The pressure difference between before and after the air filter as measured by the U$-$tube manometer is $10$ in$.$ H$2$O$.$ Air temperature is $26,$ instrument pressure is $60$ Ib$\_$f$/$in$^2.($a$)$ Find the pressure drop in units of lb$\_$f$/$in$^2$ and atm. $($b$)$ Find the error in ignoring the density of air at the manometer connection.

The answer is $($a$)0\mathrm{.}358$ lb$\_$f$/$in$^2$ and $0\mathrm{.}0245$ atm, $($b$)0\mathrm{.}62\%$

$*$Please remember that it is about lb$\_$f$,$ not just lb