Question

In an incompressible, steady flow the velocity field is described by: vec(V)=(x^(2)y-xy^(2)) vec(i)+((y^(3))/(3)-xy^(2)) vec(j) a) Does a stream function exist for this flow? If so, determine its mathematical expression. b) Determine the total vorticity contained over a square-shaped flow region with an area of 4.0 , centered at the origin using: Gamma=∬ vec(omega)* vec(n)dA c) Determine the value of the following integral along the perimeter of the square-shaped area: Gamma=int vec(V)* vec(ds) where s is a coordinate locally tangent to the perimeter. d) Compare the results for parts (b) and (c) and comment.

          In an incompressible, steady flow the velocity field is described by: vec(V)=(x^(2)y-xy^(2)) vec(i)+((y^(3))/(3)-xy^(2)) vec(j) a) Does a stream function exist for this flow? If so, determine its mathematical expression. b) Determine the total vorticity contained over a square-shaped flow region with an area of 4.0 , centered at the origin using: Gamma=∬ vec(omega)* vec(n)dA c) Determine the value of the following integral along the perimeter of the square-shaped area: Gamma=int vec(V)* vec(ds) where s is a coordinate locally tangent to the perimeter. d) Compare the results for parts (b) and (c) and comment.

Added by Cesar N.

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