Fluid Properties and Fluid Statics
Density, viscosity and vapor pressure, absolute and gauge pressure, pressure with depth, manometers, forces on walls and buoyancy.
Density, viscosity and vapor pressure
A fluid is described by a few properties. Density ρ (kg/m³) is the mass per volume; for water it is close to 1 000 kg/m³, for air about 1.2 kg/m³ at room conditions. Specific weight γ = ρ g is the weight per volume (9.81 kN/m³ for water). Viscosity measures resistance to shear: the dynamic viscosity μ (Pa·s) is the shear stress per unit velocity gradient, and the kinematic viscosity ν = μ ÷ ρ (m²/s) is what appears in the Reynolds number. Vapor pressure is the pressure at which the liquid boils at that temperature; a liquid whose pressure falls to it cavitates (see Pumps, Pump Curves and NPSH).
| Water at | Density (kg/m³) | Dynamic viscosity (mPa·s) | Kinematic viscosity (mm²/s) | Vapor pressure (kPa) |
|---|---|---|---|---|
| 0 °C | 999.8 | 1.792 | 1.792 | 0.61 |
| 20 °C | 998.2 | 1.002 | 1.004 | 2.34 |
| 40 °C | 992.2 | 0.653 | 0.658 | 7.38 |
| 60 °C | 983.2 | 0.467 | 0.475 | 19.94 |
| 80 °C | 971.8 | 0.355 | 0.365 | 47.39 |
| 100 °C | 958.4 | 0.282 | 0.294 | 101.42 |
The viscosity of water falls by a factor of 6.4 between 0 °C and 100 °C, while its density changes by only 4 percent: hot water flows far more easily than cold. Oils behave the other way and are far more viscous: a typical ISO VG 46 hydraulic oil has ν ≈ 46 mm²/s at 40 °C (μ ≈ 40 mPa·s, about 61 times that of water at the same temperature), and its viscosity falls steeply as it warms.
Gases are compressible, so their density depends on pressure and temperature through the ideal gas law ρ = p ÷ (R T), with R = 287 J/kg·K for air. Liquids are treated as incompressible for most piping problems (water’s bulk modulus is about 2.2 GPa), except when a pressure wave travels along the pipe (see Water Hammer, Cavitation and Troubleshooting).
Absolute, gauge and vacuum pressure
Pressure is force per area: 1 Pa = 1 N/m². Absolute pressure is measured from a perfect vacuum; gauge pressure is measured from the local atmosphere (about 101.325 kPa at sea level) and is what most gauges read; vacuum is the amount below atmospheric.
pabs = pgauge + patm
Worked example: gauge to absolute
- At the bottom of a 3 m water tank the gauge pressure is ρ g h = 998.2 × 9.807 × 3 = 29.37 kPa. The absolute pressure is 101.33 + 29.37 = 130.69 kPa.
- A pump suction line reads a vacuum of 60 percent of atmosphere: the absolute pressure is only 40.5 kPa. Water boils at that pressure at about 76 °C, so warm water would already be close to cavitating.
Common units: 1 bar = 100 kPa = 14.504 psi; 1 atm = 101.325 kPa = 14.696 psi; 1 m of water = 9.80 kPa; 1 mmHg = 133.3 Pa. The Pressure Converter handles the rest.
Pressure with depth
In a fluid at rest the pressure depends only on depth, not on the shape of the container. Moving down a height h increases the pressure by ρ g h.
p = p₀ + ρ g h
This is why a dam is thicker at the bottom, why a diver feels about one extra atmosphere for every 10 m of depth, and why a tank outlet low in the tank flows faster than one near the top. It also means that the height of a water column is a pressure measure: head h = p ÷ (ρ g), in meters of liquid. Pump and pipe calculations use head because it does not depend on the fluid density.
Manometers
A manometer measures a pressure difference with a column of liquid, using p = ρ g h. A U-tube filled with mercury (ρ = 13 546 kg/m³, 13.55 times denser than water) reads small pressures with short columns.
Worked example: a mercury manometer
- The two levels differ by 250 mm of mercury. Δp = ρHg g h = 13 546 × 9.807 × 0.250 = 33.2 kPa.
- The same pressure would need 3.39 m of water: a water manometer would be 13.55 times longer. A differential reading across an orifice meter (see Flow Measurement) is usually taken this way or with a transmitter.
- If the pipes contain water, subtract its weight in the legs: Δp = (ρHg − ρwater) g h = 30.8 kPa.
Force on a submerged wall
For a vertical rectangular wall of height h and width w holding back liquid to the top, the pressure rises from zero at the surface to ρ g h at the bottom, so the average pressure is ρ g h ÷ 2 and
F = ½ ρ g h² w acting at h ÷ 3 above the bottom
Worked example: a gate in a tank
- A 3 m deep tank has a 1 m wide vertical wall. F = ½ × 998.2 × 9.807 × 3² × 1 = 44.05 kN, acting 1.0 m above the bottom.
- That is the weight of 4 492 kg hanging on a wall one meter wide. Doubling the depth would quadruple the force (F ∝ h²), which is why deep tanks need strong walls and anchors.
- A gate hinged at the bottom needs a holding moment of F × 1.0 = 44.05 kN·m about the hinge.
Buoyancy
Archimedes’ principle: a body in a fluid feels an upward force equal to the weight of the fluid it displaces, Fb = ρ g V. It floats if its average density is below the fluid’s, and sits so that the displaced weight equals its own weight.
Worked example: submerged steel and a floating block
- A solid steel block 0.5 × 0.4 × 0.3 m (volume 0.060 m³) weighs 4.62 kN. Under water the buoyancy is 0.59 kN, so a crane sees only 4.03 kN: about 13 percent lighter.
- A 0.4 × 0.3 m wooden block 0.2 m thick, density 600 kg/m³, floats flat in water. The submerged fraction is 600 ÷ 998 = 0.601, so the draft is 120 mm.
- Stability: a floating body is stable when its metacenter is above its center of gravity. A wide, flat hull is stable; a tall narrow one rolls over.
Related
- Next: Continuity, Bernoulli and the Energy Equation for what happens when the fluid moves.
- Pressure Converter and Density Converter.
- Stress, Strain and Safety Factors for the structure that holds the tank.
- Fluid Mechanics and Pipe Flow: the whole guide.
FAQ
Why does pressure depend only on depth?
In a fluid at rest, the weight of the column above a point is carried by the pressure at that point. The width or shape of the container does not matter, which is the hydrostatic paradox: a thin tube of water 10 m high gives the same base pressure as a wide lake of the same depth.
What is the difference between head and pressure?
Head is the pressure expressed as a height of a given fluid, h = p ÷ (ρ g). The same pump produces the same head with any liquid but a different pressure, because the pressure scales with the density.
Do I use gauge or absolute pressure?
Absolute for gas laws, vapor pressure and cavitation checks; gauge for the loads on walls and pipes that are open to the atmosphere on the outside.
Why do boats float if steel is denser than water?
Because the hull encloses a large volume of air: the average density of the whole boat is below that of water, so it displaces its own weight before it is fully submerged.
References
- White, F. M., Fluid Mechanics, McGraw-Hill (properties, hydrostatics, manometers, buoyancy).
- Munson, B. R., et al., Fundamentals of Fluid Mechanics, Wiley.
- Çengel, Y. A. and Cimbala, J. M., Fluid Mechanics: Fundamentals and Applications, McGraw-Hill.
- IAPWS-95 and CRC Handbook of Chemistry and Physics (properties of water).
Last reviewed: October 2026. Water properties are typical handbook values.