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A channel is designed by Lacey’s theory has a mean velocity of 2 m/sec. The silt factor is taken to be unity. The hydraulic mean radius will be?
  • a)
    5 m
  • b)
    2.5 m
  • c)
    2 m
  • d)
    10 m
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A channel is designed by Lacey’s theory has a mean velocity of 2...
Hydraullic mean radius as per Lacey’s theory is given by:
Where,
V = mean velocity = 2 m/sec
f = silt factor = 1
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Most Upvoted Answer
A channel is designed by Lacey’s theory has a mean velocity of 2...
Calculation of Hydraulic Mean Radius:
To calculate the hydraulic mean radius of a channel, we can use the following formula:
\[
R_h = \frac{A}{P}
\]
where,
- \( R_h \) = Hydraulic mean radius
- \( A \) = Cross-sectional area of the channel
- \( P \) = Wetted perimeter of the channel

Given Data:
- Mean velocity (V) = 2 m/sec
- Silt factor (n) = 1

Calculation of Cross-sectional Area (A):
The cross-sectional area of a channel can be calculated using the formula:
\[
A = V \times n
\]
Substitute the given values,
\[
A = 2 \times 1 = 2 \, m^2
\]

Calculation of Wetted Perimeter (P):
The wetted perimeter of a channel can be calculated using the formula:
\[
P = \frac{A}{R_h}
\]
Substitute the given values,
\[
P = \frac{2}{2} = 1 \, m
\]

Calculation of Hydraulic Mean Radius (R_h):
Now, we can calculate the hydraulic mean radius using the formula:
\[
R_h = \frac{A}{P} = \frac{2}{1} = 2 \, m
\]
Therefore, the hydraulic mean radius of the channel designed by Lacey's theory is 2 meters.
So, the correct answer is option D) 10 m.
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A channel is designed by Lacey’s theory has a mean velocity of 2 m/sec. The silt factor is taken to be unity. The hydraulic mean radius will be?a)5 mb)2.5 mc)2 md)10 mCorrect answer is option 'D'. Can you explain this answer?
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