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 engine, we need to use the equation:
Efficiency = (Jet Velocity / Flight Velocity) * 100
Given:
Jet Velocity = 376 m/s
Flight Velocity = 11 km (convert to m) * 0.82 (Mach number)
Flight Velocity = 11 km * 1000 m/km * 0.82 = 9020 m/s
Now, substitute these values in the equation to find the jet efficiency:
Efficiency = (376 m/s / 9020 m/s) * 100
Efficiency = 0.0417 * 100
Efficiency = 4.17
Therefore, the jet efficiency of this engine is 4.17 (without the % sign).
To find the jet efficiency of the engine, we need to determine the actual velocity of the jet and the exhaust velocity.
First, let's convert the given distance into meters:
11 kilometers = 11,000 meters
Next, we need to find the actual velocity (V_actual) of the aircraft:
V_actual = Mach number * speed of sound
The speed of sound at sea level is approximately 343 meters per second, so:
V_actual = 0.82 * 343 m/s
V_actual = 281.26 m/s
Now we can calculate the exhaust velocity (V_exhaust):
V_exhaust = V_actual - jet velocity
V_exhaust = 281.26 m/s - 376 m/s
V_exhaust = -94.74 m/s
Since the exhaust velocity is negative in this case, it implies that the engine is not efficient.
To calculate the jet efficiency, we use the formula:
Jet Efficiency = (V_exhaust / V_actual) * 100
Jet Efficiency = (-94.74 m/s / 281.26 m/s) * 100
Jet Efficiency = -33.7%
Therefore, the jet efficiency of this engine is -33.7%.
To calculate the jet efficiency of the engine, we need to determine the ratio of the actual velocity of the jet to the theoretical maximum velocity it could achieve.
Let's break down the steps to get the answer:
Step 1: Convert the given speed from kilometers per hour to meters per second.
- The speed of the Boeing 777 is given as 11 kilometers (km).
- To convert km to meters, we multiply by 1000 (1 km = 1000 m).
=> 11 km = 11,000 m.
- To convert hours to seconds, we multiply by 3600 (1 hour = 3600 seconds).
=> 11,000 m = (11,000 * 3600) m/s.
=> 11,000 m/s.
Step 2: Determine the maximum theoretical velocity of the jet.
- The maximum theoretical velocity can be calculated using the formula:
Vmax = M * Ve,
where Vmax is the maximum theoretical velocity,
M is the Mach number,
and Ve is the exhaust velocity.
- The Mach number, M, is given as 0.82.
- The exhaust velocity, Ve, is given as 376 meters per second (m/s).
=> Vmax = 0.82 * 376 m/s.
=> Vmax = 307.52 m/s.
Step 3: Calculate the jet efficiency.
- Jet efficiency is determined by the ratio of the actual jet velocity to the maximum theoretical velocity.
- To calculate the jet efficiency, we divide the actual velocity by the maximum theoretical velocity and multiply by 100 to get the percentage.
=> Jet Efficiency = (Actual Velocity / Maximum Theoretical Velocity) * 100.
=> Jet Efficiency = (11,000 m/s / 307.52 m/s) * 100.
By evaluating this expression, the jet efficiency of the engine is approximately 3583.37%.
Please note that the result is expressed in percent but without the % sign, as instructed.