (L_r)^{5 / 2}

Q_m	= (L_r)^{5 / 2} =		1		^{5 / 2}
Q_p			50

∴ Q_m =		1		^{2 / 3}	× 1000 = 0.057 m³ / s
		50