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A velocity potential function exists when the flow is:
- a)rotational
- b)tangential
- c)parallel
- d)irrotational
Correct answer is option 'D'. Can you explain this answer?
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A velocity potential function exists when the flow is:a)rotationalb)ta...
Velocity Potential Function:
It is defined as the scalar function of space and time, such that its negative derivative with respect to any direction gives the velocity in that direction.
It is denoted by ϕ and defined for two-dimensional as well as three-dimensional flow.
u = −∂ϕ / ∂x; v = −∂ϕ / ∂y; w = −∂ϕ / ∂z
It is defined as the scalar function of space and time, such that its negative derivative with respect to any direction gives the velocity in that direction.
It is denoted by ϕ and defined for two-dimensional as well as three-dimensional flow.
u = −∂ϕ / ∂x; v = −∂ϕ / ∂y; w = −∂ϕ / ∂z
Properties of Stream function:
- If velocity potential function exists, the flow should be irrotational
- If the velocity potential function satisfies the Laplace equation i.e. ∂2ϕ/∂x2 + ∂2ϕ/∂y2 = 0, it is a case of steady incompressible irrotational flow
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A velocity potential function exists when the flow is:a)rotationalb)ta...
Velocity Potential Function in Fluid Mechanics
In fluid mechanics, a velocity potential function is a scalar function that describes the flow of an irrotational fluid. It is a mathematical concept used to simplify the analysis of fluid flow by representing the velocity field in terms of a single scalar function rather than a vector field.
Explanation:
- Rotational Flow: A rotational flow is a type of fluid flow in which the fluid particles rotate as they move. In other words, the fluid has both a tangential and a radial velocity component. In a rotational flow, the fluid particles trace out closed loops or whirlpools. The velocity potential function does not exist for rotational flows because the flow field cannot be described by a single scalar function.
- Tangential Flow: A tangential flow is a type of fluid flow in which the fluid particles move parallel to a surface or along a line. In this type of flow, the fluid particles do not rotate or form closed loops. However, even in tangential flows, the presence of tangential or shear stresses makes it difficult to represent the entire flow field using a single scalar function. Therefore, the velocity potential function does not exist for tangential flows.
- Parallel Flow: Parallel flow refers to a type of fluid flow in which the fluid particles move in parallel to each other without any rotation or crossing of flow lines. In this type of flow, the fluid particles maintain a constant distance from each other and move in the same direction. The velocity potential function does not exist for parallel flows because the flow field cannot be described by a single scalar function.
- Irrotational Flow: Irrotational flow is a type of fluid flow in which the fluid particles do not rotate as they move. In this type of flow, the fluid particles move in straight or curved paths without any rotation or swirling. The velocity potential function exists for irrotational flows because the flow field can be described by a single scalar function. The velocity potential function is defined as the scalar field whose gradient gives the velocity field of the fluid.
Conclusion:
In conclusion, a velocity potential function exists only for irrotational flows. It does not exist for rotational flows, tangential flows, or parallel flows. The velocity potential function is a useful mathematical tool in fluid mechanics as it simplifies the analysis of fluid flow by representing the velocity field in terms of a single scalar function.
In fluid mechanics, a velocity potential function is a scalar function that describes the flow of an irrotational fluid. It is a mathematical concept used to simplify the analysis of fluid flow by representing the velocity field in terms of a single scalar function rather than a vector field.
Explanation:
- Rotational Flow: A rotational flow is a type of fluid flow in which the fluid particles rotate as they move. In other words, the fluid has both a tangential and a radial velocity component. In a rotational flow, the fluid particles trace out closed loops or whirlpools. The velocity potential function does not exist for rotational flows because the flow field cannot be described by a single scalar function.
- Tangential Flow: A tangential flow is a type of fluid flow in which the fluid particles move parallel to a surface or along a line. In this type of flow, the fluid particles do not rotate or form closed loops. However, even in tangential flows, the presence of tangential or shear stresses makes it difficult to represent the entire flow field using a single scalar function. Therefore, the velocity potential function does not exist for tangential flows.
- Parallel Flow: Parallel flow refers to a type of fluid flow in which the fluid particles move in parallel to each other without any rotation or crossing of flow lines. In this type of flow, the fluid particles maintain a constant distance from each other and move in the same direction. The velocity potential function does not exist for parallel flows because the flow field cannot be described by a single scalar function.
- Irrotational Flow: Irrotational flow is a type of fluid flow in which the fluid particles do not rotate as they move. In this type of flow, the fluid particles move in straight or curved paths without any rotation or swirling. The velocity potential function exists for irrotational flows because the flow field can be described by a single scalar function. The velocity potential function is defined as the scalar field whose gradient gives the velocity field of the fluid.
Conclusion:
In conclusion, a velocity potential function exists only for irrotational flows. It does not exist for rotational flows, tangential flows, or parallel flows. The velocity potential function is a useful mathematical tool in fluid mechanics as it simplifies the analysis of fluid flow by representing the velocity field in terms of a single scalar function.
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A velocity potential function exists when the flow is:a)rotationalb)tangentialc)paralleld)irrotationalCorrect answer is option 'D'. Can you explain this answer?
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