Only 1 problem, multiple choice. Explain your answer though please!

Problem 1. [20] Multiple Choice Questions. Clearly indicate your answer. No partial credit. A. Which of the following statements is NOT true? a) A velocity potential exists in a 3D irrotational flow. b) A stream function exists in a 2D incompressible viscous flow. ) A velocity potential exists in a 3D rotational flow. d) A stream function exists in a 2D incompressible inviscid flow. B. Consider a source with strength A. What is the dimension (unit) of A? C. Consider a vortex with strength I" placed at the origin. Let I' > 0. Assume that all assumptions are satisfied such that we can use the potential flow theorem as we learned in class. Which of the following statements is NOT true? a) In a potential flow, the flow is irrotational. Therefore, the circulation about the unit circle with the center at the origin, is zero. b) Although the flow is irrotational, the center of the vortex is a singularity. The circulation about the unit circle with the center at the origin is non-zero. ) The direction of the velocity induced by the vortex at (x,y) = (1,0) is downwards. d) The magnitude of the velocity induced by the vortex reduces with r, the distance from the origin. D. Consider the d'Alembert paradox as discussed in class. Which of the following statements is true? a) According to d'Alembert paradox, D' = 0 on a 2D airfoil when the flow is steady, incompressible, inviscid, and irrotational. b) According to d'Alembert paradox, D' # 0 on a 2D airfoil when the flow is steady, incompressible, inviscid, and irrotational. ) According to d'Alembert paradox, D' = 0 on a 2D airfoil when the flow is steady, compressible, inviscid, and irrotational. d) According to d'Alembert paradox, D'