Chapter 1, Problem 1.7P

The drag on the hull of a ship depends in part on the height of the water waves produced by the hull. The potential energy associated with these waves therefore depends on the acceleration of gravity g. Hence, we can state that the wave drag on the hull is $D=f\left({\rho }_{\infty },V_{\infty },c,g\right)$ where c is a length scale associated with the hull, say, the maximum width of the hull. Define the drag coefficient as $C_{D}K\equiv D/q_{\infty }{c}^2$. Also, define a similarity parameter called the Frnude number, $Fr=V/\sqrt{gc}$. Using Buckingham’s pi theorem, prove that $C_D=f\left(\text{Fr}\right)$.