Question

5. The maximum depth dmax that a diver can snorkel is set by the density of the water and the fact that human lungs can function against a maximum pressure difference (between inside and outside the chest cavity) of 0.050 atm. What is the difference in dmax for fresh water and the water of the Dead Sea (the saltiest natural water in the world, with a density of 1.5 x 103 kg/m3)

Answer 1

Answer:

The $d_{max}$ value is 17.2 cm.

Explanation:

From the given,

salt water density  = $1.5\times 10^{3}kg/m^{3}=150010^{3}kg/m^{3}$

Water has density = $1000kg/m^{3}$

Pressure = 0.050 atm = 5066.25 pa

$P= h\times d\times g$

Rearrange the formula is as follows.

$h=\frac{P}{d\times g}$

For fresh water,

$h= \frac{5066.25}{1000\times9.81}= 0.516m = 51.6 cm$

For salt water,

$h= \frac{5066.25}{1500\times9.81}= 0.3446m = 34.4 cm$

The difference = Height of fresh water - Height of salt water.

                         = 51.6 - 34.4 = 17.2 cm

Therefore, The $d_{max}$ value is 17.2 cm.