A Pitot tube is mounted in the test section of a low-speed subsonic wind tunnel. The flow in the test section has a velocity, static pressure, and temperature of 150 mi/h, 1 atm, and 70∘F, respectively. Calculate the pressure measured by the Pitot tube.

Given Information:

Static Pressure = P = 1 atm

Temperature = T = 70°F

Velocity = v = 150 mi/hr

Required formation:

Pressure of Pilot Tube = P₀ = ?

Answer:

Pressure of Pilot Tube = P₀ = 2172.36 lb/ft²

Solution:

Units Conversion:

(1 atm = 2116.22 lb / ft²)

Static Pressure = P = 1 atm = 2116.22 lb/ft²

(1° F = 459.67° R)

Temperature = T = 70°F = 70 + 459.67 = 529.67° R

(1mi/hr = 1.467 ft/sec)

Velocity = v = 150 mi/hr = 220 ft/sec

Density of Test Section

Density = ρ = P/RT

Where R is the idea gas constant 1717 (ft-lbf/slug-°R)

ρ = 2116.22/1717*529.67 = 0.00232 slug/ft³

Pressure of Pilot Tube

P₀ = P + (1/2) * ρ*v²

P₀ = 2116.22 + (1/2) * 0.00232*220²

P₀ = 2172.36 lb/ft²