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The discharge through a rectangular channel is 16.62 m3/s and the wetted area is equal to 12m2. The width of the channel is 6m and the bed slope is 1 in 1000, calculate the value of the Chezy’s constant.
- a)35
- b)40
- c)45
- d)50
Correct answer is option 'B'. Can you explain this answer?
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The discharge through a rectangular channel is 16.62 m3/s and the wett...
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The Chezy formula is given by:
Q = C * A * sqrt(S)
Where:
Q = discharge (m^3/s)
C = Chezy coefficient
A = cross-sectional area of flow (m^2)
S = bed slope
Given:
Q = 16.62 m^3/s
A = 12 m^2
S = 1/1000
Width of the channel = 6m
First, calculate the hydraulic radius (R) using the formula:
R = A/Wetted perimeter = A/(2*depth + width)
Since the depth is not given, let's calculate it using the wetted area and width:
Depth = A/width = 12m^2/6m = 2m
Now, calculate the wetted perimeter:
Wetted perimeter = 2*depth + width = 2*2m + 6m = 10m
Now, calculate the hydraulic radius:
R = A/Wetted perimeter = 12m^2/10m = 1.2m
Now, substitute the known values into the Chezy formula and solve for C:
16.62 = C * 12 * sqrt(1/1000)
16.62 = 12C * sqrt(0.001)
16.62 = 0.012C
C = 16.62 / 0.012 = 1385
Therefore, the value of the Chezy coefficient is 1385.
Q = C * A * sqrt(S)
Where:
Q = discharge (m^3/s)
C = Chezy coefficient
A = cross-sectional area of flow (m^2)
S = bed slope
Given:
Q = 16.62 m^3/s
A = 12 m^2
S = 1/1000
Width of the channel = 6m
First, calculate the hydraulic radius (R) using the formula:
R = A/Wetted perimeter = A/(2*depth + width)
Since the depth is not given, let's calculate it using the wetted area and width:
Depth = A/width = 12m^2/6m = 2m
Now, calculate the wetted perimeter:
Wetted perimeter = 2*depth + width = 2*2m + 6m = 10m
Now, calculate the hydraulic radius:
R = A/Wetted perimeter = 12m^2/10m = 1.2m
Now, substitute the known values into the Chezy formula and solve for C:
16.62 = C * 12 * sqrt(1/1000)
16.62 = 12C * sqrt(0.001)
16.62 = 0.012C
C = 16.62 / 0.012 = 1385
Therefore, the value of the Chezy coefficient is 1385.
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The discharge through a rectangular channel is 16.62 m3/s and the wetted area is equal to 12m2. The width of the channel is 6m and the bed slope is 1 in 1000, calculate the value of the Chezy’s constant.a)35b)40c)45d)50Correct answer is option 'B'. Can you explain this answer?
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