A very wide rectangular channel is designed to carry a discharge

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A very wide rectangular channel is designed to carry a discharge of 5 m³ /s per meter width. The design is based on the Manning’s equation with the roughness coefficient obtained from the grain size using Strickler’s equation and results in a normal depth of 1.0 m. By mistake, however the engineer used the grain diameter in mm in the Stickler’s equation instead of in meter. What should be the correct normal depth?

1. 0.32 m
2. 0.50 m
3. 2.00 m
4. 3.20 m

Correct Option: B

R =	A	=	B × y
R =	P	=	(B + 2y)

∵ B >> y , R ≈	B × y	≈ y
	B

n =	d^{1 / 6}	( Stickler's equation )
	24

q_old =	1	R_old^{2 / 3} S^{1 / 2} =	1	× y_old^{5 / 3} . S^{1 / 2}..........(1)
	n_old		n_old

q_new =	1	× y_new^{5 / 3} . S^{1 / 2}..........(2)
	n_new

(1) ÷ (2) ,

	n_old	=	y_old^{5 / 3}
	n_new		y_new^{5 / 3}

y_new =		n_new		^{3 / 5}	× y_old
		n_old

=		1		^{3 / 5}	= 0.5 m
		1000^{1 / 6}