High School

Air at 20 kPa flows with a Mach number of 1.5. What is the stagnation pressure of this air?

A. 22.2 kPa
B. 41.7 kPa
C. 56.2 kPa
D. 73.4 kPa

Answer :

The stagnation pressure of this air is D. 73.4 kPa.

To find the stagnation pressure, we can use the formula:
P0 = P + (1/2) * ρ * V²

Where P0 is the stagnation pressure, P is the static pressure, ρ is the density of air, and V is the velocity of the air.

We are given the static pressure P as 20 kPa and the Mach number as 1.5. We can use the formula for Mach number:
Mach number = V / a

Where a is the speed of sound in air. For simplicity, we can assume that the air is at standard conditions, where a = 340 m/s.
So, 1.5 = V / 340
V = 1.5 * 340 = 510 m/s

Next, we need to find the density of air at this condition. We can use the formula:
ρ = P / (R * T)

Where ρ is the density, P is the pressure, R is the gas constant for air (287 J/kg*K), and T is the temperature. Again, assuming standard conditions, T = 273 K.
ρ = 20,000 / (287 * 273) = 0.269 kg/m³

Now we can plug in these values to find the stagnation pressure:
P0 = 20,000 + (1/2) * 0.269 * 510²
P0 = 73,360 Pa or 73.4 kPa (rounded to 3 significant figures)

Therefore, the answer is (D) 73.4 kPa.

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