Question
why is ur = 0 in the line vortex function?
be the same, except that the negative sigh on source sthe o disappear Building Block 3-Line Vortex Our third building block flow is a line vortex parallel to the z-axis. As with the previous building block, ve start with the simple case in which the line vortex is located at the origin (Fig. 10-50). Again we use cylindrical coordi- nates for convenience. The velocity components are FIGURE 10-50 Line vortex of strength I located at the origin in the ty-plane Line vorter. u.- (10-45) ar r ae r a0 r 2r where?is called the circulation or the vortex strength. Following the standard convention in mathematics, positive represents a counterclock- wise vortex, while negative r represents a clockwise vortex It is left as an exercise to integrate Eq. 10-45 to obtain expressions for the stream function and the velocity potential function. Line vortes at the origin: (10-46) 217 2m Comparing Eqs. 10-43 and 10-46, we see that a line source and line vor ex are somewhat complementary in the sense that the expressions for ? and are reversed. FIGURE 10-51 Line vortex of strength ? located at some arbitrary point (a, b in the xy-plane In situations where we would like to place the vortex somewhere other than the origin, we must transform Eq. 10-46 as we did for a line source Sketched in Fig. 10-51 is a line vortex located at some arbitrary point (a, b
Explanation / Answer
Because in line vortex motion, streamlines are circular with centre at vortex center and there is no flow in the radial direction. Flow is in circumferential direction only. Hence Ur=0 in line vortex motion.
