A circular pipe has a diameter of 1m, bed slope of 1 in

A circular pipe has a diameter of 1m, bed slope of 1 in 1000, and Manning’s roughness coefficient equal to 0.01. It may be treated as an open channel flow when it is flowing just full, i.e., the water level just touches the crest. The discharge in this condition is denoted by Q_full. Similarly, the discharge when the pipe is flowing half-full, i.e., with a flow depth of 0.5m, is denoted by Q_half.
The ratio Q_full/Q_half is:

Discharge, Q =	1	A R^2/3S^1/2
	n

Q_full =	1		π	D²			D		^2/3	S^1/2
	n		4				4

Q_half =	1	.		π	D²			D		^2/3	S^1/2
	n			8				4

Q_full	= 2
Q_half