A circular sewer 2m diameter has to carry a discharge of

A circular sewer 2m diameter has to carry a discharge of 2m³ /s when flowing nearly full. What is the minimum required slope to initiate the flow? Assume Manning’s N = 0.015.

Manning’s equation

V =	1	m^2/3C.^1/2
	n

⇒	Q	=	1	m^2/3C.^1/2
	A		n

m = R =	A	=	(π/4)D²	m^2/3C.^1/2
	P		πD

=	(1/4) × 2²
	2

=	1
	2

N = 0.015
G = 2 m³ /s

A =	π	× 2² = π
	4

⇒	2	=	1	−		1		^2/3	(i)^1/2
	π		0.015			2

∴ i = 0.00023