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Difficulty: MediumHydrostatic Pressure

At a commercial fuel distribution center, two open-top vertical storage tanks hold the exact same grade of liquid diesel. Tank X is a wide cylinder with a 12-meter12\text{-meter} base diameter. Tank Y is a tall, narrow cylinder with a 2-meter2\text{-meter} base diameter. Both tanks are currently filled with diesel to an exact depth of 8 meters8\text{ meters}. Which of the following statements correctly compares the hydrostatic pressure exerted by the fuel on the bottom surface of each tank?

  1. The pressure is identical in both tanks, because hydrostatic pressure depends only on fluid depth and density.Answer
  2. B
    The pressure in Tank X is greater, because it contains a much larger total weight and volume of fuel.
  3. C
    The pressure in Tank Y is greater, because the narrower base restricts the fuel and concentrates its force.
  4. D
    The pressure cannot be compared without first calculating the total surface area of the tank walls.

Answer

The pressure is identical in both tanks, because hydrostatic pressure depends only on fluid depth and density.
Hydrostatic pressure is determined by the formula P=ρghP = \rho gh (where ρ\rho is fluid density, gg is gravity, and hh is vertical fluid depth). Because both tanks hold the exact same fluid at the exact same depth, the pressure at the bottom is identical. The overall width, shape, or total volume of the tank does not affect hydrostatic pressure.

Step-by-Step Solution

1
Identify the standard formula for calculating hydrostatic pressure.
P=ρ⋅g⋅hP = \rho \cdot g \cdot h (Pressure = density ×\times gravity ×\times depth).
To determine which physical variables actually affect the pressure at the bottom of the fluid column.
2
Analyze the variables provided for both storage tanks.
Both tanks contain the exact same diesel fuel (identical density, ρ\rho) and are filled to the same 8-meter8\text{-meter} level (identical depth, hh).
To compare the factors that influence hydrostatic pressure in this specific scenario.
3
Evaluate the effect of the different tank diameters (12 meters12\text{ meters} vs. 2 meters2\text{ meters}).
The diameters and total fluid volumes do not appear in the hydrostatic pressure formula and therefore have no effect on the bottom pressure.
To confirm that the shape and width of the container are irrelevant to hydrostatic pressure at a given depth.

Key Concept

Hydrostatic pressure at a given depth depends strictly on the density of the fluid and the vertical depth itself, regardless of the container's shape, base width, or total fluid volume.
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Topics

Hydrostatic Pressure

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