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Water flows at a steady and uniform depth of 2m in an open channel of rectangular cross section having base width of 4m and laid at a slope of 1 in 10000. If it is desired to obtain critical flow in the channel by providing a hump in the bed. Take Manning’s coefficient = 0.01. Calculate the height of hump (in meters) required for the critical flow
- a)0.5
- b)2.5
- c)2
- d)0.94
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Water flows at a steady and uniform depth of 2m in an open channel of ...
Area A = 4 ×2 = 8, Perimeter P = 4 + 4 = 8
R = (A/P) = 1 m
Discharge per unit width q = 8/4 = 2
We know that the minimum specific energy corresponds to the point of critical depth and is given by 1.5 times the critical depth
Critical depth = (q2/g)(1/3) = 0.74 m
Minimum specific energy is 1.5 × 0.74 = 1.11 m
Specific energy should be same at all points (neglecting hydraulic losses)
So, E = Eminimum + h (this energy is at position of hump)
E = y + v2/(2*g) = 2.05
h = 2.05 – 1.11 = 0.94 m
Most Upvoted Answer
Water flows at a steady and uniform depth of 2m in an open channel of ...
's roughness coefficient (n) as 0.03 and acceleration due to gravity (g) as 9.81 m/s^2.
To obtain critical flow in the channel, the Froude number (Fr) needs to be equal to 1.
The Froude number is given by the equation:
Fr = V / sqrt(g * d)
where V is the velocity of the water, g is the acceleration due to gravity, and d is the depth of the water.
Since the water depth is given as 2m, we can rearrange the equation to solve for V:
V = Fr * sqrt(g * d)
To determine the Froude number for critical flow, we can use the equation:
Fr = sqrt(g * d) / sqrt(R)
where R is the hydraulic radius of the channel.
The hydraulic radius (R) is given by the equation:
R = (A / P)
where A is the cross-sectional area of the channel and P is the wetted perimeter.
The cross-sectional area (A) is given by the equation:
A = b * d
where b is the base width of the channel.
The wetted perimeter (P) is given by the equation:
P = b + 2d
Substituting these values into the equations, we have:
A = 4m * 2m = 8m^2
P = 4m + 2(2m) = 8m
R = 8m^2 / 8m = 1m
Now, we can solve for the Froude number (Fr) using the hydraulic radius (R) and the depth (d):
Fr = sqrt(9.81 m/s^2 * 2m) / sqrt(1m) = sqrt(19.62) / 1 = 4.43
Since the desired Froude number for critical flow is 1, we need to reduce the velocity by a factor of 4.43.
Using the Manning's equation:
V = (1 / n) * (R^(2/3)) * (S^(1/2))
where V is the velocity, n is Manning's roughness coefficient, R is the hydraulic radius, and S is the slope of the channel.
Substituting the values:
4.43V = (1 / 0.03) * (1m^(2/3)) * (1/10000)^(1/2)
Simplifying:
4.43V = 33.33 * 0.1 * 0.01^(1/2)
4.43V = 0.03333
V = 0.03333 / 4.43
V ≈ 0.0075 m/s
Therefore, to obtain critical flow in the channel, a hump in the bed should be provided to reduce the velocity to approximately 0.0075 m/s.
To obtain critical flow in the channel, the Froude number (Fr) needs to be equal to 1.
The Froude number is given by the equation:
Fr = V / sqrt(g * d)
where V is the velocity of the water, g is the acceleration due to gravity, and d is the depth of the water.
Since the water depth is given as 2m, we can rearrange the equation to solve for V:
V = Fr * sqrt(g * d)
To determine the Froude number for critical flow, we can use the equation:
Fr = sqrt(g * d) / sqrt(R)
where R is the hydraulic radius of the channel.
The hydraulic radius (R) is given by the equation:
R = (A / P)
where A is the cross-sectional area of the channel and P is the wetted perimeter.
The cross-sectional area (A) is given by the equation:
A = b * d
where b is the base width of the channel.
The wetted perimeter (P) is given by the equation:
P = b + 2d
Substituting these values into the equations, we have:
A = 4m * 2m = 8m^2
P = 4m + 2(2m) = 8m
R = 8m^2 / 8m = 1m
Now, we can solve for the Froude number (Fr) using the hydraulic radius (R) and the depth (d):
Fr = sqrt(9.81 m/s^2 * 2m) / sqrt(1m) = sqrt(19.62) / 1 = 4.43
Since the desired Froude number for critical flow is 1, we need to reduce the velocity by a factor of 4.43.
Using the Manning's equation:
V = (1 / n) * (R^(2/3)) * (S^(1/2))
where V is the velocity, n is Manning's roughness coefficient, R is the hydraulic radius, and S is the slope of the channel.
Substituting the values:
4.43V = (1 / 0.03) * (1m^(2/3)) * (1/10000)^(1/2)
Simplifying:
4.43V = 33.33 * 0.1 * 0.01^(1/2)
4.43V = 0.03333
V = 0.03333 / 4.43
V ≈ 0.0075 m/s
Therefore, to obtain critical flow in the channel, a hump in the bed should be provided to reduce the velocity to approximately 0.0075 m/s.
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Water flows at a steady and uniform depth of 2m in an open channel of rectangular cross section having base width of 4m and laid at a slope of 1 in 10000. If it is desired to obtain critical flow in the channel by providing a hump in the bed. Take Manning’s coefficient = 0.01. Calculate the height of hump (in meters) required for the critical flowa)0.5b)2.5c)2d)0.94Correct answer is option 'D'. Can you explain this answer?
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Water flows at a steady and uniform depth of 2m in an open channel of rectangular cross section having base width of 4m and laid at a slope of 1 in 10000. If it is desired to obtain critical flow in the channel by providing a hump in the bed. Take Manning’s coefficient = 0.01. Calculate the height of hump (in meters) required for the critical flowa)0.5b)2.5c)2d)0.94Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Water flows at a steady and uniform depth of 2m in an open channel of rectangular cross section having base width of 4m and laid at a slope of 1 in 10000. If it is desired to obtain critical flow in the channel by providing a hump in the bed. Take Manning’s coefficient = 0.01. Calculate the height of hump (in meters) required for the critical flowa)0.5b)2.5c)2d)0.94Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows at a steady and uniform depth of 2m in an open channel of rectangular cross section having base width of 4m and laid at a slope of 1 in 10000. If it is desired to obtain critical flow in the channel by providing a hump in the bed. Take Manning’s coefficient = 0.01. Calculate the height of hump (in meters) required for the critical flowa)0.5b)2.5c)2d)0.94Correct answer is option 'D'. Can you explain this answer?.
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