For a given specific energy E, the critical depth y_c for a rectangular channel is given by

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BPSC AE Paper VI Civil 19 Dec 2024 Official Paper

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Answer 1

Explanation:

For a given specific energy E, the critical depth yc for a rectangular channel is given by yc = 2/3E.
This relation comes from the condition of minimum specific energy for a given discharge, which occurs at the critical depth. It is derived from the energy equation in open channel flow theory.

Additional Information

Specific energy (E) is the total energy relative to the channel bottom, measured as the sum of the flow depth (y) and the velocity head (v²/2g).
For a given discharge, the specific energy varies with flow depth, and the flow can be subcritical (deep and slow), critical, or supercritical (shallow and fast).
The critical depth $y_c$ is the depth at which the specific energy is minimum for a given discharge.
At critical depth, the flow velocity equals the wave velocity (celerity), and the Froude number equals 1.