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A hydraulic jump takes place in a 6 in wide rectangular channel at a point where the upstream depth is 0.5 m (just before the jump). If the discharge in the channel is 30 rm3/s and the energy loss in the jump is 1.6 m. then the Froude number computed at the end of the jump is _________. (round off to two decimal places)
(Consider the acceleration due to gravity as 10 m/s2.)
(Consider the acceleration due to gravity as 10 m/s2.)
Correct answer is between '0.30,0.41'. Can you explain this answer?
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Most Upvoted Answer
A hydraulic jump takes place in a 6 in wide rectangular channel at a p...
Method I:
Given,
Q = 30 m3/s (discharge in channel)
B = 6 m (width of channel)
EL = 1.6 m (Energy loss)
y1 = 0.5 m (depth before jump)
F2 = ? (Provide number after jump)
We know
Fr2 = 0.32 [This should be the answer]
But Method II :
EL = 2.43 m [This is not equal to energy loss given]
So, now as per given energy loss
1.6 x 4 x 0.5 x y2 = (y2 - 0.5)3
y2 = 2.5 m, -0.0527 m, -0.947 m
∴y2 = 2.5 m
Note : We are getting two different values of Froude number from given data.
Given,
Q = 30 m3/s (discharge in channel)
B = 6 m (width of channel)
EL = 1.6 m (Energy loss)
y1 = 0.5 m (depth before jump)
F2 = ? (Provide number after jump)
We know
Fr2 = 0.32 [This should be the answer]
But Method II :
EL = 2.43 m [This is not equal to energy loss given]
So, now as per given energy loss
1.6 x 4 x 0.5 x y2 = (y2 - 0.5)3
y2 = 2.5 m, -0.0527 m, -0.947 m
∴y2 = 2.5 m
Note : We are getting two different values of Froude number from given data.
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Community Answer
A hydraulic jump takes place in a 6 in wide rectangular channel at a p...
Given data:
- Width of the rectangular channel (b) = 6 in = 0.1524 m
- Upstream depth (y1) = 0.5 m
- Discharge (Q) = 30 m^3/s
- Energy loss in the jump (ΔE) = 1.6 m
- Acceleration due to gravity (g) = 10 m/s^2
Calculating the upstream velocity:
The upstream velocity (V1) can be calculated using the discharge and the cross-sectional area of flow.
- Cross-sectional area (A1) = b * y1
- V1 = Q / A1
Calculating the downstream depth:
The downstream depth (y2) can be calculated using the specific energy equation:
- Specific energy (E) = (V^2/2g) + (y/g)
- At the jump, the specific energy remains constant, so E1 = E2
- E1 = (V1^2/2g) + (y1/g)
- E2 = (V2^2/2g) + (y2/g)
- E1 = E2
- (V1^2/2g) + (y1/g) = (V2^2/2g) + (y2/g)
- V2^2 = V1^2 + 2g(y1 - y2)
- V2 = sqrt(V1^2 + 2g(y1 - y2))
Calculating the Froude number:
The Froude number (Fr) can be calculated using the downstream velocity and the downstream depth.
- Fr = V2 / sqrt(gy2)
Solving the equations:
- First, convert the width of the channel to meters: b = 6 in = 0.1524 m
- Calculate the cross-sectional area: A1 = b * y1
- Calculate the upstream velocity: V1 = Q / A1
- Calculate the downstream velocity: V2 = sqrt(V1^2 + 2g(y1 - y2))
- Rearrange the Froude number equation to solve for y2: y2 = (V2^2 / g) / Fr^2
- Substitute the values of V2, g, and Fr into the equation to find y2
- Round off the result to two decimal places.
Final Answer:
The Froude number computed at the end of the jump is between 0.30 and 0.41.
- Width of the rectangular channel (b) = 6 in = 0.1524 m
- Upstream depth (y1) = 0.5 m
- Discharge (Q) = 30 m^3/s
- Energy loss in the jump (ΔE) = 1.6 m
- Acceleration due to gravity (g) = 10 m/s^2
Calculating the upstream velocity:
The upstream velocity (V1) can be calculated using the discharge and the cross-sectional area of flow.
- Cross-sectional area (A1) = b * y1
- V1 = Q / A1
Calculating the downstream depth:
The downstream depth (y2) can be calculated using the specific energy equation:
- Specific energy (E) = (V^2/2g) + (y/g)
- At the jump, the specific energy remains constant, so E1 = E2
- E1 = (V1^2/2g) + (y1/g)
- E2 = (V2^2/2g) + (y2/g)
- E1 = E2
- (V1^2/2g) + (y1/g) = (V2^2/2g) + (y2/g)
- V2^2 = V1^2 + 2g(y1 - y2)
- V2 = sqrt(V1^2 + 2g(y1 - y2))
Calculating the Froude number:
The Froude number (Fr) can be calculated using the downstream velocity and the downstream depth.
- Fr = V2 / sqrt(gy2)
Solving the equations:
- First, convert the width of the channel to meters: b = 6 in = 0.1524 m
- Calculate the cross-sectional area: A1 = b * y1
- Calculate the upstream velocity: V1 = Q / A1
- Calculate the downstream velocity: V2 = sqrt(V1^2 + 2g(y1 - y2))
- Rearrange the Froude number equation to solve for y2: y2 = (V2^2 / g) / Fr^2
- Substitute the values of V2, g, and Fr into the equation to find y2
- Round off the result to two decimal places.
Final Answer:
The Froude number computed at the end of the jump is between 0.30 and 0.41.
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A hydraulic jump takes place in a 6 in wide rectangular channel at a point where the upstream depth is 0.5 m (just before the jump). If the discharge in the channel is 30 rm3/s and the energy loss in the jump is 1.6 m. then the Froude number computed at the end of the jump is _________. (round off to two decimal places)(Consider the acceleration due to gravity as 10 m/s2.)Correct answer is between '0.30,0.41'. Can you explain this answer?
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A hydraulic jump takes place in a 6 in wide rectangular channel at a point where the upstream depth is 0.5 m (just before the jump). If the discharge in the channel is 30 rm3/s and the energy loss in the jump is 1.6 m. then the Froude number computed at the end of the jump is _________. (round off to two decimal places)(Consider the acceleration due to gravity as 10 m/s2.)Correct answer is between '0.30,0.41'. 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 hydraulic jump takes place in a 6 in wide rectangular channel at a point where the upstream depth is 0.5 m (just before the jump). If the discharge in the channel is 30 rm3/s and the energy loss in the jump is 1.6 m. then the Froude number computed at the end of the jump is _________. (round off to two decimal places)(Consider the acceleration due to gravity as 10 m/s2.)Correct answer is between '0.30,0.41'. 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 hydraulic jump takes place in a 6 in wide rectangular channel at a point where the upstream depth is 0.5 m (just before the jump). If the discharge in the channel is 30 rm3/s and the energy loss in the jump is 1.6 m. then the Froude number computed at the end of the jump is _________. (round off to two decimal places)(Consider the acceleration due to gravity as 10 m/s2.)Correct answer is between '0.30,0.41'. Can you explain this answer?.
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