Determine how much the pressure force acting on the eardrum of a diver with an area of 0.6 cm2

Determine how much the pressure force acting on the eardrum of a diver with an area of 0.6 cm2, located at a depth of 40 meters in sea water (), is greater than the pressure force acting on the same membrane, at the same depth, only in fresh water ().

S = 0.6 cm2 = 0.00006 m2.

g = 9.8 m / s2.

h = 40 m.

ρm = 1030 kg / m3.

ρw = 1000 kg / m3.

ΔF -?

Pressure P is a scalar physical quantity equal to the ratio of the force F to the area S on which this force acts: P = F / S.

F = P * S.

The hydrostatic pressure of the liquid at the bottom is determined by the formula: P = ρ * g * h. Where ρ is the density of the liquid, g is the acceleration of gravity, h is the height of the liquid, in our case the depth.

Fв = ρв * g * h * S.

Fm = ρm * g * h * S.

ΔF = Fm – Fw = g * h * S * (ρm – ρw).

ΔF = 9.8 m / s2 * 40 m * 0.00006 m2 * (1030 kg / m3 -1000 kg / m3) = 0.7056 N.

Answer: the force of pressure on the tympanic membrane is ΔF = 0.7056 N in sea water more than in fresh water.