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Difficulty: EasyHydrostatic Pressure

Two outdoor swimming pools are filled with fresh water to an exact depth of 3 meters3\text{ meters}. The first is a small backyard wading pool, while the second is a massive Olympic-sized pool holding a much larger total volume of water. How does the hydrostatic pressure at the very bottom of the backyard pool compare to the hydrostatic pressure at the bottom of the Olympic-sized pool?

  1. The pressure is exactly equal in both pools because they share the same fluid density and water depth.Answer
  2. B
    The pressure is significantly greater in the Olympic-sized pool because it contains a larger total mass of water.
  3. C
    The pressure at the bottom of both pools is exactly 3 Pascals3\text{ Pascals} because the depth is exactly 3 meters3\text{ meters}.
  4. D
    The pressure depends entirely on the buoyant force, which requires a heavy object to be placed in the water.

Answer

The pressure is exactly equal in both pools because they share the same fluid density and water depth.
The correct answer accurately states that hydrostatic pressure relies solely on depth and fluid density. Because both pools contain fresh water and are filled to the exact same depth of 3 meters3\text{ meters}, the pressure at the bottom of both pools is identical, despite their vast difference in total volume.

Step-by-Step Solution

1
Identify the factors that determine hydrostatic pressure in a static fluid.
Hydrostatic pressure is determined by the fluid's density, the acceleration due to gravity, and the depth of the fluid.
To evaluate whether factors like total volume or container shape influence the final pressure reading.
2
Compare the relevant factors between the two distinct swimming pools.
Both pools contain fresh water (same density) and have an exact depth of 3 meters3\text{ meters}.
To determine if there are any differences in the variables that actually calculate pressure.
3
Deduce the relative pressure at the bottom of each pool based on the identified factors.
Since both fluid density and depth are identical, the hydrostatic pressure at the bottom must be identical.
According to the principles of fluid mechanics, hydrostatic pressure is independent of the container's width or the fluid's total mass.

Key Concept

Hydrostatic pressure is dependent only on fluid density and depth, not on the container's shape or the total volume of fluid.
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Topics

Hydrostatic Pressure

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