Question

Problem 1: As shown in the figure a flying airplane produces wing-tip vortices, i.e. swirling flow near the end of its wings. In certain cases, this flow can be approximated by the velocity field, $u = -\frac{Ky}{x^2 + y^2}$ and $v = \frac{Kx}{(x^2 + y^2)}$ where $K > 0$. a) Show that the velocity field satisfy the continuity equation. b) Show that if the flow is irrotational or not. c) Wing tip vortices can reduce the efficiency of the airplane, do some research and explain what kind of measures can be taken to improve the efficiency and the strength of the wingtip vortices. You can find some impressive videos of wing tip vortices on youtube.

          Problem 1: As shown in the figure a flying airplane produces wing-tip vortices, i.e. swirling flow near the end of its wings. In certain cases, this flow can be approximated by the velocity field, $u = -\frac{Ky}{x^2 + y^2}$ and $v = \frac{Kx}{(x^2 + y^2)}$ where $K > 0$.
a) Show that the velocity field satisfy the continuity equation.
b) Show that if the flow is irrotational or not.
c) Wing tip vortices can reduce the efficiency of the airplane, do some research and explain what kind of measures can be taken to improve the efficiency and the strength of the wingtip vortices. You can find some impressive videos of wing tip vortices on youtube.

Problem 1: As shown in the figure a flying airplane produces wing-tip vortices, i.e. swirling flow near the end of its wings. In certain cases, this flow can be approximated by the velocity field, u = -(Ky)/(x^2 + y^2) and v = (Kx)/((x^2 + y^2)) where K > 0.
a) Show that the velocity field satisfy the continuity equation.
b) Show that if the flow is irrotational or not.
c) Wing tip vortices can reduce the efficiency of the airplane, do some research and explain what kind of measures can be taken to improve the efficiency and the strength of the wingtip vortices. You can find some impressive videos of wing tip vortices on youtube.

Added by Laura B.

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