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The curl of a given velocity field (∇ x -V) indicates the rate of
- a)Increase or decrease of flow at a point
- b)Twisting of the lines of flow
- c)Deformation
- d)Translation
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The curl of a given velocity field (∇ x -V) indicates the rate ofa)In...
The curl indicates the rate of deformation.
The angular velocity vector is defined as:
The vorticity of a flow field is defined as:
Rate of rotation of fluid element ABCD about the ?-axis is defined as the average of the angular speeds of two mutually perpendicular lines AB (dx element) and AD (dy element):
Most Upvoted Answer
The curl of a given velocity field (∇ x -V) indicates the rate ofa)In...
Explanation:
The curl of a vector field is a vector quantity that describes the rotation of the field. In the context of fluid mechanics, the curl of a velocity field describes the amount of local rotation or swirling motion of the fluid at a given point.
Deformation:
The curl of a given velocity field (∇ x -V) indicates the rate of deformation of the fluid at a point. Deformation refers to the change in shape or volume of a fluid element as it moves through the flow field. The curl of the velocity field gives us information about the local rate of stretching, compression, and shearing of the fluid at a given point.
Twisting:
While the curl of a velocity field does not directly indicate the twisting of the lines of flow, it does provide information about the local rotation of the fluid. This rotation can lead to the twisting or bending of the flow lines, especially in regions where the curl is large.
Increase or decrease of flow at a point:
The curl of a velocity field does not provide information about the overall increase or decrease of flow at a point. This information is captured by the divergence of the velocity field, which describes the net rate of fluid flow into or out of a given region.
Translation:
The curl of a velocity field does not provide information about the overall translation or movement of the fluid. This information is captured by the gradient of the velocity field, which describes the direction and magnitude of the velocity at each point in the flow field.
The curl of a vector field is a vector quantity that describes the rotation of the field. In the context of fluid mechanics, the curl of a velocity field describes the amount of local rotation or swirling motion of the fluid at a given point.
Deformation:
The curl of a given velocity field (∇ x -V) indicates the rate of deformation of the fluid at a point. Deformation refers to the change in shape or volume of a fluid element as it moves through the flow field. The curl of the velocity field gives us information about the local rate of stretching, compression, and shearing of the fluid at a given point.
Twisting:
While the curl of a velocity field does not directly indicate the twisting of the lines of flow, it does provide information about the local rotation of the fluid. This rotation can lead to the twisting or bending of the flow lines, especially in regions where the curl is large.
Increase or decrease of flow at a point:
The curl of a velocity field does not provide information about the overall increase or decrease of flow at a point. This information is captured by the divergence of the velocity field, which describes the net rate of fluid flow into or out of a given region.
Translation:
The curl of a velocity field does not provide information about the overall translation or movement of the fluid. This information is captured by the gradient of the velocity field, which describes the direction and magnitude of the velocity at each point in the flow field.
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The curl of a given velocity field (∇ x -V) indicates the rate ofa)In...
The curl indicates the rate of deformation.
The angular velocity vector is defined as:
The vorticity of a flow field is defined as:
Rate of rotation of fluid element ABCD about the ?-axis is defined as the average of the angular speeds of two mutually perpendicular lines AB (dx element) and AD (dy element):
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The curl of a given velocity field (∇ x -V) indicates the rate ofa)Increase or decrease of flow at a pointb)Twisting of the lines of flowc)Deformationd)TranslationCorrect answer is option 'C'. Can you explain this answer?
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