An incompressible steady flow pattern is given by u=x^3+2z^2 and w=y^3-2yz. what is the most general form of the third component v(x, y,z) which satisfies continuity?

The velocity field may be written in the rectangular Cartesian coordinate system as

where
u = x3 + 2z²
w = y³ - 2yz

For incompressible flow,

Therefore


Also,


Because x = y = 0 in the velocity field, therefore
v = f(x)

v = v(x) only.

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