Question

The human lungs can function satisfactorily up to a limit where the pressure difference between the outside and inside of the lungs is 1/19 of an atmosphere. If a diver uses a snorkel for breathing, how far below the water can she swim? Assume the diver is in salt water whose density is 1044 kg/m3.

Answer 1

Density of water (salted) \(\rho=1044 \mathrm{~kg} / \mathrm{m} 3\) Gauge pressure \(\left(P_{2}-P_{1}\right)=\frac{P_{0}}{19} \quad\left[\right.\) where \(\left.P_{0}=1.013 \times 10^{5} \mathrm{~Pa}\right]\)

$$ \begin{array}{l} =\frac{1.013 \times 10^{5} \mathrm{~Pa}}{19} \\ =5331.58 \mathrm{~Pa} \end{array} $$

The change in pressure related to depth (h) as

$$ \begin{aligned} P_{2}-P_{1} &=\rho g h \\ \text { Then } \quad h &=\frac{P_{2}-P_{1}}{\rho g} \\ &=\frac{5331.58 \mathrm{~Pa}}{\left(1044 \mathrm{~kg} / \mathrm{m}^{2}\right)\left(9.8 \mathrm{~m} / \mathrm{s}^{2}\right)} \\ &=0.52 \mathrm{~m} \end{aligned} $$

So, the driver can swim \(0.52 \mathrm{~m}\) below water.