For the axisymmetric Poiseuille flow of Prob. 4109, calculate the linear strain rates in the x- and
Question:
For the axisymmetric Poiseuille flow of Prob. 4–109, calculate the linear strain rates in the x- and r-directions, and calculate the shear strain rate εxr. The strain rate tensor in cylindrical coordinates (r, θ, x) and (ur, uθ, ux), is
Data from Problem 109
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. P4–109. (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 (θ) direction and discuss the sign of the rotation.
Fig. P4–109
Step by Step Answer:
Fluid Mechanics Fundamentals And Applications
ISBN: 9780073380322
3rd Edition
Authors: Yunus Cengel, John Cimbala