In an earlier problem we considered the GE90 engine, one of the world's most powerful engines.
It was already determined that the jet velocity of this engine is 376 metres per second. Suppose that this Boeing 777 flies at 11 kilometres at M=0.82, what is then the jet efficiency of this engine (in percent)? Do not include the % sign in your answer.
To find the jet efficiency of the GE90 engine, we need to use the formula for jet efficiency:
jet efficiency = (jet velocity / flight velocity) x 100
First, we need to convert the flight velocity from kilometers per hour to meters per second:
11 kilometers = 11,000 meters (since there are 1000 meters in one kilometer)
11,000 meters / 3600 seconds = 3.055 meters per second (approx.)
Next, we need to calculate the flight velocity at M=0.82 using the equation:
flight velocity = speed of sound x Mach number
The speed of sound at sea level is approximately 340 meters per second.
flight velocity = 340 meters per second x 0.82
flight velocity = 278.8 meters per second (approx.)
Finally, we can calculate the jet efficiency:
jet efficiency = (jet velocity / flight velocity) x 100
jet efficiency = (376 meters per second / 278.8 meters per second) x 100
jet efficiency = 134.93
The jet efficiency of the GE90 engine is approximately 134.93%.
To find the jet efficiency of the GE90 engine, we need to calculate the ratio of the actual jet velocity to the ideal jet velocity. The ideal jet velocity can be calculated using the formula:
Videal = M * speed of sound
Here, M is the Mach number and the speed of sound at sea level is approximately 340.29 meters per second.
Let's calculate the ideal jet velocity first:
M = 0.82
speed of sound = 340.29 m/s
Videal = 0.82 * 340.29 = 278.90 m/s (approx.)
Now, we can find the jet efficiency using the formula:
Efficiency = (Actual jet velocity / Ideal jet velocity) * 100
Actual jet velocity = 376 m/s (given)
Efficiency = (376 / 278.90) * 100
Efficiency ≈ 134.85
Therefore, the jet efficiency of the GE90 engine is approximately 134.85 percent.
To find the jet efficiency of the GE90 engine, we first need to know the jet thrust of the engine.
Jet thrust can be calculated using the equation:
Thrust = (Engine Mass Flow Rate) * (Jet Velocity)
We're given the jet velocity as 376 meters per second, but we don't have the engine mass flow rate. However, we can find it using the given information about the Boeing 777.
The speed of the Boeing 777 is given as 11 kilometers at M=0.82. We need to convert this speed to meters per second.
1 kilometer = 1000 meters,
So, 11 kilometers = 11,000 meters.
Mach number is the ratio of the speed of an object to the speed of sound in the medium.
To convert Mach number to velocity, we need to know the speed of sound. The speed of sound at sea level is approximately 343 meters per second.
So, to find the velocity of the Boeing 777, we can multiply the Mach number (0.82) by the speed of sound (343 m/s).
Velocity = Mach Number * Speed of Sound
Velocity = 0.82 * 343 m/s
Velocity = 281.26 m/s (approximately)
Now that we know the velocity of the Boeing 777, we can calculate the mass flow rate of the engine.
We can assume that the mass flow rate of the engine is equal to the thrust divided by the jet velocity (based on the conservation of mass).
Mass Flow Rate = Thrust / Jet Velocity
Mass Flow Rate = (Boeing Thrust) / 281.26 m/s
The thrust of the Boeing 777 at M=0.82 can be obtained from aircraft performance tables or specifications. Let's assume it is 680 kN (kilonewtons), where 1 kN = 1000 N.
Thrust = 680,000 N
Now we can calculate the mass flow rate:
Mass Flow Rate = 680,000 N / 281.26 m/s
Next, to calculate jet efficiency, we need to know the fuel flow rate of the engine.
Fuel Flow Rate can be calculated using the equation:
Fuel Flow Rate = (Engine Mass Flow Rate) / (Specific Fuel Consumption)
The specific fuel consumption is the amount of fuel required for a given amount of thrust.
To find the specific fuel consumption, we need to refer to engine performance data or specifications. Let's assume it is 15 g/(kN·s), where g is grams.
Specific Fuel Consumption = 15 g/(kN·s)
Now we can calculate the fuel flow rate:
Fuel Flow Rate = (Mass Flow Rate) / (Specific Fuel Consumption)
Fuel Flow Rate = (Engine Mass Flow Rate) / (Specific Fuel Consumption)
Finally, we can calculate the jet efficiency:
Jet Efficiency = (Jet Velocity * Jet Thrust) / (Fuel Flow Rate)
Substituting the values we obtained earlier:
Jet Efficiency = (376 m/s * Jet Thrust) / Fuel Flow Rate
Let's calculate the jet efficiency using these formulas and the values given.