Rectangular Channel

Design a rectangular concrete channel to carry 100 cfs if y/b is 0.5 and it is desired to keep the Froude number less than or equal to 0.4. Assume uniform flow.

The Froude number is defined as

for rectangular or very wide channels, where y is the water depth.

Fr < 1.0: subcritical flow
Fr = 1.0: critical flow
Fr > 1.0: supercritical flow

Hence, Fr ≤ 0.4 implies that the flow is subcritical.

The velocity is given by

The Froude number is then given by

Solve for y when Fr = 0.4:

The width b is then given by

     b = 2y = 2(3.445 ft) = 6.890 ft

In practice, round b to 7.0 ft and y to 3.5 ft. The Froude number is

which meets the design requirement.

Now, the slope needed to carry this flow can be found from Manning's equation

where

    n = 0.013 for concrete
    Q = 100 cfs
    A = (3.5)(7) = 24.5 ft²
     R = A/P = 24.5/[7 + 2(3.5)] = 1.75 ft

Solve for S_o

Use Manning equation:

and Q = V_oA

Use n = 0.012 for concrete

For full pipe: A = π d² / 4
For half-pipe: A = π d² / 8

R_h = A/P where P is the wetted perimeter
     

Given the design requirement that the pipe be half full, there will be one set of values (a diameter and a slope) for any velocity.

At the low end, V_o = 2 ft/s
   Q = VA
   10 ft³/s = (2 ft/s)(π d²/8)
   d = 3.57 ft

Solve for the corresponding slope using Manning's equation, which gives

     

     tan^-1(0.000304) = 0.0174°

At the high end, V_o = 10 fps
   Q = VA
   10 ft³/s = (10 ft/s)(π d²/8)
   d = 1.60 ft

Solve for the corresponding slope:

     

     tan^-1(0.0222) = 1.27^o