Page 385 - Introduction to Continuum Mechanics

Newtonian Viscous Fluid 369

Substituting Eq. (iv) into Eq. (ii), we obtain the parametric equations for the streakline to be

Example 6.10.4
Given the two dimensional problem

Obtain (a) the streamline passing through the point («i,«2)
(b) the pathline for the particle (Xi^X^) anc *

(c) the streakline for the particles which passed through the point («i,«2)
Solution, (a) From Eq. (i), we have

thus,

This is obviously a straight line parallel to thejtj axis,
(b) from (i), we have

thus,

Again, this is a straight line parallel to the xi axis,

(c) From the results of (b), we have

therefore,

Substituting Eq. (vii) into Eq. (v), we obtain