1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

11.8 • THE JOUKOWSKI AIRFOIL 411

Figure 11 .58

9. Consider the complex potential F (z) = -iArcsinz.

(a) Show that F (z) determines the ideal fluid flow through the aperture

from - 1 to +1, as indicated in Figure 11.59.

Figure 1 1.59

(b) Show that the streamline 1/1 ( x, y) = c for the flow is a portion of the

x2 y2

hyperbola --- --= 1.

sin^2 c cos^2 c

11.8 The Joukowski Airfoil

The Russian scientist N. E. Joukowski studied the function

1

J(z)=z+-.

z