Is the Pressure the Same 100m Below the Ocean as It Is 100m Down a Deep Swimming Pool?

The pressure at a given depth in a fluid is influenced by the density of the fluid and the gravitational force acting on it. This article explores the differences in pressure at 100 meters below the ocean and a deep swimming pool, considering the unique properties of seawater and freshwater.

Pressure in Fluids

Pressure in a fluid, whether a liquid or a gas, is a measure of the force exerted per unit area. The formula for calculating the pressure at a certain depth in a fluid is:

[ P P_0 rho g h ]

Where:

( P ) is the pressure at the given depth. ( P_0 ) is the atmospheric pressure at the surface, approximately 101.3 kPa at sea level. ( rho ) is the density of the fluid. For seawater, it is approximately 1025 kg/m3, and for freshwater, it is about 1000 kg/m3. ( g ) is the acceleration due to gravity, approximately 9.81 m/s2. ( h ) is the depth in meters.

Pressure in the Ocean vs. Swimming Pool

Let's calculate the pressure at 100 meters below the ocean and in a deep swimming pool:

Pressure in the Ocean Seawater

[P_{text{ocean}} 101.3 , text{kPa} 1025 , text{kg/m}^3 times 9.81 , text{m/s}^2 times 100 , text{m}] [P_{text{ocean}} 101.3 , text{kPa} 101512.5 , text{Pa}] [P_{text{ocean}} approx 1101.3 , text{kPa}]

Pressure in a Deep Swimming Pool Freshwater

[P_{text{pool}} 101.3 , text{kPa} 1000 , text{kg/m}^3 times 9.81 , text{m/s}^2 times 100 , text{m}] [P_{text{pool}} 101.3 , text{kPa} 98100 , text{Pa}] [P_{text{pool}} approx 1082.3 , text{kPa}]

From these calculations, we can see that the pressure at 100 meters below the ocean is approximately 1101.3 kPa, while the pressure at the same depth in a deep swimming pool is approximately 1082.3 kPa. This indicates that the pressure is slightly higher in the ocean due to the higher density of seawater.

Elevation Considerations

While the main factor is the density of the water, it's worth noting that the elevation of the pool can also influence the pressure. For instance, at an elevation of one mile, the atmospheric pressure is about 11.9 psi (compared to 14.7 psi at sea level). Therefore, the pressure at the bottom of a 100-meter swimming pool at Denver, Colorado, where the elevation is about one mile, would be about 2.8 psi less due to the lower atmospheric pressure.

Conclusion

In summary, the pressure at 100 meters below the ocean is higher than the pressure at 100 meters in a deep swimming pool. This difference is primarily due to the higher density of seawater compared to freshwater. Although the pressure at the bottom of a deep swimming pool is less than at sea level due to elevation, the density effect is the main contributor to the pressure difference at the same depth.