Answer:
The minimum gauge pressure you must produce in your lung is -3.356 x 10⁻³ atm
Explanation:
Given;
density of the lemonade, ρ = 1000 kg/m³
maximum height of the lemonade, h₂ = 3.47 cm = 0.0347 m
The minimum gauge pressure you must produce in your lung is given by Bernoulli’s equation;
P₂ + ρgh₂ = P₁ + ρgh₁
P₂ = P₁ + ρgh₁ - ρgh₂
P₂ = P₁ + ρg(h₁ - h₂)
P₂ = P₁ + ρg(0 - h₂)
P₂ = P₁ - ρgh₂
P₂ = 0 - ρgh₂
P₂ = - ρgh₂
P₁ = -(1000)(9.8)(0.0347)
P = -340.06 N/m²
The gauge pressure (in atmospheres) is given as;
P = -340.06 / 101325
P = -0.003356 atm
P = -3.356 x 10⁻³ atm
Therefore, the minimum gauge pressure you must produce in your lung is -3.356 x 10⁻³ atm
