Question

The maximum depth d_max 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 d_max for fresh water and the water of the Dead Sea (the saltiest natural water in the world, with a density of 1.5 × 10³kg/m³)?

Answer 1

17.18 m

Step-by-step explanation:

density of fresh water = 1000 kg /m^3

density of dead sea = 1500 kg/m^3

Pressure, P = 5 atm = 5 x 1.01 x 10^5 = 5.05 x 10^5 Pa

Let h be the depth in fresh water and h' be the depth in sea water

P = h x density of fresh water x g

5.05 x 10^5 = h x 1000 x 9.8

h = 51.53 m

Now for dead sea

P = h' x density of dead sea x g

5.05 x 10^5 = h' x 1500 x 9.8

h' = 34.35 m

So, the difference in height

d = h - h'

d = 51.53 - 34.35

h' = 17.18 m

Answer 2

0.17214 m

Step-by-step explanation:

P = Pressure difference between inside and outside the chest cavity = 0.05 atm

`\rho` = Density of fresh water = 1000 kg/m³

`\rho_d` = Density of water in the Dead Sea= 1500 kg/m³

h = Height

In fresh water

`P=\rho gh_1\\\Rightarrow h_1=(P)/(\rho g)\\\Rightarrow h_1=(0.05* 101325)/(1000* 9.81)\\\Rightarrow h_1=0.51643\ m`

In dead sea

`P=\rho_d gh_2\\\Rightarrow h_2=(P)/(\rho_d g)\\\Rightarrow h_2=(0.05* 101325)/(1500* 9.81)\\\Rightarrow h_2=0.34429\ m`

The difference in height is 0.51643-0.34429 = 0.17214 m