A submarine dives down to a depth 9.5 beneath the surface of the ocean. Calculate the pressure in atmospheres at that depth, assuming the density of water is 1029 kg/m3, and the air pressure at the surface is 101.5 kPa
101.5 * 10*3 + 1029 *9.81 * 9.5
= 101.5 * 10^3 + 95.898 * 10^3
= 197 k Pa
or about 2 atmospheres
note, 30 feet deep is about additional atmosphere
To calculate the pressure at a given depth in a fluid, you can use the formula:
P = P₀ + ρgh
Where:
P is the pressure at the given depth,
P₀ is the initial pressure (in this case, the air pressure at the surface),
ρ is the density of the fluid,
g is the acceleration due to gravity, and
h is the depth.
Using the given values:
P₀ = 101.5 kPa (which can be converted to 101500 Pa)
ρ = 1029 kg/m³
g = 9.8 m/s²
h = 9.5 m
Let's substitute these values into the formula and solve for P:
P = 101500 + (1029 * 9.8 * 9.5)
First, we calculate the product of ρ, g, and h:
P = 101500 + (99533.2)
Then, we add this value to the initial pressure:
P = 201033.2 Pa
Finally, we need to convert the pressure from Pascals to atmospheres, where 1 atm is approximately equal to 101325 Pa:
P = 201033.2 / 101325
P ≈ 1.98 atmospheres
Therefore, the pressure at a depth of 9.5 meters beneath the surface of the ocean is approximately 1.98 atmospheres.