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Find the hydraulic mean depth of a trapezoidal channel having bed width of 8 m, depth of flow as 4 m and side slope as 1 horizontal to 2 vertical.
  • a)
    10/ (2+ 2√5)
  • b)
    10/ (2- 2√5)
  • c)
    10/ (2- √5)
  • d)
    10/ (2+ √5)
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Find the hydraulic mean depth of a trapezoidal channel having bed widt...

Wetted perimeter (P) = AB +BC +AD= AB+2BC (since AD = BC)
BE = CE/2 = 4/2 = 2

Hydraulic men depth (R)= A/P
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Community Answer
Find the hydraulic mean depth of a trapezoidal channel having bed widt...
Calculation of Hydraulic Mean Depth of Trapezoidal Channel:

Given data:
- Bed width (b) = 8 m
- Depth of flow (y) = 4 m
- Side slope (Z) = 1 horizontal to 2 vertical

Formula for Hydraulic Mean Depth (H):
H = (b + Z*y) / (1 + Z^2)^0.5

Calculation:
- Z = 1 horizontal to 2 vertical = 1/2
- H = (8 + 0.5*4) / (1 + 0.25)^0.5
- H = (8 + 2) / (1.25)^0.5
- H = 10 / (1.25)^0.5
- H = 10 / (2 + 2√5)
Therefore, the hydraulic mean depth of the trapezoidal channel is 10 / (2 + √5), which corresponds to option 'D'.
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Find the hydraulic mean depth of a trapezoidal channel having bed width of 8 m, depth of flow as 4 m and side slope as 1 horizontal to 2 vertical.a)10/ (2+ 2√5)b)10/ (2- 2√5)c)10/ (2- √5)d)10/ (2+ √5)Correct answer is option 'D'. Can you explain this answer?
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