A cylindrical water storage tank is filled to a depth of 4\text{ meters}, creating a hydro… — Armed Services Vocational Aptitude Battery (ASVAB)

A cylindrical water storage tank is filled to a depth of $4\text{ meters}$ , creating a hydrostatic pressure of $40,000\text{ Pascals}$ at the tank's flat bottom. If water is drained from the tank until the depth is exactly $1\text{ meter}$ , what is the new hydrostatic pressure at the bottom in Pascals? (Assume the density of water and gravity remain constant.)

Answer: 10000 Pascals

Answer

10000

Because hydrostatic pressure is directly proportional to depth (

P = \rho g h

), reducing the depth to one-fourth of its original value (

1\text{ meter}

instead of

4\text{ meters}

) also reduces the pressure exactly to one-fourth of its original value (

40,000 / 4 = 10,000

Step-by-Step Solution

Identify the relationship between hydrostatic pressure and fluid depth.

Hydrostatic pressure is directly proportional to depth (

P \propto h

) when density and gravity are constant.

This fundamental principle allows us to solve the problem using a simple ratio.

Calculate the pressure per unit of depth.

\frac{40,000\text{ Pascals}}{4\text{ meters}} = 10,000\text{ Pascals per meter}

Finding the rate of pressure change per meter simplifies the calculation for the new depth.

Multiply the pressure per meter by the new depth.

10,000\text{ Pascals/meter} \times 1\text{ meter} = 10,000\text{ Pascals}

This yields the final pressure at the reduced depth.

Key Concept

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

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