$8\mathrm{.}7$ Given a diesel engine with a bore $=125$ mm$,$ stroke $=150$ mm$,$ compression ratio $=15.$ The fuel flow rate at $1800$ rev$/$min is $1\mathrm{.}6$ g$/$s per cylinder. The intake air flow rate is measured to be $80$ g$/$s at an intake temperature and pressure of $300$ K$,1$ atm. Optical diagnostics are used to measure the CO$2$ and O$2$ concentration in$-$cylinder before the exhaust valve opens and it is determined that the equivalence ratio of the trapped gases is $0\mathrm{.}5.$ Find $($a$)$ the charging efficiency, $($b$)$ the delivery ratio, and $($c$)$ the trapping efficiency.