Irrigation, Drainage & Pumping Systems

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 $R = d/2$.

Factors affecting surface tension:
Temperature: Surface tension of a liquid is directly and significantly dependent on temperature. As temperature increases, the kinetic energy of molecules increases, expanding intermolecular spacing and reducing the cohesive attractive forces between liquid molecules. Consequently, surface tension decreases monotonically with increasing temperature, reaching zero at the critical point.

Hydraulic radius definition:

where \(R\) is hydraulic radius, \(A\) is cross-sectional flow area, and \(P\) is wetted perimeter.
For a given constant cross-sectional area (\(A = \text{constant}\)): \(R\) is inversely proportional to the wetted perimeter \(P\) (\(R \propto 1/P\)).