Question

A scuba diver must decompress after a deep dive to allow excess nitrogen to exit safely from his bloodstream. The length of time required for decompression depends on the total change in pressure that the diver experienced. Find this total change in pressure for a diver who starts at a depth of d = 18.9 m in the ocean (density of seawater = 1024 kg/m^3) and then travels aboard a small plane (with an unpressurized cabin) that rises to an altitude of h = 4600 m above sea level.

Answer 1

The pressure at the depth d
p1= ρ•g•d + p (atm) =1024•9.8•18.9 + 101325 =2.91•10 ⁵ Pa,
The pressure at the height h
p=p₀exp{-μgh/RT)
Since we don’t know the temperature, we use another expression.
Air pressure above sea level can be calculated as
p = 101325 (1 - 2.25577 10⁻⁵ h)⁵‧²⁶ , where
p = air pressure (Pa)
h = altitude above sea level (m)
p2=101325(1-2.26•10⁻⁵•4600)^5.26=5.68•10⁴ Pa
ΔP=2.91•10 ⁵-5.68•10⁴=2.34•10⁵ Pa

Answer 2

thanks!