Air enters a jet engine through section 1 with an area of A1=0.5 m2 at a (relative) speedof 250 m/s. The pressure at the entrance is atmospheric pressure (approximately 105 Pa)and the temperature is 300 K. Inside the engine, the injected fuel mixes perfectly withair, with fuel to air mass ratio of 1:30. The enthalpy and the kinetic energy flow rate ofthe fuel can be neglected at the fuel inlet. The combustion releases a heat per unit mass(of air) of 200 kJ/kg, after which the mixture is expanded through a nozzle to the exitsection 2 whose area is A2= 0.4 m2. The product of combustion can be taken to havethe same properties of air (such as Cp=1.005 kJ/kg k, γ=1.4 and so on). The nozzleperfectly expands the flow such that at the exit 2, the pressure is atmospheric pressure.The temperature of the flow at the exit is 400 K. The figure below shows a roughschematic of the engine and the flow. Find the thrust generated by the engine.
Question
Air enters a jet engine through section 1 with an area of A1=0.5 m2 at a (relative) speedof 250 m/s. The pressure at the entrance is atmospheric pressure (approximately 105 Pa)and the temperature is 300 K. Inside the engine, the injected fuel mixes perfectly withair, with fuel to air mass ratio of 1:30. The enthalpy and the kinetic energy flow rate ofthe fuel can be neglected at the fuel inlet. The combustion releases a heat per unit mass(of air) of 200 kJ/kg, after which the mixture is expanded through a nozzle to the exitsection 2 whose area is A2= 0.4 m2. The product of combustion can be taken to havethe same properties of air (such as Cp=1.005 kJ/kg k, γ=1.4 and so on). The nozzleperfectly expands the flow such that at the exit 2, the pressure is atmospheric pressure.The temperature of the flow at the exit is 400 K. The figure below shows a roughschematic of the engine and the flow. Find the thrust generated by the engine.
Solution
To find the thrust generated by the engine, we need to calculate the mass flow rate, the exit velocity, and the entrance velocity.
-
First, we calculate the mass flow rate using the equation: Mass flow rate = Density * Area * Velocity We know that the density of air can be calculated using the equation: Density = Pressure / (R * Temperature) Where R is the specific gas constant for air, which is approximately 287 J/kgK. So, the density at the entrance is: Density = 105 Pa / (287 J/kgK * 300 K) = 1.22 kg/m^3 Therefore, the mass flow rate is: Mass flow rate = 1.22 kg/m^3 * 0.5 m^2 * 250 m/s = 152.5 kg/s
-
Next, we calculate the exit velocity using the equation: Velocity = sqrt(2 * Cp * (T_exit - T_0)) Where Cp is the specific heat capacity at constant pressure, T_exit is the exit temperature, and T_0 is the initial temperature. So, the exit velocity is: Velocity = sqrt(2 * 1.005 kJ/kg*K * (400 K - 300 K)) = 447.21 m/s
-
The entrance velocity is given as 250 m/s.
Finally, we calculate the thrust using the equation: Thrust = Mass flow rate * (Exit velocity - Entrance velocity) So, the thrust is: Thrust = 152.5 kg/s * (447.21 m/s - 250 m/s) = 30,089.775 N
Therefore, the thrust generated by the engine is approximately 30,089.775 N.
Similar Questions
A perfect gas stored in a large reservoir exhausts into the atmosphere through aconvergent duct. The reservoir pressure is P0 and temperature is T0. The jet emergesfrom the nozzle at choked conditions with average velocity u, Mach number M,pressure p, temperature T, and density . If the reservoir pressure is increased,then(A) u, M, p, T, and increase(B) u, p, T, and increase, but M remains the same(C) u, M, and T remain the same, but p and increase(D) u, M, T and remain the same, but p increasesQ.40 Consider a general aviation airplane with weight 10 kN and a wing planform areaof 15 m2. The drag coefficient of the airplane is given as02D D LC C KC= + with0 0.025DC =and0.05K = . For level flight at an altitude where the density is0.60 kg/m3 and thrust 1 kN, the maximum cruise speed is(rounded off to the nearest integer)(A) 87 m/s(B) 30 m/s(C) 36 m/s(D) 101 m/s
A gaseous air‑fuel mixture in a sealed car engine cylinder has an initial volume of 600.mL at 1.0atm. To prepare for ignition of the fuel, a piston moves within the cylinder, reducing the volume of the air‑fuel mixture to 50.mL at constant temperature. Assuming ideal behavior, what is the new pressure of the air‑fuel mixture?
If the temperature of the intake air in an internal combustion (IC) engine increases,then its efficiency willGroup of answer choicesDecreaseRemain sameIncreaseNone of these
If the latent heat of vaporisation of liquid Jet-A were accounted for, the fuel-air ratio that gives a particular turbine inlet temperature would be, relative to the case where its latent heat is ignored: Group of answer choices10UnchangedLowerHigher
A diesel engine's piston compresses 16 cm3 of fuel-air mixture into 1 cm3. The pressure changes from 1 atmosphere to 48 atmospheres. If the initial temperature of the gas was 305 K, what was the final temperature?Note: As long as the units for pressure and volume are the same on both sides of the equation, they will cancel. Temperature, however, must be in units of kelvin. Be sure to use the proper number of significant figures.900 K100 K915 K1.09 x 10 -3 K
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.