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A rectangular channel of width 2√5 m carries a discharge of 40 m3/s. The critical depth of water flowing through the channel is (Take g = 10 m/s2)
  • a)
    2.00 m
  • b)
    3.45 m
  • c)
    4.20 m
  • d)
    8.00 m
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A rectangular channel of width 2√5 m carries a discharge of 40 m...
For a rectangular channel, the critical depth is given by

where q = discharge per unit width and g = acceleration due to gravity.

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Most Upvoted Answer
A rectangular channel of width 2√5 m carries a discharge of 40 m...
Given data:
- Width of rectangular channel (b) = 2√5 m
- Discharge (Q) = 40 m3/s
- Acceleration due to gravity (g) = 10 m/s2

Calculating Critical Depth (yc):
- Critical depth (yc) in a rectangular channel is given by the formula: yc = (Q2 / (g * b))^(1/3)
- Substituting the given values, yc = (40^2 / (10 * 2√5))^(1/3) = (1600 / (20√5))^(1/3)
- yc = (80 / √5)^(1/3) = (80 / 2.236)^(1/3) ≈ 35.78^(1/3) ≈ 2.00 m
Therefore, the critical depth of water flowing through the channel is approximately 2.00 m. Hence, option 'A' is the correct answer.
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A rectangular channel of width 2√5 m carries a discharge of 40 m3/s. The critical depth of water flowing through the channel is (Take g = 10 m/s2)a)2.00 mb)3.45 mc)4.20 md)8.00 mCorrect answer is option 'A'. Can you explain this answer?
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