For the axisymmetric Poiseuille flow of Prob. 4-108. calculate the linear strain rates in the x- and r-directions, and calculate the shear strain rate ɛxr. The strain rate tensor in cylindrical coordinates (r, θ. x) and (ur,uθ. ux). is
PROBLEM: Consider fully developed axisymmetric Poiseuille flow—flow in a round pipe of radius R(diameter D = 2 R), with a forced pressure gradient dP/dx driving the flow as illustrated in Fig. P11–53. (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.
Step 1 of 4
The velocity component of the flow is given. Using the velocity component calculate the linear strain in x and r direction, that is calculate and . Also calculate the shear strain .