Find the rate of flow and conveyance for a rectangular channel `7.5 m` wide for uniform flow at a depth of `2.25 m`. The channel is having bed slope as 1 in 1000. Take Chezy���?�s constant `C = 55`. Also state whether the flow is tranquil or rapid.

Solution:
 Width of the rectangular channel, b=7.5m'>b=7.5mb=7.5m
 Depth of flow, y=2.25m'>y=2.25my=2.25my=2.25m
Bed slope, S0'>S0S0S0 =11000'>110001100011000
Chezy's constant, C=55'>C=55C=55C=55
Now, we have,
Rate of flow, Q=A�??V=A�??CR�??S0.......(I)'>Q=A�??V=A�??CR�??S0�??�??�??�??�??�??.......(I)Q=A�??V=A�??CR�??S0�??�??�??�??�??�??.......(I)Q=A�??V=A�??CR�??S0�??�??�??�??�??�??.......(I)
Where, Flow area, A=b�??y=7.5�??2.25=16.875m2'>A=b�??y=7.5�??2.25=16.875m2A=b�??y=7.5�??2.25=16.875m2A=b�??y=7.5�??2.25=16.875m2
Wetted perimeter, P=b+2y=7.5+2�??2.25=12.0'>P=b+2y=7.5+2�??2.25=12.0P=b+2y=7.5+2�??2.25=12.0P=b+2y=7.5+2�??2.25=12.0
Also,
hydraulic radius, R=AP=16.87512.0=1.406'>R=AP=16.87512.0=1.406R=AP=16.87512.0=1.406R=AP=16.87512.0=1.406
Thus from equation (I)'>(I)(I)(I),
Q=A�??V=A�??CR�??S0=16.875'>Q=A�??V=A�??CR�??S0�??�??�??�??�??�??=16.875Q=A�??V=A�??CR�??S0�??�??�??�??�??�??=16.875Q=A�??V=A�??CR�??S0�??�??�??�??�??�??=16.875�??....

Solution:
 Width of the rectangular channel, b=7.5m'>b=7.5m$b=7.5m$
 Depth of flow, y=2.25m'>y=2.25my=2.25my=2.25m
Bed slope, S0'>S0S0S0 =11000'>110001100011000
Chezy's constant, C=55'>C=55C=55C=55
Now, we have,
Rate of flow, Q=A�??V=A�??CR�??S0.......(I)'>Q=A�??V=A�??CR�??S0�??�??�??�??�??�??.......(I)Q=A�??V=A�??CR�??S0�??�??�??�??�??�??.......(I)Q=A�??V=A�??CR�??S0�??�??�??�??�??�??.......(I)
Where, Flow area, A=b�??y=7.5�??2.25=16.875m2'>A=b�??y=7.5�??2.25=16.875m2A=b�??y=7.5�??2.25=16.875m2A=b�??y=7.5�??2.25=16.875m2
Wetted perimeter, P=b+2y=7.5+2�??2.25=12.0'>P=b+2y=7.5+2�??2.25=12.0P=b+2y=7.5+2�??2.25=12.0P=b+2y=7.5+2�??2.25=12.0
Also,
hydraulic radius, R=AP=16.87512.0=1.406'>R=AP=16.87512.0=1.406R=AP=16.87512.0=1.406R=AP=16.87512.0=1.406
Thus from equation (I)'>(I)(I)(I),
Q=A�??V=A�??CR�??S0=16.875'>Q=A�??V=A�??CR�??S0�??�??�??�??�??�??=16.875Q=A�??V=A�??CR�??S0�??�??�??�??�??�??=16.875Q=A�??V=A�??CR�??S0�??�??�??�??�??�??=16.875�??'>�??�??�??551.406�??11000'>551.406�??11000�??�??�??�??�??�??�??�??�??�??�??551.406�??11000�??�??�??�??�??�??�??�??�??�??�??551.406�??11000�??�??�??�??�??�??�??�??�??�??�??
or, Q=34.76m3sec'>Q=34.76m3secQ=34.76m3secQ=34.76m3sec
Also, Conveyance,K=A�??cR=16.875'>K=A�??cR�??�??�??=16.875K=A�??cR�??�??�??=16.875K=A�??cR�??�??�??=16.875�??'>�??�??�??55'>555555�??'>�??�??�??1.406'>1.406�??�??�??�??�??1.406�??�??�??�??�??1.406�??�??�??�??�??=1100.5'>=1100.5=1100.5=1100.5
Again, Froude's number, Fr=Vg�??y=C�??R�??S09.81�??2.25=0.438'>Fr=Vg�??y�??�??�??�??�??=C�??R�??S0�??�??�??�??�??�??9.81�??2.25�??�??�??�??�??�??�??�??�??=0.438Fr=Vg�??y�??�??�??�??=C�??R�??S0�??�??�??�??�??�??9.81�??2.25�??�??�??�??�??�??�??�??�??=0.438Fr=Vg�??y�??�??�??�??�??=C�??R�??S0�??�??�??�??�??�??9.81�??2.25�??�??�??�??�??�??�??�??�??=0.438
Since froudes number,Fr'>FrFrFr is less than 1'>111, the flow in the channel is of tranquil in nature.