An airplane is flying in air with a density of 1.29 kg/m3. A pressure gauge measures
the difference in pressure between a point on the nose of the airplane and a point on
the fuselage. The pressure on the nose is higher by 75.0 kPa. What is the speed of
the plane relative to the air?

341 m/s

Explanation:

Use Bernoulli equation:

P₁ + ½ ρ v₁² + ρgh₁ = P₂ + ½ ρ v₂² + ρgh₂

Assuming no elevation change, h₁ = h₂.

P₁ + ½ ρ v₁² = P₂ + ½ ρ v₂²

The velocity of the air at the nose is 0 m/s, so:

P₁ = P₂ + ½ ρ v₂²

ΔP = ½ ρ v₂²

Plugging in values:

75000 Pa = ½ (1.29 kg/m³) v²

v = 341 m/s

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