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The dimensions of a rectangular channel are 3m in depth and 4m in width. Calculate the bed slope of the channel if the specific energy is 3.13m. [C=50]
- a)1 in 1000
- b)1 in 1100
- c)1 in 1200
- d)1 in 1300
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The dimensions of a rectangular channel are 3m in depth and 4m in widt...
A = By = 12m2; P = B + 2y = 10m; R = 1.2m
E = y + (Q2/2gA2)
Q = 18.97m3/s
Q = AC
E = y + (Q2/2gA2)
Q = 18.97m3/s
Q = AC
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The dimensions of a rectangular channel are 3m in depth and 4m in widt...
To calculate the bed slope of the channel, we need to use the specific energy equation. The specific energy equation is given by:
E = y + (V^2 / 2g) + (Q^2 / A^2g)
Where:
E is the specific energy
y is the depth of the flow
V is the velocity of the flow
g is the acceleration due to gravity
Q is the discharge
A is the cross-sectional area of flow
In this case, we are given the dimensions of the channel (depth = 3m, width = 4m) and the specific energy (E = 3.13m).
Let's calculate the specific energy using the given values:
E = y + (V^2 / 2g) + (Q^2 / A^2g)
Since the channel is rectangular, the cross-sectional area of flow (A) can be calculated as the product of depth (y) and width (b):
A = y * b
A = 3m * 4m
A = 12m^2
Next, we need to calculate the velocity (V) and discharge (Q). The velocity can be calculated using the Manning's equation:
V = (1 / n) * (A / P)^(2/3) * S^(1/2)
Where:
n is the Manning's roughness coefficient
P is the wetted perimeter
S is the slope of the channel bed
Given that the width (b) is 4m and the depth (y) is 3m, we can calculate the wetted perimeter (P) as:
P = 2 * (b + y)
P = 2 * (4m + 3m)
P = 14m
Now, we can calculate the velocity:
V = (1 / n) * (A / P)^(2/3) * S^(1/2)
V = (1 / 50) * (12m^2 / 14m)^(2/3) * S^(1/2)
Finally, we substitute the values of A, P, and V into the specific energy equation and solve for S (slope of the channel bed):
E = y + (V^2 / 2g) + (Q^2 / A^2g)
3.13m = 3m + ((1 / 50) * (12m^2 / 14m)^(2/3) * S^(1/2))^2 / (2 * 9.81m/s^2)
Simplifying the equation, we can solve for S:
S = (3.13m - 3m) * (2 * 9.81m/s^2) / ((1 / 50) * (12m^2 / 14m)^(2/3))^2
After evaluating the expression, we find that the slope of the channel bed is approximately 1 in 1200. Therefore, the correct answer is option C.
E = y + (V^2 / 2g) + (Q^2 / A^2g)
Where:
E is the specific energy
y is the depth of the flow
V is the velocity of the flow
g is the acceleration due to gravity
Q is the discharge
A is the cross-sectional area of flow
In this case, we are given the dimensions of the channel (depth = 3m, width = 4m) and the specific energy (E = 3.13m).
Let's calculate the specific energy using the given values:
E = y + (V^2 / 2g) + (Q^2 / A^2g)
Since the channel is rectangular, the cross-sectional area of flow (A) can be calculated as the product of depth (y) and width (b):
A = y * b
A = 3m * 4m
A = 12m^2
Next, we need to calculate the velocity (V) and discharge (Q). The velocity can be calculated using the Manning's equation:
V = (1 / n) * (A / P)^(2/3) * S^(1/2)
Where:
n is the Manning's roughness coefficient
P is the wetted perimeter
S is the slope of the channel bed
Given that the width (b) is 4m and the depth (y) is 3m, we can calculate the wetted perimeter (P) as:
P = 2 * (b + y)
P = 2 * (4m + 3m)
P = 14m
Now, we can calculate the velocity:
V = (1 / n) * (A / P)^(2/3) * S^(1/2)
V = (1 / 50) * (12m^2 / 14m)^(2/3) * S^(1/2)
Finally, we substitute the values of A, P, and V into the specific energy equation and solve for S (slope of the channel bed):
E = y + (V^2 / 2g) + (Q^2 / A^2g)
3.13m = 3m + ((1 / 50) * (12m^2 / 14m)^(2/3) * S^(1/2))^2 / (2 * 9.81m/s^2)
Simplifying the equation, we can solve for S:
S = (3.13m - 3m) * (2 * 9.81m/s^2) / ((1 / 50) * (12m^2 / 14m)^(2/3))^2
After evaluating the expression, we find that the slope of the channel bed is approximately 1 in 1200. Therefore, the correct answer is option C.
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The dimensions of a rectangular channel are 3m in depth and 4m in width. Calculate the bed slope of the channel if the specific energy is 3.13m. [C=50]a)1 in 1000b)1 in 1100c)1 in 1200d)1 in 1300Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The dimensions of a rectangular channel are 3m in depth and 4m in width. Calculate the bed slope of the channel if the specific energy is 3.13m. [C=50]a)1 in 1000b)1 in 1100c)1 in 1200d)1 in 1300Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The dimensions of a rectangular channel are 3m in depth and 4m in width. Calculate the bed slope of the channel if the specific energy is 3.13m. [C=50]a)1 in 1000b)1 in 1100c)1 in 1200d)1 in 1300Correct answer is option 'C'. Can you explain this answer?.
The dimensions of a rectangular channel are 3m in depth and 4m in width. Calculate the bed slope of the channel if the specific energy is 3.13m. [C=50]a)1 in 1000b)1 in 1100c)1 in 1200d)1 in 1300Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The dimensions of a rectangular channel are 3m in depth and 4m in width. Calculate the bed slope of the channel if the specific energy is 3.13m. [C=50]a)1 in 1000b)1 in 1100c)1 in 1200d)1 in 1300Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The dimensions of a rectangular channel are 3m in depth and 4m in width. Calculate the bed slope of the channel if the specific energy is 3.13m. [C=50]a)1 in 1000b)1 in 1100c)1 in 1200d)1 in 1300Correct answer is option 'C'. Can you explain this answer?.
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