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For a maximum discharge in a circular channel section, the ratio of the depth of flow to that of diameter of the channel is
  • a)
    0.30
  • b)
    0.5
  • c)
    0.95
  • d)
    0.81
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
For a maximum discharge in a circular channel section, the ratio of t...
So for Qmax = d / D = 0.95
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For a maximum discharge in a circular channel section, the ratio of t...
Ratio of Depth of Flow to Diameter for Maximum Discharge in Circular Channel

For a circular channel section, the ratio of depth of flow to diameter of the channel is important in determining the maximum discharge that can occur. The correct answer to this question is option C, which is 0.95. Let’s understand why.

Relationship between Depth of Flow and Diameter

The maximum discharge in a circular channel section is dependent on the depth of flow and the diameter of the channel. The two are related by the following equation:

Q = (π/4)D^2 √(2gds)

where Q is the discharge, D is the diameter of the channel, g is the acceleration due to gravity, d is the depth of flow, and s is the slope of the channel.

Deriving the Ratio of Depth of Flow to Diameter

To determine the ratio of depth of flow to diameter for maximum discharge, we need to differentiate the above equation with respect to d, and set it equal to zero. This gives us:

d/D = 0.95

Therefore, the ratio of depth of flow to diameter for maximum discharge in a circular channel section is 0.95. This means that the depth of flow should be about 95% of the diameter of the channel for maximum discharge to occur.

Conclusion

In summary, the ratio of depth of flow to diameter for maximum discharge in a circular channel section is 0.95. This is an important concept in hydraulic engineering and should be kept in mind when designing and analyzing circular channels.
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For a maximum discharge in a circular channel section, the ratio of the depth of flow to that of diameter of the channel isa) 0.30b) 0.5c) 0.95d) 0.81Correct answer is option 'C'. Can you explain this answer?
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