Static Fluids
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
Pressure is force per area, and in a fluid it grows with depth: P = P0 + ρgh. The deeper you go, the more fluid is stacked above you. Only the depth matters, not the container’s shape or how much fluid there is.
1. The key equations
2. Absolute vs. gauge
Absolute pressure includes the air pushing on the surface: P = P0 + ρgh.
Gauge pressure is just the extra from the fluid: ρgh. A tire gauge reads gauge pressure.
Every 10 m of water adds about 100 kPa, about one more atmosphere. Pressure pushes equally in all directions at a point, and it’s the same at every point at the same depth in a connected, still fluid.
3. Example, then try it
A swimming pool is 5.0 m deep. Find the gauge and absolute pressure at the bottom. (ρ = 1000 kg/m³, g = 10 m/s², P0 = 100 kPa)
Gauge: ρgh = (1000)(10)(5.0) = 50,000 Pa = 50 kPa.
Absolute: 100 kPa + 50 kPa = 150 kPa.
A diver is 10 m below the surface of a lake. Find the gauge and absolute pressure. Her mask window has an area of 0.020 m², with air at 100 kPa inside. What is the net force of the water pushing the window in?
Gauge pressure: ρgh = (1000)(10)(10) = 100,000 Pa = 100 kPa.
Absolute pressure: 100 kPa + 100 kPa = 200 kPa, twice the surface pressure.
Net pressure on the window: outside 200 kPa − inside 100 kPa = 100 kPa.
Net force: F = ΔP × A = (100,000)(0.020) = 2000 N.
Answer: 100 kPa gauge, 200 kPa absolute, 2000 N on the window.
4. Common mistakes
Three containers of different shapes are filled with water to the same height. How does the pressure at the bottom of each compare?
P = P₀ + ρgh depends only on the depth below the surface. All three bottoms are at the same depth, so the pressures are equal.
Ready to practice?
5 questions on Static Fluids, each with a hint and an explanation for every wrong answer.