Question

Determine the cross-section of the greatest hydraulic efficiency for a trapezoidal channel with side slope of 1 vertical to 2 horizontal if the design discharge is 10 m3/s. The channel slope is 0.001 and Manning’s roughness factor is 0.020.

Answer 1

Find the uniform flow depth in the trapezoidal channel using the manning’s formula.

Denote the Discharge in the channel as, Area of trapezoidal channel as A, Hydraulic radius as, Manning’s roughness coefficient as n, and Bottom slope as .

Substitute for and for .

…… (1)

Denote the Bottom width of trapezoidal channel as , depth of flow as y, and Side slope as 1 vertical to horizontal.

Design the trapezoidal channel for maximum discharge

Select the channel with minimum wetted perimeter for a given discharge.

Express the hydraulic radius formula.

Express the area of flow in the channel formula.

Find the Bottom width of the trapezoidal.

…… (2)

Find the uniform flow depth.

Substitute for A, 0.020 for n, 0.001 for and for R in Equation (1).

Thus, the flow depth of the trapezoidal channel is .

Find the bottom width of the trapezoidal channel.

Substitute 1.9328 m for y in Equation (2).

Thus, the bottom width of the trapezoidal channel is .

Thus, the cross-section with greatest hydraulic efficiency is .