Question

The circumferential velocities in a free vortex and forced vortex , respectively, u 0=C/r and uo=wr, where r is the radius in meter , velocity is in m/s, C is 4 m^2/s, and w=1.0 rad/s. for both cases , calculate the circulation around a circular path with a radius of 1m and center at (0,0) .Are these inviscid flows? note that ur=0 ?

Answer 1

Unit of circulation is m2/s

Please find below answer

First let assume a unit circle center at origin as shown

Now

Circulation can be found by integrating tangential velocity along the circumference

These flow are not invisicid because in vortex flow adjustant stream lines move with different velocity. So there is a friction and hence energy loss. So it's not invisicid flow