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)?
To find the jet efficiency, we need to calculate the actual velocity of the jet.
Given:
Speed of sound at sea level (Mach 1) = 343 meters per second
We are told that the Boeing 777 flies at M=0.82, which means:
Actual velocity of the aircraft = M * Speed of sound
= 0.82 * 343 m/s
= 281.26 m/s (approx.)
Now, the efficiency of the jet engine is given by the formula:
Jet efficiency (%) = (Actual velocity / Jet velocity) * 100
Plugging in the values, we get:
Jet efficiency (%) = (281.26 / 376) * 100
= 74.77% (approx.)
Therefore, the jet efficiency of this engine is approximately 74.77%.
To determine the jet efficiency of this engine, we need to calculate the ratio of the actual jet velocity to the ideal jet velocity.
First, let's convert the speed of the Boeing 777 from kilometers per hour to meters per second. We know that 1 kilometer is equal to 1000 meters and 1 hour is equal to 3600 seconds. So, the speed becomes:
11 kilometers/hour = (11 * 1000 meters) / (3600 seconds)
Simplifying,
= 11,000 meters / 3600 seconds
= 3.0556... meters/second (approximately 3.056 meters/second)
Next, we need to calculate the ideal jet velocity. The ideal jet velocity is the theoretical maximum velocity achievable by the engine at a given Mach number. The formula to calculate the ideal jet velocity is as follows:
Ideal jet velocity = Mach number × speed of sound
The speed of sound can be calculated using the formula:
Speed of sound = sqrt(gamma × R × temperature)
Where:
- gamma is the specific heat ratio of the gas (approximately 1.4 for air)
- R is the specific gas constant for air (approximately 287 J/kg·K)
- temperature is in Kelvin
Since the specific heat ratio and the specific gas constant are known values, the only missing information is the temperature.
Without the temperature data, it is not possible to accurately calculate the speed of sound and subsequently the ideal jet velocity. The temperature data would be required to accurately determine the jet efficiency of the engine.
Therefore, without the temperature information, we cannot determine the jet efficiency of this engine.
To calculate the jet efficiency of the engine, we need to determine the actual velocity of the plane and then use the equation for jet efficiency.
Step 1: Convert the given speed in kilometers per hour to meters per second.
11 kilometers = 11000 meters (since there are 1000 meters in a kilometer)
11000 meters / (3600 seconds in an hour) = approximately 3.06 meters per second
Step 2: Calculate the actual velocity of the plane using the Mach number.
Mach number (M) = actual velocity / speed of sound
Given M = 0.82 and the speed of sound is approximately 343 meters per second (at sea level and 20 degrees Celsius):
0.82 = actual velocity / 343
Solving for the actual velocity:
actual velocity = 0.82 * 343
actual velocity ≈ 281 meters per second
Step 3: Calculate the jet efficiency using the following equation:
Jet Efficiency = (actual velocity - jet velocity) / actual velocity * 100
Given the jet velocity is 376 meters per second:
Jet Efficiency = (281 - 376) / 281 * 100
Jet Efficiency = -95 / 281 * 100
Jet Efficiency ≈ -33.81
Therefore, the jet efficiency of this engine is approximately -33.81%. Please note that a negative value indicates that the engine is not operating efficiently in this scenario.