# 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.

Question-AnswerCategory: Fluid MechanicsA 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.

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.

Step: 1

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

Step: 2

Thus the magnitude of the velocity is

Therefore the expression for the velocity at any point in the flow field is

Step: 3

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

Step: 4

From the equation for the flow field is  we can say that the flow field is a family of parabolas symmetric about the