For the two-dimensional Poiseuille flow of Prob. 4–99, calculate the linear strain rates in the x- and y-directions, and calculate the shear strain rate ε_xy.

Data from Problem 99

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/dx driving the flow as illustrated in Fig. P4–99. (dP/dx is constant and negative.)

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?

 Fig. P4–99.

Transcribed Image Text:

u 1 dp 2μ dx -(y² - hy) v=0