Question

a high-speed subsonic boeing 777 airliner is flying at a pressure altitude of 12 km. a pitot tube on the vertical tail measures a pressure of 2.96x104 n/m2. at what mach number is the airplane flying?

Answer 1

To find the Mach number, we can use the formula: Mach number = velocity of the airplane / speed of sound. By calculating the velocity of the airplane using Bernoulli's equation and the given pressure, and finding the speed of sound at the given altitude, we can determine the Mach number to be approximately 0.882.

Step-by-step explanation:

To determine the Mach number at which the airplane is flying, we need to use the formula:

Mach number = velocity of the airplane / speed of sound

First, let's find the speed of sound. At an altitude of 12 km, the speed of sound is approximately 295 m/s.

Next, we need to find the velocity of the airplane. Velocity can be calculated using Bernoulli's equation as follows:

velocity = √(2 * pressure / density)

Using the given pressure of 2.96x10^4 N/m2 and assuming standard air density (1.225 kg/m3), we can plug in the values to find the velocity.

velocity = √(2 * 2.96x10^4 / 1.225) ≈ 260.23 m/s

Now we can calculate the Mach number:

Mach number = 260.23 / 295 ≈ 0.882

Therefore, the airplane is flying at a Mach number of approximately 0.882.