Consider fully developed axisymmetric Poiseuille flow-flow in a round pipe of radius R (diameter D = 2R),with a forced pressure gradient dP/dx driving the flow as illustrated in Fig. P4-90. (dP/dx is constant and negative.)The flow is steady, incompressible, and axisymmetric about the x-axis. The velocity components are given by

Where μ is the fluid's viscosity. Is this flow rotational or irrotational? If it is rotational, calculate the vorticity component in the circumferential (u) direction and discuss the sign of the rotation.