If the force on the tympanic membrane (eardrum) increases by about 1.50 Nabove the force from atmospheric pressure, the membrane can be damaged. When you go scuba diving in the ocean, below what depth could damage to your eardrum start to occur? The eardrum is typically 8.20 mm in diameter. Take the density of seawater to be equal 1.03\times 10^3 kg/m^3.

I tried to work out the length of a column of sea-water that is 8.2mm diameter and has a weight (force = mass x acceleration due to gravity) of 1.5 newtons.

The calculation came to 2.81m. That sounds about right, eh?

Working:

1. volume of a cylinder = (area of circle) x (length of cylinder).

2. area of a circle = pi x radius squared

3. diameter = 2 x radius

4. 1 meter = 1000 mm (8.2mm = .0082m)

5. mass of a solid = volume x density

6. force = mass x acceleration (due to gravity)

So:

Force = ( volume of column x density of sea water ) x g
1.5 = (pi x .0082/2 ^ 2) x depth x 1.03 x 10^3 x 9.81
1.5 = 0.533 x depth

depth = 2.81m