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A hydraulically efficient trapezoidal section of open channel flow carries water at the optimal depth of 0.6 m. Chezy coefficient is 75 and bed slope is 1 in 250. What is the discharge through the channel?
- a)1.44 m3/s
- b)1.62 m3/s
- c)1.92 m3/s
- d)2.24 m3/s
Correct answer is option 'B'. Can you explain this answer?
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To calculate the discharge through the channel, we can use the Manning's equation, which relates the cross-sectional properties of the channel to the flow rate. The equation is as follows:
Q = (1/n) * A * R^(2/3) * S^(1/2)
where:
Q is the discharge (m^3/s)
n is the Manning's roughness coefficient
A is the cross-sectional area of flow (m^2)
R is the hydraulic radius (m)
S is the bed slope (m/m)
Given:
n = 75
depth (y) = 0.6 m
bed slope (S) = 1/250
1. Determine the cross-sectional properties:
The channel has a trapezoidal section, which can be divided into a rectangle and a triangle. The area (A) of the flow can be calculated as the sum of these two areas:
A = A_rectangle + A_triangle
A_rectangle = base_rectangle * y
A_triangle = (1/2) * base_triangle * y
2. Determine the hydraulic radius:
The hydraulic radius (R) can be calculated as the ratio of the flow area to the wetted perimeter (P):
R = A / P
The wetted perimeter can be calculated as the sum of the rectangle and triangle perimeters:
P = P_rectangle + P_triangle
P_rectangle = 2 * base_rectangle + 2 * y
P_triangle = base_triangle + 2 * sqrt(base_triangle^2 + y^2)
3. Calculate the discharge:
Substitute the values into the Manning's equation:
Q = (1/n) * A * R^(2/3) * S^(1/2)
Simplify the equation using the values calculated above and solve for Q.
The correct answer is option B: 1.62 m^3/s.
Q = (1/n) * A * R^(2/3) * S^(1/2)
where:
Q is the discharge (m^3/s)
n is the Manning's roughness coefficient
A is the cross-sectional area of flow (m^2)
R is the hydraulic radius (m)
S is the bed slope (m/m)
Given:
n = 75
depth (y) = 0.6 m
bed slope (S) = 1/250
1. Determine the cross-sectional properties:
The channel has a trapezoidal section, which can be divided into a rectangle and a triangle. The area (A) of the flow can be calculated as the sum of these two areas:
A = A_rectangle + A_triangle
A_rectangle = base_rectangle * y
A_triangle = (1/2) * base_triangle * y
2. Determine the hydraulic radius:
The hydraulic radius (R) can be calculated as the ratio of the flow area to the wetted perimeter (P):
R = A / P
The wetted perimeter can be calculated as the sum of the rectangle and triangle perimeters:
P = P_rectangle + P_triangle
P_rectangle = 2 * base_rectangle + 2 * y
P_triangle = base_triangle + 2 * sqrt(base_triangle^2 + y^2)
3. Calculate the discharge:
Substitute the values into the Manning's equation:
Q = (1/n) * A * R^(2/3) * S^(1/2)
Simplify the equation using the values calculated above and solve for Q.
The correct answer is option B: 1.62 m^3/s.
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A hydraulically efficient trapezoidal section of open channel flow carries water at the optimal depth of 0.6 m. Chezy coefficient is 75 and bed slope is 1 in 250. What is the discharge through the channel?a)1.44 m3/sb)1.62 m3/sc)1.92 m3/sd)2.24 m3/sCorrect answer is option 'B'. Can you explain this answer?
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A hydraulically efficient trapezoidal section of open channel flow carries water at the optimal depth of 0.6 m. Chezy coefficient is 75 and bed slope is 1 in 250. What is the discharge through the channel?a)1.44 m3/sb)1.62 m3/sc)1.92 m3/sd)2.24 m3/sCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A hydraulically efficient trapezoidal section of open channel flow carries water at the optimal depth of 0.6 m. Chezy coefficient is 75 and bed slope is 1 in 250. What is the discharge through the channel?a)1.44 m3/sb)1.62 m3/sc)1.92 m3/sd)2.24 m3/sCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hydraulically efficient trapezoidal section of open channel flow carries water at the optimal depth of 0.6 m. Chezy coefficient is 75 and bed slope is 1 in 250. What is the discharge through the channel?a)1.44 m3/sb)1.62 m3/sc)1.92 m3/sd)2.24 m3/sCorrect answer is option 'B'. Can you explain this answer?.
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