A flow field is described by the equation ψ = y-x² Sketch the streamlines ψ = 0, ψ=1,and ψ = 2. Derive an expression for the velocity V at any point in the flow field.Calculate the vorticity.
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The equation for the flow field is
From the condition for stream function we get the velocity coordinate as
Similarly we get the velocity coordinate as
Thus the magnitude of the velocity is
Therefore the expression for the velocity at any point in the flow field is
The vorticity of the flow is determined by using the relation
Since the vorticity of the flow is not equal to zero we can say that the flow is rotational
From the equation for the flow field is we can say that the flow field is a family of parabolas symmetric about the