In a jet engine, air enters from the front, fuel is added farther downstream in the engine, and the fuel and air burn. Thrust is produced when the hot combustion gases leave the engine by expanding through a nozzle at high velocity. Consider a case where a jet engine is being tested on the ground. It is operating at steady-state and uses 0.25 kg/s of jet fuel. The velocity, v, and temperature, T, profiles of the gases exiting the round nozzle have been measured and found to depend only on the radial distance, r, from the center of the nozzle. They are not dependent on the azimuthal position around the nozzle. The measured data can be described approximately by:
T(r) = 1350K - 675 K(r/R) and v(r) = 420m/s - 105m/s (r/R)^2.
where R = 0.25 m is the radius of the nozzle exit of the engine. The pressure and molecular weight of the gas are uniform at the exit with values of 1.0 bar and 28.1 kg/kmol.
A) Using the measured profiles, determine the fuel-air ratio of the engine, i. e., the mass flow rate of fuel entering the engine divided by the mass flow rate of air entering the engine.