$6\mathrm{.}1.$ Using the identity given in equation $(6\mathrm{.}10),$ show that the vorticity distribution

$()=2U_{}\frac{1+cos}{sin}$

satisfies the condition that flow is parallel to the surface $[$i$.$e$.,$ equation $(6\mathrm{.}8)].$ Show that the

Kutta condition is satisfied. Sketch the $2\frac{}{U_{}}$ distribution as a function of $\frac{x}{c}$ for a section

lift coefficient of $0\mathrm{.}5.$ What is the physical significance of $2\frac{}{U_{}}?$ What angle of attack is

required for a symmetric airfoil to develop a section lift coefficient of $0\mathrm{.}5?$

Using the vorticity distribution, calculate the section pitching moment about a point

$0\mathrm{.}75$ chord from the leading edge. Verify your answer, using the fact that the center of pres$-$

sure $(x_{cp})$ is at the quarter chord for all angles of attack and the definition for lift.