It has been observed for critical depth (yc) in a rectangular channel carrying a constant discharge that 1. Specific energy is maximum 2. Froude number is 1 3. Specific energy = 1.33 yc 4. Specific force is minimum Which of the observations are correct?
- A1, 2 and 3
- B2, 3 and 4
- C1 and 4
- D2 and 4Correct
Solution
Concept
Characteristics of critical flow in a rectangular channel
Formula
yc = (q²/g)1/3, Emin = 1.5 yc, Fr = 1
Step-by-step solution
1. At critical depth, specific energy is MINIMUM for a given discharge (statement 1 is false). 2. Froude number = 1 (statement 2 true). 3. E = yc + yc/2 = 1.5 yc (statement 3 false; 1.33 is not correct). 4. Specific force is minimum at critical depth for a given discharge (statement 4 true).
Explanation
At critical depth the specific energy is minimum (for a given discharge) and the specific force is minimum. The minimum specific energy is 1.5 times the critical depth for a rectangular channel, not 1.33.
Shortcut
Critical flow: E minimum, M minimum, Fr = 1, E = 1.5 yc, V²/2g = yc/2.
Common mistake
Taking 1.33 yc (that is 4/3 yc, which applies to a different channel shape or to the head over a weir).
Correct answer: D) 2 and 4