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The depth and widths of a rectangular channel are 2m and 5m respectively, calculate the discharge of water through the channel if the bed slope is 1 in 500 and Chezy’s constant being 60.
  • a)
    28.27 m3/s
  • b)
    38.27 m3/s
  • c)
    48.27 m3/s
  • d)
    58.27 m3/s
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The depth and widths of a rectangular channel are 2m and 5m respective...
The discharge of water through a channel can be calculated using the Manning's equation:

Q = (1.49/n) * A * R^(2/3) * S^(1/2)

Where:
Q = Discharge (m^3/s)
n = Manning's roughness coefficient (dimensionless)
A = Cross-sectional area of flow (m^2)
R = Hydraulic radius (m)
S = Bed slope (dimensionless)

Given:
Depth (h) = 2m
Width (b) = 5m
Bed slope (S) = 1/500
Chezy coefficient (C) = 50 (assumed)

First, we need to calculate the hydraulic radius (R):

R = A/P
A = h * b = 2m * 5m = 10m^2
P = 2h + 2b = 2(2m) + 2(5m) = 14m

R = 10m^2 / 14m = 0.714 m

Now, we can calculate the discharge (Q) using the Manning's equation:

Q = (1.49/n) * A * R^(2/3) * S^(1/2)
Q = (1.49/50) * 10m^2 * (0.714m)^(2/3) * (1/500)^(1/2)
Q = 0.0298 m^3/s

Therefore, the discharge of water through the channel is approximately 0.0298 cubic meters per second.
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The depth and widths of a rectangular channel are 2m and 5m respective...
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The depth and widths of a rectangular channel are 2m and 5m respectively, calculate the discharge of water through the channel if the bed slope is 1 in 500 and Chezy’s constant being 60.a)28.27 m3/sb)38.27 m3/sc)48.27 m3/sd)58.27 m3/sCorrect answer is option 'A'. Can you explain this answer?
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