Calculate the vorticity component in the z-direction

Calculate the vorticity component in the z-direction/

Mechanical Engineering
Consider fully developed two-dimensional Poiseuille flow-flow between two infinite parallel plates separated bydistance h, with both the top plate and bottom plate stationary, and a forced pressure gradient dP/dx driving the flow as illustrated in Fig. P4-82. (dP/dx is constant and negative.)
width=

The flow is steady, incompressible, and two-dimensional in the xy-plane. The velocity components are given by
width=

where µ is the fluid’s viscosity. Is this flow rotational or irrotational? If it is rotational, calculate the vorticity component in the z-direction. Do fluid particles in this flow rotate clockwise or counterclockwise?

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