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(4) (25 Points) Consider a fully developed axisymmetric Poiseuille flow - flow in a round pipe of radius with a forced pressure gradient dP/dx driving the flow as illustrated in the figure. The flow s steady, incompressible, and axisymmetric about x-axis. The velocity components are given by u = (1)/(4μ)(dP)/(dx) (r^2 - R^2) ur = uθ = 0 Where μ is the fluid's viscosit. Is this flow rotational or irrotational? If it is rotational, calculate the vorticity component in the circumferential d
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