$9\mathrm{.}19$ An $8\mathrm{.}0-$in$.-$diameter elbow meter has a coefficient $C=0\mathrm{.}75$ when installed in a water line. The meter is connected to a mercury manometer having a $24-$in$.$ scale that is graduated in units of $0\mathrm{.}05$ in$.$

$($a$)$ Determine the sensitivity of the instrument in terms of cubic feet per second and inches of nereury.

$($b$)$ When $h=20\mathrm{.}0$ inches of mercury, what is the change in volume flow rate $Q$ corresponding to a scale reading error of $0\mathrm{.}10$ in$.?$

$($c$)$ How significant is the $0\mathrm{.}10-$ in$.$ reading error when $h=4\mathrm{.}0$ in$.?$