A hydrostatic pressure sensor at the bottom of an upright agricultural water cistern reads… — Armed Services Vocational Aptitude Battery (ASVAB)

A hydrostatic pressure sensor at the bottom of an upright agricultural water cistern reads $45\text{ psi}$ when the water depth is $30\text{ feet}$ . During a dry season, the water level drops to a depth of $18\text{ feet}$ . Assuming the fluid density remains constant, what is the new hydrostatic pressure reading in $\text{psi}$ at the sensor?

Answer: 27 psi

Answer

Since hydrostatic pressure is directly proportional to depth (

P = \rho \cdot g \cdot h

), the ratio of pressure to depth remains constant. The initial ratio is

45\text{ psi} / 30\text{ feet} = 1.5\text{ psi/ft}

. At a new depth of

18\text{ feet}

, the pressure is

18\text{ feet} \times 1.5\text{ psi/ft} = 27\text{ psi}

Step-by-Step Solution

Identify the relationship between hydrostatic pressure and fluid depth.

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

The formula for hydrostatic pressure is

P = \rho \cdot g \cdot h

, meaning if density (

\rho

) and gravity (

g

) are constant, the pressure changes linearly with depth (

h

Determine the pressure per foot of water depth.

45\text{ psi} \div 30\text{ feet} = 1.5\text{ psi}

per foot.

This establishes the constant of proportionality for the fluid in this specific cistern.

Calculate the new pressure at the reduced depth.

1.5\text{ psi/foot} \times 18\text{ feet} = 27\text{ psi}

Multiplying the pressure per foot by the new depth yields the corresponding hydrostatic pressure.

Key Concept

Hydrostatic pressure is directly proportional to fluid depth.

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