Start with expressions for specific thrust and thrust for a turbofan engine. Assume and pe$=$pa$.$ Assuming $U_{e,p}=4u$ and $U_{e,f}=2u,$ and flight speed of $u,$ derive expressions for

$($a$)$ Thrust Ratio $($thrust of bypass flow to primary flow$)$

$($b$)$ Specific Thrust $($use the total mass flow of air for this$)$

$($c$)$ Thrust Specific Fuel Consumption