Answer:
1.75 atm
Explanation:
Mass is conserved, so the mass flow before the constriction equals the mass flow after the constriction.
m₁ = m₂
ρQ₁ = ρQ₂
Q₁ = Q₂
v₁A₁ = v₂A₂
v₁ πd₁²/4 = v₂ πd₂²/4
v₁ d₁² = v₂ d₂²
Now use Bernoulli equation:
P₁ + ½ ρ v₁² + ρgh₁ = P₂ + ½ ρ v₂² + ρgh₂
Since h₁ = h₂:
P₁ + ½ ρ v₁² = P₂ + ½ ρ v₂²
Writing v₂ in terms of v₁:
P₁ + ½ ρ v₁² = P₂ + ½ ρ (v₁ d₁²/d₂²)²
P₁ + ½ ρ v₁² = P₂ + ½ ρ v₁² (d₁/d₂)⁴
P₁ + ½ ρ v₁² (1 − (d₁/d₂)⁴) = P₂
Plugging in values:
P₂ = 2 atm + ½ (1000 kg/m³) (4.4 m/s)² (1 − (3.3 cm / 2.4 cm)⁴) (1 atm / 1.013×10⁵ Pa)
P₂ = 1.75 atm
