Solve the problem.
-The radial flow field of an incompressible fluid is shown below. For which of the closed paths is the circulation not necessarily zero?
A) none of these
B) A, B, and C
C) A and B only
D) C only

Question

Solve the problem.
-The radial flow field of an incompressible fluid is shown below. For which of the closed paths is the circulation not necessarily zero?
A) none of these 
B) A, B, and C 
C) A and B only 
D) C only

Quizplus · Accepted Answer

The circulation of a fluid around a closed path is given by the line integral of the flow velocity around the path. Since the velocity in this flow field is purely radial, the circulation around any closed path will be zero, except for paths that contain the origin (point O) where the velocity is not defined. Path C contains the origin, so the circulation around path C is not necessarily zero. Therefore, the correct answer is D, only path C.

Solve the Problem. -The Radial Flow Field of an Incompressible Fluid Is Shown