Question

3. Consider a vortex filament of strength  in the shape of a closed circular loop of radius R. Obtain an expression for the velocity induced at the center of the loop in terms of  and R, no other variables. Tip: Draw the loop on your page. If the vortices on the filament curve inward over the top of the loop, then the velocity vector points into the page, and vice-versa. Draw your vectors (dl and r) clearly to ensure you get the sign of the velocity vector correct. Your result will be a vector

Answer 1

Step-by-step explanation:

Given that Г is the strength of vortex filament

R is closed circular loop radius

Attached is the expression for the induced velocity in vector form