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Difficulty: MediumHydrostatic Pressure

A structural engineer is evaluating two submerged sensor housings within a continuous freshwater facility. Housing X is mounted at the bottom of a narrow vertical standpipe, exactly 12 meters12\text{ meters} below the water's surface. Housing Y is mounted on the open floor of the main reservoir, also exactly 12 meters12\text{ meters} below the water's surface. Both locations share the same body of water. Which of the following statements correctly compares the hydrostatic pressure acting on the two housings?

  1. The hydrostatic pressure is equal on both housings because they are situated at the identical vertical depth.Answer
  2. B
    The hydrostatic pressure is greater on Housing Y because the expansive reservoir holds a much larger total weight of water.
  3. C
    The hydrostatic pressure is greater on Housing X because the narrow standpipe concentrates the fluid's downward force into a smaller area.
  4. D
    The hydrostatic pressure cannot be compared directly unless the depth measurements are mathematically converted into volumetric flow rates.

Answer

The hydrostatic pressure is equal on both housings because they are situated at the identical vertical depth.
The correct answer accurately states that hydrostatic pressure depends only on fluid depth. Because both housings are situated exactly 12 meters12\text{ meters} below the surface of the same continuous body of water, the pressure exerted upon them is identical, regardless of the surrounding container geometry.

Step-by-Step Solution

1
Identify the factors that determine hydrostatic pressure.
Hydrostatic pressure (PP) depends on fluid density (ρ\rho), gravity (gg), and vertical depth (hh) according to the formula P=ρ⋅g⋅hP = \rho \cdot g \cdot h.
This establishes the physical law governing the scenario.
2
Evaluate the fluid conditions for both housings.
Both housings are in the same continuous freshwater system, meaning the fluid density (ρ\rho) is identical.
Eliminates fluid density as a variable between the two locations.
3
Compare the depth (hh) and container shapes for both housings.
Housing X is in a narrow pipe at a 12 m12\text{ m} depth, and Housing Y is in a wide reservoir at a 12 m12\text{ m} depth. Container width and total fluid volume are not variables in the hydrostatic pressure formula.
Demonstrates that despite the drastically different container shapes, the equal depth guarantees equal pressure.

Key Concept

Hydrostatic pressure relies strictly on the vertical depth and density of the fluid, and is completely unaffected by the shape of the container or the total volume of the fluid.
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Topics

Hydrostatic Pressure

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