Physics for ME · Chapter 13 of 16 · Intermediate · Fluids preview
Fluids: Pressure, Buoyancy, and Flow Intuition
Pressure, Archimedes, continuity, and a first feel for Bernoulli. Deliberately introductory: the full Fluid Mechanics course comes later.
Readiness check
From Chapters 1, 4, and 6. Tick only what you can do closed-notes.
- Work with pressure units: Pa, kPa, bar.
- Compute forces from F = PA with unit care.
- Use density ρ = m/V fluently.
- Run an energy audit (for Bernoulli intuition).
- Draw an FBD with a pressure force on a surface.
The core idea
Pressure is force spread over area, it grows with depth, and enclosed fluids transmit it everywhere.
P = F/AP = P₀ + ρghFb = ρfluidgVPascal's principle (pressure transmitted undiminished) powers every hydraulic machine. Archimedes' buoyancy is hydrostatics applied to a submerged body. For moving fluid, continuity (Av constant) and Bernoulli (pressure-velocity trade) supply the first intuition.
What this chapter covers
- 13.1 Pressure and its units: Pa, bar, atm, gauge versus absolute.
- 13.2 Hydrostatics: P = P₀ + ρgh; manometers and dams.
- 13.3 Pascal's principle: hydraulic force multiplication.
- 13.4 Buoyancy: Archimedes and floating stability intuition.
- 13.5 Continuity: A₁v₁ = A₂v₂ for incompressible flow.
- 13.6 Bernoulli intuition: the pressure-velocity-height trade, ideal case only.
Engineering connection: a preview, not the full course; prepares hydraulics, pumps, and the Fluid Mechanics course (Çengel and Cimbala).
Worked example: the hydraulic lift
A workshop lift supports a 12 000 N car on a 200 cm² piston. The effort piston has an area of 10 cm². Find the required effort force, the working pressure, and the distance trade-off.
- ProblemFind the effort force and system pressure in Figure 1, and the stroke ratio.
- Given / findLoad 12 000 N on A₂ = 200 cm² = 0.02 m²; effort area A₁ = 10 cm² = 0.001 m².
- AssumptionsIncompressible fluid, negligible piston weights and friction, equal piston heights.
- ModelPascal: the pressure under both pistons is the same, so F₁/A₁ = F₂/A₂.
- EquationsP = F₂/A₂ F₁ = P·A₁
- SolveP = 12 000/0.02 = 600 kPa (6 bar). F₁ = 600 000 × 0.001 = 600 N: a 20:1 multiplication. Volume conservation makes the effort piston travel 20 times farther than the car rises.
- CheckEnergy audit (Chapter 6): F₁d₁ = 600 × 20h = 12 000 × h = F₂d₂. Force is multiplied, work is not: no free lunch, just a force-distance trade like a lever.
- ConclusionSix bar, a hand-scale force, and geometry hold a car: that is all of fluid power. Brakes, presses, and excavators scale this same triangle of P, A, and stroke.
Misconceptions and diagnostics
| Mistake | Symptom | Diagnostic question | Correction |
|---|---|---|---|
| Pressure depends on tank width | Wide reservoirs assumed to press harder | "What does P = ρgh contain?" | Depth, density, gravity: width never appears. A thin standpipe loads a dam's base like a lake. |
| Buoyancy linked to the object's weight | "Heavy things get less lift" | "Whose density sits in ρgV?" | The fluid's. Buoyancy depends on displaced volume only; weight decides sink or float. |
| Hydraulics as free energy | 20× force celebrated without the stroke cost | "What happened to the distances?" | Work in = work out (minus losses): the force gain is paid in travel. |
| Bernoulli everywhere | Ideal pressure-velocity trades in long, narrow, real pipes | "Are losses negligible on this path?" | Bernoulli is the frictionless ideal. Real pipe networks need the loss terms of Fluid Mechanics. |
Practice ladder
Find the gauge pressure 3.5 m below the surface of a water tank, and the force on a 20 × 20 cm inspection hatch at that depth.
Show answer
P = 1000 × 9.81 × 3.5 = 34.3 kPa. F = PA = 34 300 × 0.04 = 1373 N: a hatch the size of a sheet of paper carries a person's weight and a half.
A solid aluminium part (ρ = 2700 kg/m³) of volume 0.002 m³ hangs from a crane scale, fully submerged in water. What does the scale read?
Show answer
Weight = 2700 × 0.002 × 9.81 = 53.0 N. Buoyancy = 1000 × 0.002 × 9.81 = 19.6 N. Scale: 33.4 N. Submerged weighing measures volume: Archimedes' original trick.
Water flows at 2 m/s in a 50 mm pipe that necks down to 25 mm. Find the speed in the neck and state (Bernoulli intuition) what happens to the pressure there.
Show answer
Area ratio 4:1, so v = 8 m/s in the neck. Faster means lower pressure in the ideal trade: the venturi principle behind carburetors and flow meters.
Examine one real hydraulic device (car jack, brake system, log splitter spec sheet). Identify both areas or bore sizes, compute the force ratio and working pressure at rated load, and check the pressure against the hose or seal rating.
What good work looks like
Bore data sourced, the F/A arithmetic shown, the system pressure compared with a component rating, and the stroke trade-off mentioned.
Working with AI, and proving it yourself
Use AI as an examiner, not a solver
Portfolio task
Verify Archimedes at home: weigh an object, then weigh it submerged (hang it from a kitchen scale into water). Compute its volume and density from the difference and identify the material.
Retrieval and spaced review
Closed notes. Answer out loud, then reveal.
1. Write the hydrostatic pressure law and its three ingredients.
P = P₀ + ρgh: surface pressure, fluid density, depth. Geometry of the container is absent.
2. State Pascal's principle and its machine consequence.
Pressure applied to an enclosed fluid transmits undiminished: F₂ = F₁·A₂/A₁, the hydraulic lever.
3. State Archimedes' principle precisely.
The buoyant force equals the weight of the displaced fluid: Fb = ρfluidgVdisplaced, upward.
4. What does continuity conserve, and what follows in a neck?
Volume flow Av for incompressible fluid: smaller area, faster flow.
5. What is Bernoulli's trade, and its standing assumption?
Along an ideal streamline, pressure + ½ρv² + ρgh stays constant: valid only when losses are negligible.
Textbook mapping
| Item | Mapping |
|---|---|
| Main source | OpenStax University Physics Vol. 1, Fluid Mechanics chapter |
| Bridge reference | Çengel and Cimbala, Fluid Mechanics: Fundamentals and Applications (the later full course) |
| Core topics | 13.1 Pressure · 13.2 Hydrostatics · 13.3 Pascal · 13.4 Buoyancy · 13.5 Continuity · 13.6 Bernoulli intuition |
| Engineering connection | Hydraulics and fluid power now; the Fluid Mechanics course later. Kept introductory by design. |
| Read next | Chapter 14: Electricity, Circuits, and Magnetism for Mechanical Engineers. |