Which of the following statement(s) is/are correct? (A) In... | Agrigyan

Bernoulli's Theorem in fluid mechanics:
For the steady, incompressible, frictionless (inviscid), and irrotational flow of a fluid along a streamline, total mechanical energy per unit weight is conserved:

where:

• \(\frac{p}{\rho g}\) = Pressure head
• \(\frac{v^2}{2g}\) = Velocity head - \(z\) = Elevation (potential) head

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.