13 11/25

1. According to potential flow theory, what would be the lift per unit span of a flat-plate airfoil of chord 2 m moving at 100 m/s at sea level at an angle of attack of 10 degrees? What would be the drag? What would be the circulation around the airfoil?

2. Compute approximate values of the Reynolds number of the following flows:
   1. your car, assuming it drives;
   2. a passenger plane flying somewhat below the speed of sound (assume an aerodynamic chord of 30 ft);
   3. flow in a 1 cm water pipe if it comes out of the faucet at .5 m/s,
   In the last example, how fast would it come out if the Reynolds number is 1? How fast at the transition from laminar to turbulent flow?

3. Using suitable neat graphics, show that the boundary layer variables for the boundary layer around a circular cylinder of radius $r_0$ in a cross flow with velocity at infinity equal to $U$ and pressure at infinity $p_\infty$ are given by:
   
   $$x=r_0\theta \qquad y=r-r_0 \qquad u=v_\theta \qquad v=v_r$$
   
   

4. Write the appropriate equations for the unsteady boundary layer flow around a circular cylinder in terms of the boundary layer variables above. Next rewrite these equations in terms of the polar coordinates $r$, $\theta$, $v_r$, $v_\theta$, and $p$.

5. Compare the equations you got above with the exact equations in polar coordinates, (the continuity equation and the $r$ and $\theta$ momentum equations). Explain for each discrepancy why the difference is small if the boundary layer is thin.