A rectangular channel is twice as broad as deep If it is to discharge 50m /s; determine the section Take slope of bed as 1 in 1000 and Chezy’s constant as 50

Given data :

Discharge, Q = 50 m³/s

Slope, i = 1 in 1000 = 1 / 1000

Chezy’s constant, C = 50

Area of rectangle, A = b × d

Width, b = 2 × d ( b = 2d , is also the condition of most economical rectangular channel )

therefore, area of rectangle, A = 2 × d × d = 2d²

and parameter of rectangle , P = d + b + d = b + 2d = 2d + 2d = 4d

Also we know that,

Discharge, Q = A × C × √( m × i )

50 = A × 50 × √ [ ( A / P ) × 1/1000 ]

50/50 = A × √ ( A / P ) × 0.031

1/ 0.031 = ( 2 × d² ) × √ 2d² / 4d

32.25 = 2d² × 0.707 √d

32.25 = 1.414 × d²√d

now, d = 3.49 m

b = 2 × d = 6.98 m

Hence, the section of the rectangular channel are b = 6.98 m and d = 3.49 m