Question

The greatest ocean depths on earth are found in the Marianas Trench near the Philippines, where the depth of the bottom of the trench is about 11.0 km. Calculate the pressure due to the ocean at a depth of 10.4 km, assuming sea water density is constant all the way down. (The validity of the assumption of constant density is examined in one of the integrated concept problems)
___ atm

Answer 1

Pressure at depth h beyond liquid surface:

p = p₀ + ρ∙g∙h

Here,

p₀ atmospheric pressure at liquid surface usually p₀ = 1atm = 101325Pa (1Pa = kg/ms²)

ρ liquid density

g gravitational acceleration

So at 10.4 km ( = 10400 m ) depth:

Substitute all varibles in the equation

p = 101325Pa + ( 1000kg/m³ ) ∙( 9.81m/s² ) ∙( 10400 m )

= 1.02×10⁸ Pa

= (1.02×10⁸ Pa ) ( 1 atm /  101325 Pa )

= 1007.89 atm

Round off the result to 3 significant digits

p = 1010 atm