11 11/14

1. Find the ideal flow about an ellipse whose horizontal axis length is $\frac53$ its vertical axis. Is the velocity still $2U$ at the top of the ellipse like for a cylinder? If not, how big is it?

2. From the airfoil program page,, click on and read program airfoil.m. Save airfoil.m as type ``all files'' and run it in Matlab or octave 3.0 or higher. You will get plots of flow past a cylinder in the $\zeta$ plane ($\zeta_2$ in your notes) and an unimpressive flush flow past an infinitely thin plate. So set the radius r0 to a value a bit greater than one to give the airfoil thickness. Use screen capture or the print command to make a hardcopy of the airfoil plot. The airfoil does not seem to produce much lift. Set the angle of attack alp to a suitable value to fix that and plot. Darn, still no lift. Set the circulation Gamma to some nonzero value (the program will correct the value you put in.) Replot.

3. Plot the lines of constant pressure coefficient $C_p=(p-p_\infty)/\frac12\rho U^2$ on the airfoil with alpha equal to 20 and r0 equal to 1.1. Stay completely in complex variables to compute the pressure coefficient. You can use the abs function to get the magnitude of $W$ after you have found it. Use the chain rule. Print out the modified program and the isobars.

4. Would it not be nice to have some camber? Change program airfoil.m to produce an airfoil with positive camber. You will need to correct one line in the program. Print out the modified program and the airfoil.

5. 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?

6. 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?