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Difficulty: MediumHydrostatic Pressure

A remote-controlled submersible is conducting an inspection in a freshwater lake. It initially hovers at a static depth of 10 meters10\text{ meters} below the surface. Later, the operator commands the submersible to descend to a depth of 3,000 centimeters3,000\text{ centimeters}. Assuming the water density remains constant, how does the hydrostatic pressure on the submersible at the new depth compare to the pressure at the initial depth?

  1. The hydrostatic pressure is exactly 3 times3\text{ times} as great.Answer
  2. B
    The hydrostatic pressure is exactly 300 times300\text{ times} as great.
  3. C
    The hydrostatic pressure remains the same because the volume of the submersible displacing the water has not changed.
  4. D
    The hydrostatic pressure increases exponentially because the deeper water is highly compressed to a greater density.

Answer

The hydrostatic pressure is exactly 3 times as great.
Hydrostatic pressure is calculated using the formula P=ρ⋅g⋅hP = \rho \cdot g \cdot h. Because the fluid (freshwater) and gravity remain constant, the pressure is directly proportional to the depth (hh). To accurately compare the depths, they must be in the same unit. Converting the new depth to meters (3,000 cm=30 m3,000\text{ cm} = 30\text{ m}) reveals that the submersible has gone from 10 meters10\text{ meters} to 30 meters30\text{ meters}. Since the depth has increased by a factor of 3, the hydrostatic pressure also increases by a factor of 3.

Step-by-Step Solution

1
Identify the formula for hydrostatic pressure.
P=ρ⋅g⋅hP = \rho \cdot g \cdot h, meaning pressure is directly proportional to depth (hh) when density (ρ\rho) and gravity (gg) are constant.
Establishing the mathematical relationship is necessary to compare the two states.
2
Convert the second depth into meters to match the initial depth's units.
3,000 cm÷100 cm/m=30 meters3,000\text{ cm} \div 100\text{ cm/m} = 30\text{ meters}.
Physical quantities must be in the same units before they can be accurately compared or divided.
3
Compare the new depth to the initial depth.
30 meters÷10 meters=330\text{ meters} \div 10\text{ meters} = 3.
Because the depth has tripled, the directly proportional hydrostatic pressure also triples.

Key Concept

Hydrostatic pressure in an incompressible fluid is directly proportional to its depth.
Estimated Time:1m 0s
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Topics

Hydrostatic Pressure

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