Student #: Question 3 (20 Points): In low speed, incompressible flow, the following experimental data are obtained for an NACA 4412 airfoil section at an angle of attack of 4^circ ,C_(1)=0.85 and c_(m,c/4)=-0.09 Calculate the location of center of pressure.

To calculate the location of the center of pressure for an airfoil section in low-speed, incompressible flow, we can use the following formula:<br /><br />\[ x_{cp} = \frac{c_{1} \cdot x_{0} + c_{m,c/4} \cdot \frac{c_{1} \cdot x_{0}}{4}}{c_{1}} \]<br /><br />Where:<br />- \( x_{cp} \) is the location of the center of pressure<br />- \( c_{1} \) is the lift coefficient<br />- \( c_{m,c/4} \) is the center of pressure coefficient<br />- \( x_{0} \) is the chord length<br /><br />Given:<br />- \( c_{1} = 0.85 \)<br />- \( c_{m,c/4} = -0.09 \)<br />- \( x_{0} = 1 \) (assuming the chord length is 1 for simplicity)<br /><br />Substituting the given values into the formula:<br /><br />\[ x_{cp} = \frac{0.85 \cdot 1 + (-0.09) \cdot \frac{0.85 \cdot 1}{4}}{0.85} \]<br /><br />\[ x_{cp} = \frac{0.85 - 0.01875}{0.85} \]<br /><br />\[ x_{cp} = \frac{0.83125}{0.85} \]<br /><br />\[ x_{cp} \approx 0.98 \]<br /><br />Therefore, the location of the center of pressure is approximately 0.98 chord lengths from the leading edge.