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Design irrigation channel to carry 50 cumecs of discharge. The channel is to be laid at a slope of 1 in 4000.Take Critical Velocity ratio for the soil as 1.1 Use Kutters Rugosity coefficient as 0.023
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Given,

Q=50cumecs

S=14000

m=1.1

n=0.023


As we know the equation for critical velocity is,

V0=0.55 my0.64


Assume a depth equal to 2m,

V=0.551.120.64=0.6051.558=0.942m/sec

A=QV0=500.942=53.1m2


Assume side slopes as 12:1[12H=1V]

Now,

A=y[b+y12]

Therefore,53.1=2(b+1)

or, b=25.55m

And,

P=b+21+14y

P=b+253y=25.55+52=30.03

R=AP=53.130.03=1.77m


But from Kutters formula,

V=y[1n+(23+0.00155S)1+(23+0.00155SnR)RS]


V=y[10.023+(23+0.001551/4000)1+(23+0.001551/40000.0231.77)1.7714000]


V=y[43.5+(23+6.2)1+(29.20.023)1.331.33163.3]


72.71+0.5051.33163.3=1.016 m/sec > 0.942


In order to increase the critical velocity (V0), we have to increase the depth


Use 3m depth:

V=0.605(3)0.64=0.6052.02=1.22m/sec

A=501.22=40.8m2

40.8=3(b+123)

or, b=12.1m

P=12.1+2523=12.1+6.72=18.82

R=AP=40.818.82=2.17m

After calculating the V weget, V=1.16 m/sec < 1.22 or V<V0


Use 2.5m depth:

V=0.6052.050.64=1.087m/sec

A=501.087=46m2

46=2.5(b+122.5)

or, b=17.15m

P=17.15+52.5=17.15+5.58=22.73

R=422.73=2.02m

After calculating the V weget, V=1.1 m/sec > 1.087 or V>V0

Actual velocity V tallies with V0.


Use 2.7m depth:

V=0.6051.189=1.147m/sec

A=501.147=43.5m2

43.5=2.8(b+122.8)

or, b=14.14m

P=14.14+52.8=14.14+6.26=20.40

R=43.520.4=2.13m

After calculating the V weget, V=1.148 m/sec = 1.147 or V=V0

Actual velocity V tallies with V0.

Hence, use the depth equal to 2.7m and base width 14.14m with slopes 12:1 of trapezoidal section.

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