A river reach of 2.0 km long with maximum flood discharge

A river reach of 2.0 km long with maximum flood discharge of 10000 m³ /s is to be physically modeled in the laboratory where maximum available discharge is 0.20 m³ /s. For a geometrically similar model based on equality of Froude number, the length of the river reach (m) in the model is

F_r =	V
	√gy

	V_m	=	V_p
	√g y_m		√g y_p

∴ V_r = √L_r
Q_r = A_r V_r
= A × L_r²
= √L_r × L_r² = (L_r)^{5 / 2}
∴ L_r = (Q_r)^{2 / 5}

=		0.2		^{2 / 5}	= 0.0131
		10⁴

	L_m	= L_r
	L_p

L_m = L_r × L_p
= 0.0131 × 2000 = 26.4 m.