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The stream function ψ = x3- y3 is observed for a two-dimensional flow field. What is the magnitude of the velocity at point (1, -1)?
  • a)
    4.24
  • b)
    2.83
  • c)
    0
  • d)
    -2.83
Correct answer is option 'A'. Can you explain this answer?
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The stream function ψ = x3- y3is observed for a two-dimensional fl...
Resultant velocity at (1,-1):
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The stream function ψ = x3- y3is observed for a two-dimensional fl...
The stream function is a mathematical concept used in fluid dynamics to describe the flow of a fluid. It is a scalar function that represents the flow of fluid particles along a streamline.

In two-dimensional flow, the stream function is defined as the double integral of the velocity components with respect to the position variables. It is denoted by the symbol Ψ.

The stream function is useful in describing irrotational flows, where the fluid particles do not rotate as they move along the streamlines. In these flows, the stream function is constant along a streamline and the velocity components can be derived from it.

The stream function can also be used to determine the circulation around a closed curve in the flow field. The circulation is the line integral of the velocity components along the closed curve, and it is equal to the difference in the stream function values at the end points of the curve.

The stream function can be visualized using streamlines, which are curves that are tangent to the velocity vector at every point. The streamlines are obtained by solving the stream function equation, which is a partial differential equation that describes the flow field.

In summary, the stream function is a mathematical tool used to describe fluid flow in two dimensions. It is a scalar function that represents the flow of fluid particles along streamlines and is useful in describing irrotational flows and determining circulation.
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The stream function ψ = x3- y3is observed for a two-dimensional flow field. What is the magnitude of the velocity at point (1, -1)?a)4.24b)2.83c)0d)-2.83Correct answer is option 'A'. Can you explain this answer?
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