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For an irrotation flow, the velocity potential lines and the streamlines are always
- a)parallel to each other
- b)coplanar
- c)orthogonal to each other
- d)inclined to the horizontal
Correct answer is option 'C'. Can you explain this answer?
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For an irrotation flow, the velocity potential lines and the streamlin...
Explanation:
An irrotational flow is a type of fluid flow in which the fluid particles do not rotate as they move through the flow field. In other words, the fluid flow is characterized by a zero vorticity.
Velocity potential lines and streamlines are two important concepts used in the analysis of fluid flows.
Velocity potential lines are imaginary lines drawn in a fluid flow field to represent the variation of the velocity potential of the fluid. These lines are always perpendicular to the equipotential surfaces of the flow field.
Streamlines, on the other hand, are the paths traced by fluid particles as they move through the flow field. They are tangent to the velocity vector at any point in the flow field.
For an irrotational flow, the velocity potential lines and the streamlines are always orthogonal to each other. This means that they intersect at right angles.
This is because the velocity potential in an irrotational flow can be expressed as the negative gradient of a scalar potential function, which is a scalar field that satisfies Laplace's equation.
Since the gradient of a scalar function is always perpendicular to the equipotential surfaces, the velocity potential lines are always perpendicular to the equipotential surfaces.
Since the streamlines are tangent to the velocity vector at any point in the flow field, they are always parallel to the equipotential surfaces. Therefore, the streamlines are always orthogonal to the velocity potential lines in an irrotational flow.
An irrotational flow is a type of fluid flow in which the fluid particles do not rotate as they move through the flow field. In other words, the fluid flow is characterized by a zero vorticity.
Velocity potential lines and streamlines are two important concepts used in the analysis of fluid flows.
Velocity potential lines are imaginary lines drawn in a fluid flow field to represent the variation of the velocity potential of the fluid. These lines are always perpendicular to the equipotential surfaces of the flow field.
Streamlines, on the other hand, are the paths traced by fluid particles as they move through the flow field. They are tangent to the velocity vector at any point in the flow field.
For an irrotational flow, the velocity potential lines and the streamlines are always orthogonal to each other. This means that they intersect at right angles.
This is because the velocity potential in an irrotational flow can be expressed as the negative gradient of a scalar potential function, which is a scalar field that satisfies Laplace's equation.
Since the gradient of a scalar function is always perpendicular to the equipotential surfaces, the velocity potential lines are always perpendicular to the equipotential surfaces.
Since the streamlines are tangent to the velocity vector at any point in the flow field, they are always parallel to the equipotential surfaces. Therefore, the streamlines are always orthogonal to the velocity potential lines in an irrotational flow.
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For an irrotation flow, the velocity potential lines and the streamlines are alwaysa)parallel to each otherb)coplanarc)orthogonal to each otherd)inclined to the horizontalCorrect answer is option 'C'. Can you explain this answer?
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