The pipe orifice in Fig. $58$ has a diameter of $4$ in$.$ and a coefficient of discharge of $0\mathrm{.}650.$ The pipe diameter is $10$ in$.$ The manometer connections are attached to a differential gage partly filled with mercury, the remainder of the tube being filled with the same liquid as that flowing in the pipe, which is a heavy fuel oil at $70\backslash$deg F$.$ Compute the discharge when the difference in mercury levels in the gage is: $($a$)2\mathrm{.}10$ in$.$; $(6)13\mathrm{.}5$ in$.$; $($c$)27\mathrm{.}6$ in$.$; $($d$)52\mathrm{.}2$ in$.$ Provide illustration and complete solution. Final answer given is $0\mathrm{.}715,1\mathrm{.}82,2\mathrm{.}60,3\mathrm{.}57$ cfs$.$