Consider fully developed two-dimensional Poiseuille flow—flow between two infinite paralle...

Consider fully developed two-dimensional Poiseuille flow—flow between two infinite parallel plates separated by distance h,with both the top plate and bottom plate stationary, and a forced pressure gradient dP/dxdriving the flow as illustrated in Fig. P11–48. (dP/dxis constant and negative.)

FIGURE P11-48

The flow is steady, incompressible, and two-dimensional in the xy-plane. 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 z-direction. Do fluid particles in this flow rotate clockwise or counterclockwise?