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Difficulty: HardHydrostatic Pressure

Evaluate the gauge hydrostatic pressure exerted at the specific points in the four situations described below. Rank them in order from the HIGHEST hydrostatic pressure to the LOWEST hydrostatic pressure.

Assume standard gravity (gg) applies equally to all scenarios.

  1. 1A pressure sensor located at the bottom of a 20-meter tall, extremely narrow vertical pipe filled entirely with oil (fluid density = 800 kg/m3800\text{ kg/m}^3).
  2. 2A scuba diver swimming 15 meters below the surface of a calm freshwater lake (fluid density = 1000 kg/m31000\text{ kg/m}^3).
  3. 3The exterior hull of a submersible operating 12 meters below the surface of a saltwater ocean (fluid density = 1025 kg/m31025\text{ kg/m}^3).
  4. 4A drain valve positioned at the flat bottom of a massive, wide municipal water reservoir containing freshwater to a depth of 10 meters (fluid density = 1000 kg/m31000\text{ kg/m}^3).

Answer

The correct ranking from highest to lowest pressure is: the narrow pipe with oil, the scuba diver in the lake, the submersible in the ocean, and finally the municipal water reservoir.
The correct sequence is found by calculating the relative pressure factor (density multiplied by depth) for each situation. The narrow pipe with oil has a factor of 16,000, making it the highest. The scuba diver is next at 15,000. The submersible is third at 12,300, and the municipal reservoir is lowest at 10,000. The shape and total volume of the containers are irrelevant distractors.

Step-by-Step Solution

1
Identify the relevant formula and variables for gauge hydrostatic pressure.
The formula is P=ρ⋅g⋅hP = \rho \cdot g \cdot h. Since gravity (gg) is constant across all scenarios, we only need to compare the product of density (ρ\rho) and depth (hh) to determine the relative pressures.
This establishes a direct mathematical way to compare the situations without needing to calculate the exact final pressure in Pascals.
2
Evaluate whether container shape or total fluid volume affects the pressure.
We must ignore the 'extremely narrow' pipe and the 'massive, wide' reservoir descriptions.
According to the principles of fluid mechanics, hydrostatic pressure at a specific depth depends only on depth and density, not on the total volume or the shape of the container (this is known as the hydrostatic paradox).
3
Calculate the pressure factor (ρ⋅h\rho \cdot h) for each scenario.
Submersible: 1025⋅12=12,3001025 \cdot 12 = 12,300. Narrow pipe: 800⋅20=16,000800 \cdot 20 = 16,000. Reservoir: 1000⋅10=10,0001000 \cdot 10 = 10,000. Scuba diver: 1000⋅15=15,0001000 \cdot 15 = 15,000.
These proportional values allow us to easily and accurately rank the pressures.
4
Rank the calculated values from highest to lowest.
Highest: 16,00016,000 (Narrow pipe). Second: 15,00015,000 (Scuba diver). Third: 12,30012,300 (Submersible). Lowest: 10,00010,000 (Reservoir).
This provides the final correct ordering required by the question.

Key Concept

Hydrostatic pressure at a given depth is determined solely by the fluid's density and the vertical depth (P=ρghP = \rho g h), and is completely independent of the container's shape or the total volume of fluid.
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Topics

Hydrostatic Pressure

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