To find the thrust of the jet engine, we can use the conservation of momentum principle. By this principle, the rate of change of momentum of the exhaust gases must equal the total force acting on the system. We have to find the net momentum flux and then the thrust.
First, let's find the momentum flux of the incoming air.
momentum_flux_in = (mass_flow_rate_air) * (velocity_air)
momentum_flux_in = (77.0 kg/s) * (180 m/s) = 13860 kg*m/s²
Then, we'll find the momentum flux of the exhaust gases.
momentum_flux_exhaust = (mass_flow_rate_exhaust) * (velocity_exhaust)
mass_flow_rate_exhaust = (77.0 kg/s + 3.15 kg/s) = 80.15 kg/s
velocity_exhaust = (180 m/s + 595 m/s) = 775 m/s
momentum_flux_exhaust = (80.15 kg/s) * (775 m/s) = 62096.25 kg*m/s²
Now we can find the net momentum flux or change in momentum per unit time (dm/dt).
net_momentum_flux= momentum_flux_exhaust - momentum_flux_in
net_momentum_flux = 62096.25 kg*m/s² - 13860 kg*m/s² = 48236.25 kg*m/s²
Finally, we can calculate the thrust of the jet engine using the definition of thrust (T).
T = (dm/dt)
Plugging the net momentum flux we found above,
T = 48236.25 kg*m/s²
To express the thrust in kiloNewtons (kN), we have to divide it by 1000.
T = 48236.25 kg*m/s² / 1000 = 48.23625 N.
However, the correct answer is given as 33.8 kN. So, somewhere we have made a mistake. Let's verify the solution.
At second glance, we notice that we have made an error in calculating the velocity of exhaust gases. It was given that exhaust gases are ejected at 595 m/s *relative to the speed of the aircraft*.
This means that we should use 595 m/s as the velocity of the exhaust gases instead of adding it to the aircraft's speed. Now let's correct the calculations.
momentum_flux_exhaust = (mass_flow_rate_exhaust) * (velocity_exhaust_relative)
momentum_flux_exhaust = (80.15 kg/s) * (595 m/s) = 47689.25 kg*m/s²
Now we can find the net momentum flux with the corrected values.
net_momentum_flux = momentum_flux_exhaust - momentum_flux_in
net_momentum_flux = 47689.25 kg*m/s² - 13860 kg*m/s² = 33829.25 kg*m/s²
Now, we can calculate the thrust of the jet engine.
T = (dm/dt) = 33829.25 kg*m/s²
Converting the thrust to kiloNewtons (kN),
T = 33829.25 kg*m/s² / 1000 = 33.82925 kN
Rounding off to one decimal place, the thrust of the jet engine is 33.8 kN, which matches the correct answer.
A jet aircraft is traveling at 180 m/s in horizontal flight. The engine takes in air at a rate of 77.0 kg/s and burns fuel at a rate of 3.15 kg/s. The exhaust gases are ejected at 595 m/s relative to the speed of the aircraft. Find the thrust of the jet engine. (Take the direction the jet is going to be the positive direction. Indicate the direction with the sign of your answer.)
The correct answer is 33.8 kN can someone show me how to get that answer??
1 answer