A) The flow does not satisfy the continuity equation
B) The flow is rotational
C) The flow is irrotational
D) None of the above
Correct Answer: C
Solution :
\[u=x-4\,v,\] \[v=-\,y-4x\] \[\frac{\partial u}{\partial x}=1,\] \[\frac{\partial u}{\partial y}=-4,\] \[\frac{\partial v}{\partial x}=-\,4,\] \[\frac{\partial v}{\partial y}=-\,1\] Continuity equation is: \[\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=1-1=0\]Hence continuity equation is satisfied. For the flow to be irrotational, \[\frac{\partial u}{\partial x}=\frac{\partial v}{\partial y}\] i.e., \[-\,4=-\,4.\] hence the flow is irrorational
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