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Difficulty: MediumHydrostatic Pressure

A vertical standpipe in a building's fire suppression system is completely filled with fresh water. The top of the water column is exactly 25 meters25\text{ meters} above a closed test valve on the ground floor. What is the hydrostatic pressure exerted by the water directly on this valve?

(Assume the density of water is 1000 kg/m31000\text{ kg/m}^3 and the acceleration due to gravity is 10 m/s210\text{ m/s}^2. Provide your answer in kilopascals, kPa\text{kPa}.)

Answer: 250 kPa

Answer

250
The hydrostatic pressure at the bottom of the water column is found using the equation P=ρghP = \rho g h. Substituting the given values gives 1000×10×25=250,000 Pascals1000 \times 10 \times 25 = 250,000\text{ Pascals}. To express this in kilopascals, you divide by 1,000, resulting in exactly 250 kPa250\text{ kPa}.

Step-by-Step Solution

1
Identify the relevant formula for hydrostatic pressure.
P=ρghP = \rho g h
Hydrostatic pressure at a given depth depends strictly on the fluid's density, gravity, and the depth of the fluid column.
2
Substitute the given values into the formula.
P=1000 kg/m3×10 m/s2×25 mP = 1000\text{ kg/m}^3 \times 10\text{ m/s}^2 \times 25\text{ m}
These are the precise physical parameters provided in the scenario.
3
Calculate the total pressure in standard SI units (Pascals).
P=250,000 PaP = 250,000\text{ Pa}
Multiplying the standard SI units yields the pressure in Pascals, since 1 Pa=1 kg/(m⋅s2)1\text{ Pa} = 1\text{ kg}/(\text{m}\cdot\text{s}^2).
4
Convert the pressure from Pascals to kilopascals.
250,000/1000=250 kPa250,000 / 1000 = 250\text{ kPa}
The question specifically requests the final numerical answer in kilopascals.

Key Concept

Hydrostatic pressure is directly proportional to the density of the fluid, the acceleration due to gravity, and the vertical depth of the fluid column (P=ρghP = \rho g h), regardless of the total fluid volume.
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Topics

Hydrostatic Pressure

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