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 10.1 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.)
To calculate the pressure due to the ocean at a depth of 10.1 km, we can use the formula for pressure in a fluid:
P = ρgh
Where:
P is the pressure,
ρ is the density of the fluid,
g is the acceleration due to gravity, and
h is the depth of the fluid.
In this case, the depth is 10.1 km, which is equivalent to 10,100 meters. The density of sea water is approximately 1,030 kg/m^3. The acceleration due to gravity, g, is approximately 9.8 m/s^2.
Plugging in these values into the formula, we get:
P = (1,030 kg/m^3) * (9.8 m/s^2) * (10,100 m)
P = 101,274,000 N/m^2
Converting this to units of pressure, we have:
P = 101,274,000 Pa
Therefore, the pressure due to the ocean at a depth of 10.1 km is approximately 101,274,000 Pa (pascals).