Question 6.13: For the pipeline and conditions described in Example 6.9, ca......

Understanding Hydraulics [985713]

For the pipeline and conditions described in Example 6.9, calculate the mean velocity using the Manning equation.

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$V = ({0.397}/{n}) D^{{2}/{3}} S_{F}^{{1}/{2}}$ (6.24)

The pipe is described as ‘smooth’ so use a low concrete roughness value from Table 8.1, say n = 0.012 ${s}/{m^{{1}/{3}}}$ (for rough concrete use a higher value). As before, D = 1.2 m and $S_{F}$ = 1 in 250 = 0.004.

V = ({0.397}/{0.012}) \times 1.2^{{2}/{3}} \times 0.004^{{1}/{2}}

V = 2.361 m/s

In Example 6.9, the Colebrook-White equation gave V = 2.363 m/s. The simple Manning equation gives almost the same answer, although it obviously depends upon the assumed value of n.

Table 8.1 Typical values of Manning’s n for different types of surface
	Conduit type, surface roughness and channel alignment	n(s/ $m^{{1}/{3}}$ )
Canals	Earth, straight	0.018 – 0.025
	Earth, meandering	0.025 – 0.040
	Rock, straight	0.025 – 0.045
Lined	Perspex	0.009
channels	Glass	0.009 – 0.010
	Cement mortar	0.011 – 0.015
	Concrete	0.012 – 0.017
	Dressed, jointed stone	0.013 – 0.020
Swale	Water depth ≤ height of grass	0.250
	Water depth > height of grass	0.100
Rivers	Earth, straight	0.020 – 0.025
	Earth, poor alignment	0.030 – 0.050
	Earth, with weeds and poor alignment	0.050 – 0.150
	Stones 75 – 150 mm diameter, straight, good condition	0.030 – 0.040
	Stones 75 – 150 mm diameter, poor alignment	0.040 – 0.080
	Stones > 150 mm, boulders, steep slope, good condition	0.040 – 0.070
Floodplain	Short grass	0.025 – 0.035
	Long grass	0.030 – 0.050
	Medium to dense brush, in winter	0.045 – 0.110
Pipes	Cast iron	0.010 – 0.014
	Concrete	0.011 – 0.015

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