Most economical / efficient trapezoidal channel section:
For a given cross-sectional area and bed slope, discharge is maximized when the hydraulic radius $R = A/P$ is maximum (wetted perimeter $P$ is minimum).
The geometric condition for the most economical trapezoidal section requires that the side slopes and bottom are tangent to a semi-circle described on the water surface.
When $\theta$ is the angle of inclination of the side slope with the horizontal channel bed, the bed width is related to flow depth by:

Under this condition, the top width $T = 2 \times \text{sloping side}$, and $R = d/2$.