Question

A wind tunnel draws atmospheric air at 20°C and 101.3 kPa by a large fan located near the exit of the tunnel. If the air velocity in the tunnel is 80 m/s, determine the pressure in the tunnel.

Answer 1

The pressure in the tunnel is 97.45 kPa

Step-by-step explanation:

Given;

atmospheric pressure, P₁ = 101.3 kPa

air velocity in the tunnel, v₂ = 80 m/s

density of air at 20°C, ρ = 1.204 kg/m³

pressure in the tunnel, P₂ = ?

Apply Bernoulli's equation;

P₁ + ¹/₂ρv₁² + ρgz₁ = P₂ + ¹/₂ρv₂² + ρgz₂

v₁ = 0

z₁ = z₂ = 0

P₁ = P₂ + ¹/₂ρv₂²

P₂ = P₁ - ¹/₂ρv₂²

P₂ = 101.3 kPa - (0.5 x 1.204 x 80²)

P₂ = 101.3 kPa - 3.8528 kPa

P₂ = 97.45 kPa

Therefore, the pressure in the tunnel is 97.45 kPa