Combination Fields of Flow Continued—Kutta-Joukowski Theorem

Abstract

Taking, as before, the rectilinear flow parallel to —X we have from II 4; IV 8:

$$\varphi = - Ux + \mu \log \frac{{{r_2}}}{{{r_1}}}$$

(1.1)

$$\psi = - Uy + \mu ({\theta _2} - {\theta _1})$$

(1.2)

$$w = - Uz + \mu \log \frac{{z - a}}{{z + a}}$$

(1.3)

$$u = - U + \mu \left[ {\frac{{x - a}}{{r_2^2}} - \frac{{x + a}}{{r_1^2}}} \right]$$

(1.4)

$$v = uy\left[ {\frac{1}{{r_2^2}} - \frac{1}{{r_1^2}}} \right]$$

(1.5)