Question

A source of strength m, which by itself produces radial streamlines as indicated by the dashed arrows, is placed a distance L away from a vertical wall (occupying the yz-plane), at point S (x=L,y= 0). To compute the flow field in the presence of the wall, the method of images can be employed: A second source of strength m is placed a distance L from the wall on the other side, at S′ (x=−L,y= 0). The combined flow field of the two sources (solid arrows) simulates the presence of the wall. (a) Assuming incompressibility, write down the velocity potential for the combined flow of S and S′. (b) Show that there is no flow through the plane occupied by the wall. (c) Determine the velocity distribution along the wall. (d) Determine the pressure distribution along the wall, assuming p = p0 far away from the source and the wall. Gravity is absent.

Answer 1

paje 1 SCUTCC (a) The wbily pen mln ,tr a Source Source s'(1-L ; y=0 、 1-L Now usth principle potn tel is given y CS

page-2 (T-L) (mL) (t-L) 2xy (b) The plane accupitdby the ll R-L

pige -3 Laplace efuckimis satisfred (c) The velačty dsthrbutorn alig the well at(Lo) みーDx ry 2 TYx r'ty -2my and V2 d) vly presure dshibukin olany the t 2 at p ox ay CS