Consider fully developed axisymmetric Poiseuille flow—flow in a round pipe of radius R(dia...

Consider fully developed axisymmetric Poiseuille flow—flow in a round pipe of radius R(diameter D = 2 R), with a forced pressure gradient dP/dxdriving the flow as illustrated in Fig. P11–53. (dP/dxis 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 (θ) direction and discuss the sign of the rotation.

FIGURE P11-53