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McDonnell Aircraft's F2H Banshee fighter first flew in 1947 and some served into the 1960s. The aircraft used 2 Westinghouse J34 -WE-30 turbojets delivering 14,000 N of thrust each.giving a maximum speed of 945km/h and a range of almost 2090 km . The F2H could climb at about 2250m/min and reach a service ceiling of 14,800 m. If the airplane is operating at an altitude of 6100 m with a choked nozzle exit (Me=1, Ye=1.33) and the nozzle exit area A_(e)=0.116m^2 and the exit pressure is p_(e)=62 kPa find the following; (a) gross thrust produced, (b) percentage of gross thrust caused by the pressure imbalance at the nozzle exit, (c) exit mass flow if T_(e)=537.8^circ C (d) ram drag at a flight velocity of 167.6m/s f/a=0.02 (e) net thrust, (f) thrust power produced, (g) exit velocity V_(e) (h) effective exhaust velocity V_(eff) (i) propulsive efficiency n_(p) (i) nth and n_(0) for Q_(f)=43.96MJ/kg) (k) the specific fuel consumption, cj
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To solve the given problem, we need to use various principles of fluid dynamics and thermodynamics. Let's go through each part step-by-step.### Given Data:- Altitude:
m- Choked nozzle exit:
- Specific heat ratio:
- Nozzle exit area:
m²- Exit pressure:
kPa- Exit temperature:
K (converted to Kelvin)- Flight velocity:
m/s- Fuel-to-air ratio:
- Heat of combustion:
MJ/kg### Constants:- Universal gas constant:
J/(kg·K)### Part (a): Gross Thrust ProducedGross thrust (
) is given by:
Since the nozzle is choked, the exit Mach number
, and we can find the exit velocity
using:
Next, we need the mass flow rate (
):
Where
is the density at the exit, which can be found using the ideal gas law:
Now, calculate the mass flow rate:
Finally, calculate the gross thrust:
Assuming standard atmospheric pressure at 6100 m altitude is approximately 47.35 kPa:
### Part (b): Percentage of Gross Thrust Caused by Pressure Imbalance
Percentage of gross thrust due to pressure imbalance:
### Part (c): Exit Mass Flow if
Already calculated in part (a):
### Part (d): Ram Drag at a Flight Velocity of 167.6 m/sRam drag (
) is given by:
### Part (e): Net ThrustNet thrust (
) is given by:
### Part (f): Thrust Power ProducedThrust power (
) is given by:
### Part (g): Exit Velocity
Already calculated in part (a):
### Part (h): Effective Exhaust Velocity
Effective exhaust velocity (
) is given by:
### Part (i): Propulsive Efficiency
Propulsive efficiency (
) is given by:
### Part (j): Thermal Efficiency
and Overall Efficiency
Thermal efficiency (
) is given by:
Where
is the fuel mass flow rate:
Now, calculate thermal efficiency:
Overall efficiency (
) is given by:
### Part (k): Specific Fuel Consumption
Specific fuel consumption (
) is given by:
These calculations provide the required answers for each part of the problem.