Example

Question:

What is the pressure on a swimmer 10 m below the surface of a lake?

Solution:

Here, \(h = 10\,\mathrm{m}\) and \(\rho = 1000\,\mathrm{kg\,m^{-3}}\). Take \(g = 10\,\mathrm{m\,s^{-2}}\).
From Eq. (9.7): \[ P = P_a + \rho g h \] \[ = 1.01 \times 10^5\,\mathrm{Pa} + 1000\,\mathrm{kg\,m^{-3}} \times 10\,\mathrm{m\,s^{-2}} \times 10\,\mathrm{m} \] \[ = 2.01 \times 10^5\,\mathrm{Pa} \approx 2\,\mathrm{atm} \]
This is a 100% increase in pressure from surface level. At a depth of 1 km, the increase in pressure is 100 atm! Submarines are designed to withstand such enormous pressures.