सिंचाई, जल निकास एवं पंपिंग प्रणाली

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.

Open channel hydraulics and design:
(A) is correct: In irrigation channel engineering, channels are designed using Manning's uniform flow equation for maximum design discharge, assuming normal depth and steady uniform flow conditions.
(B) is correct: Water flow in canals controlled by head regulators is typically maintained at a constant discharge rate over prolonged operating periods, making it steady flow (\(\partial Q / \partial t = 0\)).
(D) is correct: When cross-sectional dimensions, bed width, or depth vary along the reach of a channel, velocity and depth change with distance, which is the definition of non-uniform (varied) flow (\(\partial v / \partial s \neq 0\)).
In the official answer key, Option 4: (A), (B) and (D) only is the designated correct answer.