Question

A P - 51 Musta ng (WWII plane) is tested in the large wind tunnel at NASA Ames. The plane has a pitot - static probe system mounted. We want to test the P - 51 at a flight speed of 160 mph and altitude of 40,000 ft. T he wind tunnel’s test section has a cross - sectional area of 5000 ft 2 and a reservoir area of 100,000 ft 2 .

What pressure is needed in the reservoir to drive this flow?

a. Does Bernoulli’s equation apply here? i. Hint: What flow condition is required for Bernoulli’s equation?

b. If 1 60 mph is the true airspeed, what is the static and stagnation pressure? i. Hint: You are given the flight altitude as 40,000 ft.

c. W h at reservoir pressure is needed to achieve this test section velocity and pressure?

Answer 1

Bernoulli equation requires the condition that the density is invariant along stream line. Here, in this case the plane velocity is less than 0.3 Mach thus the flow can be considered incompressible and also at that height the viscosity is also less and can be neglected. Thus the Bernoulli's equation can be applied.

Static pressure at 40,000ft = 2.73 Psi = 18.82 kpa

b)Apply Bernoulli's equation between stagnation point and any point along streamline on atmosphere

v = 75 m/s

P_s = 19.632 kpa = 2.847 Psi

c) apply Bernoulli equation between reservoir and wind tunnel

In the reservoir the air is assumed to be stored at same density

From above equation we know the RHS equals 19.632kpa

Let us assume the air is stored at

Reservoir pressure = 19.632 * 0.3026*9.81

= 58.277K.pa = 8.45 Psi