Question 9.6: A Pain in the Ear BIO GOAL Calculate a pressure difference a...
A Pain in the Ear BIO
GOAL Calculate a pressure difference at a given depth and estimate a force.
PROBLEM Estimate the net force exerted on your eardrum due to the water above when you are swimming at the bottom of a pool that is 5.0 m deep.
STRATEGY Use Equation 9.11 to find the pressure difference across the eardrum at the given depth. The air inside the ear is generally at atmospheric pressure. Estimate the eardrum’s surface area, then use the definition of pressure to get the net force exerted on the eardrum.
P=P_{0}+\rho g h [9.11]
Use Equation 9.11 to calculate the difference between the water pressure at the depth h and the pressure inside the ear:
\Delta P=P-P_0=\rho g h
=\left(1.00 \times 10^3 kg / m ^3\right)\left(9.80 m / s ^2\right)(5.0 m )
=4.9 \times 10^4 Pa
Multiply by area A to get the net force on the eardrum associated with this pressure difference, estimating the area of the eardrum as 1 cm².
F_{\text {net }}=A \Delta P \approx\left(1 \times 10^{-4} m ^2\right)\left(4.9 \times 10^4 Pa \right) \approx 5 N
REMARKS Because a force on the eardrum of this magnitude is uncomfortable, swimmers often “pop their ears” by swallowing or expanding their jaws while underwater, an action that pushes air from the lungs into the middle ear. Using this technique equalizes the pressure on the two sides of the eardrum and relieves the discomfort.