Calculate the absolute pressure at the bottom of a lake at a depth of 32.8 m. Assume the density of the water…

Analyze the question

We need the absolute pressure at depth, which is the pressure from the water plus the atmospheric pressure acting on the surface.

Concept

Absolute pressure: P = P₀ + ρgh

• P₀ = 101.3 kPa (air pressure)
• ρ = 1 × 10³ kg/m³
• g = 9.8 m/s²
• h = 32.8 m

Solution

1. Pressure due to water: ρgh = 1000 × 9.8 × 32.8 = 321,440 Pa = 321.44 kPa

2. Add atmospheric pressure: P = 101.3 + 321.44 = 422.74 kPa

Check against the options

• A. 422.7 matches our result of 422.74 kPa.
• D. 321.74 is close to the water pressure alone (321.44), so it is a trap for students who forget to add atmospheric pressure.

Answer: A (≈ 422.7 kPa)

Tip: The word "absolute" tells you to add atmospheric pressure. If the question asked for "gauge pressure", you would use only ρgh. Also, convert carefully: 321,440 Pa = 321.44 kPa, so divide by 1000.