$(10$ pts$.)$ A turbofan engine with a bypass ratio $=5$ operates with a compressor pressure ratio of $30$ and a combustor exit temperature of $1700K.$ Determine the specific thrust, specific fuel consumption, and the overall efficiency for a fan pressure ratio of ${}_f=1\mathrm{.}5$ with the efficiency ${}_f=0\mathrm{.}85.$ The flight Mach number is $M=0\mathrm{.}85$ at an altitude of $40,000ft(12,200m)$ where the ambient pressure and temperature are $18\mathrm{.}75$ kPa and $216\mathrm{.}7K,$ respectively. The fuel heating value is $h_{PR}=45,000k\frac{J}{k}g,$ and the component efficiencies listed below. Assume $=1\mathrm{.}4$ for the inlet, fan, and compressor, and $=1\mathrm{.}33$ for the combustor, turbine, and nozzle. Take the gas everywhere to have a constant molecular weight of $29k\frac{g}{k}$mol, and use the approximation $m_t^{}{c}_{pt}=m_c^{}{c}_{pc}$ to account for the fuel flow.

Component efficiencies: Diffuser $($core and fan$),{}_d=0\mathrm{.}97$; compressor, ${}_c=0\mathrm{.}85$; burner, ${}_b=0\mathrm{.}96$; turbine, ${}_t=0\mathrm{.}90$; and nozzle $($core and fan$){}_n=0\mathrm{.}98.$

How do the specific thrust, specific fuel consumption, and the overall efficiency change if the bypass ratio is increased to $=10?$