A fluid is any substance that flows and conforms to the shape of its container—liquids and gases both qualify. Unlike solids, fluids cannot support shear stress over time; instead they transmit forces as pressure, a scalar quantity measured perpendicular to any surface.
Pressure: Definition and units
Pressure is force per unit area:
\[ P = \frac{F}{A} \]
where \( F \) is the normal force and \( A \) is the area over which it acts. SI unit: pascal (Pa), equivalent to N/m². Other common units: atm (101,325 Pa), bar (100,000 Pa), psi (pounds per square inch).
The pascal is tiny—1 Pa is the weight of a 100 g mass spread over 1 m². Atmospheric pressure at sea level ≈ 101 kPa (1 atm).
Why pressure, not force?
Pressure unifies how different fluids respond. A sharp tack concentrates force on a small area, producing high pressure and piercing skin. The same force distributed over your palm produces low pressure and causes no injury. In fluid mechanics, pressure is the relevant quantity because fluids adapt to any container shape and transmit force uniformly over all surfaces in contact.
Worked example: Atmospheric pressure on your hand
Atmospheric pressure at sea level is \( P_{\text{atm}} \approx 101,325 \) Pa. Consider your hand's palm area: roughly 0.01 m² (100 cm²).
Problem: What is the total force exerted by the atmosphere on one palm?
Solution: \[ F = P \cdot A = 101,325 \text{ Pa} \times 0.01 \text{ m}^2 = 1013.25 \text{ N} \approx 1 \text{ kN} \]
This is roughly equivalent to the weight of a 100 kg mass pressing on your hand. Yet you don't feel it because your body maintains equal pressure from inside (blood, cellular fluids), so the net force is zero. If the internal pressure were removed (a vacuum), your hand would be crushed.
Pressure in fluids at rest
In a static fluid, pressure acts equally in all directions at a given point (Pascal's principle). This isotropy comes from the fact that fluid elements can rotate freely and cannot support shear. At any depth, the local pressure depends only on the weight of the fluid above, not on the container shape or orientation.
Gauge pressure vs absolute pressure
- Absolute pressure: measured from zero (perfect vacuum). Always positive.
- Gauge pressure: measured relative to atmospheric pressure. A car tire at "32 psi gauge" has absolute pressure of 32 + 14.7 ≈ 47 psi. Most practical gauges read gauge pressure because atmospheric pressure cancels out as a baseline.
Molecular picture
Microscopically, pressure arises from the random thermal motion of molecules. Gas molecules strike the container walls, transferring momentum and producing pressure. Increasing temperature speeds molecules, raising pressure. Decreasing volume compresses molecules into a smaller space, increasing collision frequency and pressure. For liquids, pressure involves both molecular motion and the cohesive forces between molecules.
Real-world applications
Hydraulic systems exploit pressure uniformity: a small force on a small piston generates high pressure, transmitted undiminished to a larger piston, producing a large force (force amplification). This principle runs brakes in cars, lifts in hospitals, and heavy machinery.
Diving: underwater pressure increases with depth as the weight of water accumulates. At 10 m depth, pressure is roughly 2 atm (2× atmospheric). At 40 m (recreational diving limit), pressure exceeds 4 atm, requiring careful decompression.
What you should be able to do
- Define pressure and calculate it from force and area
- Convert between pascal, atm, bar, and psi
- Explain why pressure, not force, is the relevant quantity in fluids
- Distinguish absolute and gauge pressure
- Recognize that pressure is independent of direction in a static fluid
Preview of §14.2
Hydrostatic pressure: how pressure changes with depth in a fluid at rest.
📚 See also: Halliday Vol 2, Ch 14, §14.1.
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