Question

(a) Write a code to demonstrate flow over a Rankine half body using contour and vector plots. Rankine half body given that q the strength of the source q-9 m/s and the uniform flow magnitude U m/s is the number against your name. (b) Plot a pressure profile as a function of distance (c) Describe an application for a Rankine half body.

Answer 1

Flow Around a Rankine Half-Bodv The Rankine half-body is the curve that satisfies the equation equation r =-, cot( The parameter h describes the width of the half-bodv Indeed. as x →。о ) for-h s, sh t is easy to see that y-th 2-and that total width of the body approaches h Here s a graph of the Ran ne half-body ParametricPlot[{-tcot [2자] , t}, {t,-h , h}, PlotRanget-h, 3h), t-h, . AspectRatio → Automatic, PlotLabel -"Graph of the Rankine Half-Body']: (So that the x and Y axes have the same scale ) Graph of the Rankine Half-Body 1. 0.75 0. 5 0.25 -0.5 0. 5 1.5 2.5 -0.2 -0.5 0.75 Note that the Rankine half-body does not pass through the origin; rather its vertex is at the point --, o) : indeed Clear [hl Series[-yCot [___ ] a tY,0, 4) {Y 2π 3h 45 h The vector field that described the flow of a fluid around a Rankine half-body is given by with the parameters h - which gives the width of the Rankine half-body, and U - which gives the velocity of the fluid far from the body