A manometer $90$cm long $7\mathrm{.}0$mm inside diameter glass tube is $2/3$rd filled with water. The manometer is subjected to a pressure differential of $5500$N$/$m$2.$Determine $($a$)$ Time constant, $($b$)$ Damping coefficient. Suggest design of the manometer considering the initial transient state. Given: Density of water$=1000$kg$/$m$3,$ viscosity of water$=1$mN$-$s$/$m$2.$