To suck lemonade of density 1000 kg/m3 up a straw to a maximum height of 3.47 cm, what minimum gauge pressure (in atmospheres) must you produce in your lungs?

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

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