Consider the two-dimensional Poiseuille flow of Prob. 4–99. The fluid between the plates is water at 408C. Let the gap height h = 1.6 mm and the pressure gradient dP/dx = –230 N/m³. Imagine a hydrogen bubble wire stretched vertically through the channel at x = 0 (Fig. P4–106). The wire is pulsed on and off such that bubbles are produced periodically to create timelines. Five distinct timelines are generated at t = 0, 2.5, 5.0, 7.5, and 10.0 s. Calculate and plot what these five timelines look like at time t = 12.5 s.

Fig. P4–106

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:

h H₂ wire y X u(y)