The given steady two-dimensional velocity
profile is
where u = 3(x2 - y2) and v = -6xy.
Since and,
thus.
The continuity equation is satisfied, and it can be concluded that the flow is incompressible.
To this end, the flow field is known to be two-dimensional and incompressible,
hence a stream function can be introduced.
According to the definition of the stream function,
The two equations above can be integrated to yield,
ψ = 3x2y - y3 +
f1(x)
ψ = 3x2y
+ f2(y)
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