The method of images uses precisely oriented collections of sources, sinks, and vortices to establish artificial walls and so simulate more complicated flow fields. One such flow field is formed by positioning two counter-rotating vortices a distance, \(d\), from the location of the hypothetical wall (Figure P9.21). The stream function for this flow is given by:

\[\psi=\frac{q_{o}}{4 \pi}\left\{\ln \left[(x-d)^{2}+y^{2}\right]+\ln \left[(x+d)^{2}+y^{2}\right]\right\}\]

a. Demonstrate that there is no flow through the wall.

b. How does the velocity vary along the length of the wall?

c. What is the pressure distribution along the wall?

Transcribed Image Text:

FIGURE P9.21 Image Vortex Vortex