Find 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 wher 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=Aâ??V=Aâ??CRâ??S0.......(I)'>Q=Aâ??V=Aâ??CRâ??S0â??â??â??â??â??â??.......(I)Q=Aâ??V=Aâ??CRâ??S0â??â??â??â??â??â??.......(I)Q=Aâ??V=Aâ??CRâ??S0â??â??â??â??â??â??.......(I)
Where, Flow area, A=bâ??y=7.5â??2.25=16.875m2'>A=bâ??y=7.5â??2.25=16.875m2A=bâ??y=7.5â??2.25=16.875m2A=bâ??y=7.5â??2.25=16.875m2
Wetted perimeter, P=b+2y=7.5+2â??2.25=12.0'>P=b+2y=7.5+2â??2.25=12.0P=b+2y=7.5+2â??2.25=12.0P=b+2y=7.5+2â??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=Aâ??V=Aâ??CRâ??S0=16.875'>Q=Aâ??V=Aâ??CRâ??S0â??â??â??â??â??â??=16.875Q=Aâ??V=Aâ??CRâ??S0â??â??â??â??â??â??=16.875Q=Aâ??V=Aâ??CRâ??S0â??â??â??â??â??â??=1....

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=Aâ??V=Aâ??CRâ??S0.......(I)'>Q=Aâ??V=Aâ??CRâ??S0â??â??â??â??â??â??.......(I)Q=Aâ??V=Aâ??CRâ??S0â??â??â??â??â??â??.......(I)Q=Aâ??V=Aâ??CRâ??S0â??â??â??â??â??â??.......(I)
Where, Flow area, A=bâ??y=7.5â??2.25=16.875m2'>A=bâ??y=7.5â??2.25=16.875m2A=bâ??y=7.5â??2.25=16.875m2A=bâ??y=7.5â??2.25=16.875m2
Wetted perimeter, P=b+2y=7.5+2â??2.25=12.0'>P=b+2y=7.5+2â??2.25=12.0P=b+2y=7.5+2â??2.25=12.0P=b+2y=7.5+2â??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=Aâ??V=Aâ??CRâ??S0=16.875'>Q=Aâ??V=Aâ??CRâ??S0â??â??â??â??â??â??=16.875Q=Aâ??V=Aâ??CRâ??S0â??â??â??â??â??â??=16.875Q=Aâ??V=Aâ??CRâ??S0â??â??â??â??â??â??=16.875â??'>â??â??â??551.406â??11000'>551.406â??11000â??â??â??â??â??â??â??â??â??â??â??551.406â??11000â??â??â??â??â??â??â??â??â??â??â??551.406â??11000â??â??â??â??â??â??â??â??â??â??â??
or, Q=34.76m3sec'>Q=34.76m3secQ=34.76m3secQ=34.76m3sec
Also, Conveyance,K=Aâ??cR=16.875'>K=Aâ??cRâ??â??â??=16.875K=Aâ??cRâ??â??â??=16.875K=Aâ??cRâ??â??â??=16.875â??'>â??â??â??55'>555555â??'>â??â??â??1.406'>1.406â??â??â??â??â??1.406â??â??â??â??â??1.406â??â??â??â??â??=1100.5'>=1100.5=1100.5=1100.5
Again, Froude's number, Fr=Vgâ??y=Câ??Râ??S09.81â??2.25=0.438'>Fr=Vgâ??yâ??â??â??â??â??=Câ??Râ??S0â??â??â??â??â??â??9.81â??2.25â??â??â??â??â??â??â??â??â??=0.438Fr=Vgâ??yâ??â??â??â??=Câ??Râ??S0â??â??â??â??â??â??9.81â??2.25â??â??â??â??â??â??â??â??â??=0.438Fr=Vgâ??yâ??â??â??â??â??=Câ??Râ??S0â??â??â??â??â??â??9.81â??2.25â??â??â??â??â??â??â??â??â??=0.438
Since froudes number,Fr'>FrFrFr is less than 1'>111, the flow in the channel is of tranquil in nature.