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Difficulty: EasyHydrostatic Pressure

An underwater research drone is deployed in a freshwater lake. It records a hydrostatic pressure reading at a depth of 10 meters. The drone then descends vertically and records a second pressure reading at a depth of 40 meters. Assuming the water density is uniform, how does the second pressure reading compare to the first?

  1. The second reading is four times as large as the first reading.Answer
  2. B
    The second reading is one-fourth the magnitude of the first reading.
  3. C
    Both readings display equivalent values since they were taken in the same body of water.
  4. D
    The pressure difference depends on the weight of the drone rather than the change in depth.

Answer

The second reading is four times as large as the first reading.
Hydrostatic pressure is calculated using the equation P=ρghP = \rho g h. Because the density of the water (ρ\rho) and the acceleration due to gravity (gg) remain constant in this scenario, the pressure (PP) is directly proportional to the depth (hh). When the drone descends from 10 meters to 40 meters, the depth increases by a factor of 4. Therefore, the hydrostatic pressure also increases by exactly a factor of 4.

Step-by-Step Solution

1
Identify the mathematical formula for hydrostatic pressure.
P=ρghP = \rho g h, where PP is pressure, ρ\rho is density, gg is gravity, and hh is depth.
This formula establishes the mathematical relationship between fluid pressure and depth.
2
Determine the proportional relationship between the two recorded depths.
The second depth (40 meters) is exactly four times the first depth (10 meters).
Calculating the ratio of the depths allows for a direct comparison of the resulting pressures.
3
Apply the depth ratio to the pressure formula.
Since density and gravity are constant, increasing hh by a factor of 4 increases PP by a factor of 4.
Hydrostatic pressure is directly proportional to fluid depth.

Key Concept

Hydrostatic pressure is directly proportional to the depth of the fluid.
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Topics

Hydrostatic Pressure

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