P$7\mathrm{.}96$ A Savonius rotor $($Fig$.6\mathrm{.}29$b$)$ can be approximated by the two open half$-$tubes in Fig. P$7\mathrm{.}96$ mounted on a central axis. If the drag of each tube is similar to that in Table $7\mathrm{.}2,$ derive an approximate formula for the rotation rate $\backslash (\backslash$Omega $\backslash )$ as a function of $\backslash ($ U$,$ D$,$ L $\backslash ),$ and the fluid properties $\backslash ((\backslash$rho$,\backslash$mu$)\backslash ).$