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A sluice gate discharges water into a horizontal rectangular channel with a velocity of 12 m/s and depth of flow of 1 m. What is the depth offlow after the hydraulic jump?
- a)6.42 m
- b)5·84 m
- c)4.94 m
- d)2.21 m
Correct answer is option 'C'. Can you explain this answer?
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A sluice gate discharges water into a horizontal rectangular channel w...
Ans. (c)
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Solution:
Given data:
Velocity of water at sluice gate = 12 m/s
Depth of flow at sluice gate = 1 m
To find: Depth of flow after the hydraulic jump
The depth of flow after the hydraulic jump can be calculated using the following formula:
y2 = y1/[(1 + Froude number^2)]
where,
y1 = Depth of flow before the hydraulic jump
y2 = Depth of flow after the hydraulic jump
Froude number = (V1 / √(g*y1))
where,
V1 = Velocity of water before the hydraulic jump
g = Acceleration due to gravity = 9.81 m/s^2
Now, let's calculate the value of Froude number:
V1 = 12 m/s
Froude number = (12 / √(9.81*1)) = 3.872
Since the Froude number is greater than 1, there will be a hydraulic jump. Let's calculate the depth of flow after the hydraulic jump:
y2 = 1/[(1 + 3.872^2)] = 0.494 m = 4.94 cm
Therefore, the depth of flow after the hydraulic jump is 4.94 cm (approx). Hence, option (c) is the correct answer.
Given data:
Velocity of water at sluice gate = 12 m/s
Depth of flow at sluice gate = 1 m
To find: Depth of flow after the hydraulic jump
The depth of flow after the hydraulic jump can be calculated using the following formula:
y2 = y1/[(1 + Froude number^2)]
where,
y1 = Depth of flow before the hydraulic jump
y2 = Depth of flow after the hydraulic jump
Froude number = (V1 / √(g*y1))
where,
V1 = Velocity of water before the hydraulic jump
g = Acceleration due to gravity = 9.81 m/s^2
Now, let's calculate the value of Froude number:
V1 = 12 m/s
Froude number = (12 / √(9.81*1)) = 3.872
Since the Froude number is greater than 1, there will be a hydraulic jump. Let's calculate the depth of flow after the hydraulic jump:
y2 = 1/[(1 + 3.872^2)] = 0.494 m = 4.94 cm
Therefore, the depth of flow after the hydraulic jump is 4.94 cm (approx). Hence, option (c) is the correct answer.
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A sluice gate discharges water into a horizontal rectangular channel with a velocity of 12 m/s and depth of flow of 1 m. What is the depth offlow after the hydraulic jump?a)6.42 mb)5·84 mc)4.94 md)2.21 mCorrect answer is option 'C'. Can you explain this answer?
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