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The maximum depth dmaxthat 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 0.050atm.What is the difference indmaxfor fresh water and the water of the Dead Sea (the saltiest natural water in the world, with a density of1.5103kg/m3)?

Short Answer

Expert verified

Difference in depth of fresh water and water in Dead Sea is0.17m

Step by step solution

01

The given data

(i) Density of dead sea water,=1500kg/m3

(ii) Density of fresh water,=998kg/m3

(iii) Maximum pressure,p=0.05atmor5056Pa

02

Understanding the concept of hydrostatic pressure

Using the formula for hydrostatic pressure difference in terms of density and height, we can find the height d for fresh water and the Dead Sea water and find the difference. Hydrostatic pressure is that, which is exerted by a fluid at any point of time at equilibrium due to the force applied by gravity.

Formula:

Pressure applied on a fluid surface, p=gh (i)

Net pressure applied on a body, p=p2-p1 (ii)

03

Calculation of pressure difference

Using equation (i), the depth can be given as:

d=ppg

Hence the difference in depth for fresh water and dead water sea is as follows:

dmax=ppwg-ppseag=50569.81998-11500=0.17m

Hence, the value of dmax is 0.17 m.

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