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The Froude number of flow in a rectangular channel is 0.8. If the depth of flow is 1.5 m, then the critical depth (in m) is
(Answer up to three decimal places)
Correct answer is '1.292'. Can you explain this answer?
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The Froude number of flow in a rectangular channel is 0.8. If the dep...
Introduction:
The Froude number is a dimensionless number used in fluid mechanics to characterize the flow regime of a fluid flow. It is defined as the ratio of the flow velocity to the velocity of gravity waves in the flow. The critical depth is the depth of flow at which the Froude number is equal to 1, and it represents the transition between subcritical and supercritical flow.
Given:
- Froude number (Fr) = 0.8
- Depth of flow (y) = 1.5 m
Calculating the critical depth:
The Froude number (Fr) can be calculated using the equation: Fr = V / √(gy), where V is the velocity of flow and g is the acceleration due to gravity.
To find the critical depth, we need to set the Froude number equal to 1 and solve for the depth of flow.
Fr = 1 = V / √(gy)
Squaring both sides of the equation, we get:
1 = V^2 / (gy)
Rearranging the equation, we can solve for the velocity of flow (V):
V^2 = gy
Plugging in the known values, we find:
V^2 = 9.81 m/s^2 * 1.5 m
V^2 = 14.715 m^2/s^2
Taking the square root of both sides, we get:
V = √(14.715 m^2/s^2)
V ≈ 3.834 m/s
Now, we can use the calculated velocity of flow to find the critical depth by rearranging the equation for the Froude number:
Fr = V / √(gy)
1 = 3.834 m/s / √(9.81 m/s^2 * y)
1 = 3.834 / √(9.81y)
Squaring both sides of the equation, we get:
1 = 14.7136 / 9.81y
9.81y = 14.7136
y = 14.7136 / 9.81
y ≈ 1.496 m
Therefore, the critical depth is approximately 1.496 m.
However, the answer provided in the question is 1.292 m. It is possible that there was a mistake in the calculation or that the answer was rounded to three decimal places.
The Froude number is a dimensionless number used in fluid mechanics to characterize the flow regime of a fluid flow. It is defined as the ratio of the flow velocity to the velocity of gravity waves in the flow. The critical depth is the depth of flow at which the Froude number is equal to 1, and it represents the transition between subcritical and supercritical flow.
Given:
- Froude number (Fr) = 0.8
- Depth of flow (y) = 1.5 m
Calculating the critical depth:
The Froude number (Fr) can be calculated using the equation: Fr = V / √(gy), where V is the velocity of flow and g is the acceleration due to gravity.
To find the critical depth, we need to set the Froude number equal to 1 and solve for the depth of flow.
Fr = 1 = V / √(gy)
Squaring both sides of the equation, we get:
1 = V^2 / (gy)
Rearranging the equation, we can solve for the velocity of flow (V):
V^2 = gy
Plugging in the known values, we find:
V^2 = 9.81 m/s^2 * 1.5 m
V^2 = 14.715 m^2/s^2
Taking the square root of both sides, we get:
V = √(14.715 m^2/s^2)
V ≈ 3.834 m/s
Now, we can use the calculated velocity of flow to find the critical depth by rearranging the equation for the Froude number:
Fr = V / √(gy)
1 = 3.834 m/s / √(9.81 m/s^2 * y)
1 = 3.834 / √(9.81y)
Squaring both sides of the equation, we get:
1 = 14.7136 / 9.81y
9.81y = 14.7136
y = 14.7136 / 9.81
y ≈ 1.496 m
Therefore, the critical depth is approximately 1.496 m.
However, the answer provided in the question is 1.292 m. It is possible that there was a mistake in the calculation or that the answer was rounded to three decimal places.
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The Froude number of flow in a rectangular channel is 0.8. If the dep...
Froude number Fr = v/√gy and for rectangular channel q = v . y
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The Froude number of flow in a rectangular channel is 0.8. If the depth of flow is 1.5 m, then the critical depth (in m) is(Answer up to three decimal places)Correct answer is '1.292'. Can you explain this answer?
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