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Difficulty: EasyHydrostatic Pressure

A narrow vertical pipe and a massive, wide cylindrical storage tank are both placed on a flat horizontal surface and filled with fresh water. The water level in both containers reaches an exact depth of 15 feet. Based on the principles of fluid mechanics, how does the hydrostatic pressure at the bottom of the narrow pipe compare to the pressure at the bottom of the wide tank?

  1. A
    The pressure is greater in the tank because it holds a much larger total weight of water.
  2. The pressure is exactly the same at the bottom of both containers.Answer
  3. C
    The pressure is greater in the pipe because the water is concentrated over a smaller bottom area.
  4. D
    The pressure is greater in the tank because the large volume of water compresses the fluid at the bottom.

Answer

The pressure is exactly the same at the bottom of both containers.
Hydrostatic pressure in an open container is determined entirely by the density of the fluid and its depth. Because both containers hold the same fluid (fresh water) at the exact same depth (15 feet), the pressure exerted on the bottom of each container is identical. The shape of the container and the total volume of the water do not alter the pressure at a given depth.

Step-by-Step Solution

1
Identify the factors that determine hydrostatic pressure in a fluid.
Hydrostatic pressure is determined by the formula P=ρghP = \rho g h, where ρ\rho is density, gg is gravity, and hh is depth.
This formula establishes that pressure in a resting fluid is independent of the container's shape or total fluid volume.
2
Compare the fluid properties and depth in both containers.
Both containers hold fresh water (same density, ρ\rho) and the water reaches exactly 15 feet in both (same depth, hh).
Comparing the variables in the hydrostatic pressure formula reveals if the pressure differs.
3
Determine the relative pressure at the bottom of each container.
Since both the density and the depth are identical, the pressure calculated by P=ρghP = \rho g h is exactly the same for both containers.
Container width and total water weight do not factor into the calculation for hydrostatic pressure at a specific point.

Key Concept

Hydrostatic pressure depends exclusively on the depth and density of the fluid, not on the shape of the container or the total volume of fluid it holds.
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Topics

Hydrostatic Pressure

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