Fluid Properties
Viscosity, Density, Surface Tension, Compressibility — Every Property Defined with Formulas & Units
Last Updated: March 2026
📌 Key Takeaways
- A fluid is any substance that deforms continuously under shear stress — liquids and gases are both fluids.
- Density (ρ) = mass per unit volume (kg/m³). Specific weight (γ) = ρg (N/m³). Specific gravity (SG) = ρ/ρwater.
- Viscosity measures resistance to flow. Dynamic viscosity μ (Pa·s) and kinematic viscosity ν = μ/ρ (m²/s).
- Surface tension (σ) creates the membrane-like behaviour at liquid surfaces — measured in N/m.
- Compressibility is measured by the bulk modulus K (Pa). Liquids have very high K (nearly incompressible); gases have low K (highly compressible).
- These properties appear in every fluid mechanics equation — understanding them is essential before studying flow behaviour.
1. What is a Fluid?
A fluid is any substance that cannot resist a shear stress when at rest — it deforms continuously under even the smallest applied shear force. This distinguishes fluids from solids: a solid deforms by a fixed amount under shear and then stops; a fluid keeps deforming as long as the shear stress is applied.
Both liquids and gases are fluids. The key difference is that liquids have a definite volume and a free surface (they do not expand to fill a container), while gases expand to fill any container and have no free surface. Despite this difference, the same equations of fluid mechanics apply to both — the only distinction is that gases are typically compressible while liquids are nearly incompressible under normal conditions.
The continuum hypothesis is the fundamental assumption in fluid mechanics: we treat fluids as continuous substances rather than collections of individual molecules. This is valid when the characteristic length scale of the flow (pipe diameter, channel width) is much larger than the mean free path between molecules — which is true for virtually all engineering applications.
2. Density, Specific Weight & Specific Gravity
Density
ρ = m / V
Mass per unit volume. SI unit: kg/m³
Water at 4°C: ρ = 1,000 kg/m³. Air at 20°C, 1 atm: ρ = 1.204 kg/m³.
Specific Weight (Weight Density)
γ = ρg
Weight per unit volume. SI unit: N/m³
Water: γ = 1000 × 9.81 = 9,810 N/m³ ≈ 9.81 kN/m³
Specific Gravity (Relative Density)
SG = ρsubstance / ρwater
Dimensionless ratio. SG = 1 for water. SG > 1 → sinks. SG < 1 → floats.
Specific Volume
v = 1/ρ = V/m
Volume per unit mass. SI unit: m³/kg
| Fluid | ρ (kg/m³) | SG |
|---|---|---|
| Water (4°C) | 1,000 | 1.00 |
| Mercury | 13,600 | 13.6 |
| Seawater | 1,025 | 1.025 |
| Engine oil | 880 | 0.88 |
| Air (20°C, 1 atm) | 1.204 | 0.0012 |
| Petrol/Gasoline | 720 | 0.72 |
3. Viscosity — Dynamic & Kinematic
Viscosity is a fluid’s resistance to deformation by shear stress. Think of it as “internal friction” — honey has high viscosity (flows slowly), water has low viscosity (flows easily), and air has very low viscosity.
Newton’s Law of Viscosity
τ = μ (du/dy)
Where: τ = shear stress (Pa = N/m²), μ = dynamic viscosity (Pa·s = N·s/m²), du/dy = velocity gradient perpendicular to the flow (s⁻¹)
This equation says that the shear stress in a fluid is proportional to the rate at which velocity changes across the fluid. The proportionality constant is the dynamic viscosity μ.
Dynamic (Absolute) Viscosity
μ — measures the force needed to shear a fluid
SI unit: Pa·s (= N·s/m² = kg/(m·s))
CGS unit: Poise (P). 1 Pa·s = 10 P. Common: centipoise (cP). 1 cP = 10⁻³ Pa·s
Kinematic Viscosity
ν = μ / ρ
SI unit: m²/s
CGS unit: Stokes (St). 1 St = 10⁻⁴ m²/s. Common: centistokes (cSt). 1 cSt = 10⁻⁶ m²/s
Temperature effect: For liquids, viscosity decreases with increasing temperature (molecules move faster, resist less). For gases, viscosity increases with temperature (more molecular collisions). This is a common exam question.
| Fluid (20°C) | μ (Pa·s) | ν (m²/s) |
|---|---|---|
| Water | 1.002 × 10⁻³ | 1.004 × 10⁻⁶ |
| Air | 1.81 × 10⁻⁵ | 1.51 × 10⁻⁵ |
| Engine oil (SAE 30) | 0.1–0.3 | ~1 × 10⁻⁴ |
| Mercury | 1.55 × 10⁻³ | 1.14 × 10⁻⁷ |
| Honey | 2–10 | ~2 × 10⁻³ |
4. Newtonian vs Non-Newtonian Fluids
Fluids are classified by their shear stress vs shear rate behaviour:
| Type | Behaviour | Examples |
|---|---|---|
| Newtonian | τ = μ(du/dy) — linear relationship, constant μ | Water, air, oils, mercury, most common fluids |
| Shear-thinning (pseudoplastic) | Viscosity decreases as shear rate increases | Blood, paint, ketchup, polymer solutions |
| Shear-thickening (dilatant) | Viscosity increases as shear rate increases | Cornstarch in water, wet sand |
| Bingham plastic | Behaves as solid below yield stress, then flows as Newtonian | Toothpaste, mayonnaise, concrete (wet) |
In engineering fluid mechanics (and GATE), all fluids are assumed Newtonian unless stated otherwise. Newton’s law of viscosity τ = μ(du/dy) applies.
5. Surface Tension & Capillarity
Surface Tension
σ = force per unit length along the surface
SI unit: N/m
Water at 20°C: σ = 0.0728 N/m. Mercury at 20°C: σ = 0.465 N/m.
Surface tension arises because molecules at the surface of a liquid experience a net inward attraction from neighbouring molecules below and beside them, but no attraction from above (where there is air or vacuum). This creates a “skin” effect that minimises surface area — which is why small droplets form spheres (the shape with minimum surface area for a given volume).
Pressure Inside a Droplet
ΔP = 2σ/r (spherical droplet)
ΔP = 4σ/r (soap bubble — two surfaces)
Where: r = radius, σ = surface tension
Capillary Rise
h = 4σ cos(θ) / (ρgd)
Where: h = capillary rise (m), θ = contact angle, ρ = fluid density, g = 9.81 m/s², d = tube diameter (m)
Water in glass: θ ≈ 0° (wets the surface, rises). Mercury in glass: θ ≈ 140° (does not wet, depresses).
6. Compressibility & Bulk Modulus
Bulk Modulus of Elasticity
K = −ΔP / (ΔV/V) = ΔP / (Δρ/ρ)
SI unit: Pa (or GPa for liquids)
Water: K ≈ 2.2 GPa (very hard to compress). Air (isothermal): K = P ≈ 101.3 kPa (easily compressible).
Compressibility
β = 1/K
SI unit: Pa⁻¹. Higher β = more compressible.
Engineering implication: Liquids are treated as incompressible (constant density) in nearly all engineering calculations. Gases are compressible but can be treated as incompressible when the Mach number is below 0.3 (flow velocity less than 30% of the speed of sound). This simplification is valid for most pipe flow, pump, and low-speed aerodynamics problems.
7. Vapour Pressure & Cavitation
Vapour pressure (Pv) is the pressure at which a liquid begins to boil at a given temperature. Every liquid has a vapour pressure that increases with temperature — water at 20°C has Pv = 2.34 kPa; at 100°C, Pv = 101.3 kPa (atmospheric pressure, which is why water boils at 100°C at sea level).
Cavitation occurs when the local pressure in a flowing liquid drops below its vapour pressure. The liquid vaporises, forming bubbles. When these bubbles are carried to a higher-pressure region, they collapse violently, creating intense shock waves that can erode and damage metal surfaces. Cavitation is a serious problem in pumps, propellers, turbines, and valves.
| Temperature (°C) | Vapour Pressure of Water (kPa) |
|---|---|
| 10 | 1.23 |
| 20 | 2.34 |
| 40 | 7.38 |
| 60 | 19.9 |
| 80 | 47.4 |
| 100 | 101.3 |
Exam tip: In Bernoulli’s equation problems, always check whether the minimum pressure in the system drops below the vapour pressure. If it does, cavitation occurs and the flow assumptions break down.
8. Property Values — Water, Air, Mercury (at 20°C, 1 atm)
| Property | Water | Air | Mercury |
|---|---|---|---|
| Density ρ (kg/m³) | 998 | 1.204 | 13,600 |
| Specific weight γ (kN/m³) | 9.79 | 0.0118 | 133.4 |
| Dynamic viscosity μ (Pa·s) | 1.002 × 10⁻³ | 1.81 × 10⁻⁵ | 1.55 × 10⁻³ |
| Kinematic viscosity ν (m²/s) | 1.004 × 10⁻⁶ | 1.51 × 10⁻⁵ | 1.14 × 10⁻⁷ |
| Surface tension σ (N/m) | 0.0728 | — | 0.465 |
| Bulk modulus K (GPa) | 2.2 | ~0.0001 | 28.5 |
| Vapour pressure Pv (kPa) | 2.34 | — | ~0 |
9. Common Mistakes Students Make
- Confusing dynamic and kinematic viscosity: Dynamic viscosity (μ, Pa·s) measures force resistance. Kinematic viscosity (ν = μ/ρ, m²/s) accounts for density. The Reynolds number uses kinematic viscosity: Re = VD/ν. Using the wrong viscosity gives a dimensionally incorrect Reynolds number.
- Forgetting temperature dependence: Viscosity of liquids decreases with temperature; viscosity of gases increases. Exam problems that specify temperature expect you to use the correct viscosity value, not a room-temperature default.
- Using gauge pressure when absolute is needed: Cavitation analysis and the Bernoulli equation require absolute pressures. Using gauge pressure (which ignores atmospheric pressure) leads to wrong conclusions about whether cavitation occurs.
- Assuming all fluids are Newtonian: While this is standard in engineering analysis, exam problems sometimes explicitly mention non-Newtonian behaviour. Read the problem statement carefully — if it mentions yield stress or variable viscosity, Newtonian assumptions do not apply.
- Mixing CGS and SI units for viscosity: 1 Poise = 0.1 Pa·s. 1 Stokes = 10⁻⁴ m²/s. Forgetting these conversion factors is a common error in numerical problems.
10. Frequently Asked Questions
What is the difference between dynamic viscosity and kinematic viscosity?
Dynamic viscosity (μ) measures the shear force needed to deform a fluid — it is the proportionality constant in Newton’s law of viscosity (τ = μ du/dy) with units Pa·s. Kinematic viscosity (ν = μ/ρ) divides out the density effect, giving a measure of how quickly a fluid flows under gravity, with units m²/s. The Reynolds number Re = VD/ν uses kinematic viscosity because it naturally combines both viscous and inertial effects.
What is specific gravity?
Specific gravity is the dimensionless ratio of a substance’s density to the density of water (for liquids) or air (for gases) at standard conditions. SG = ρsubstance/ρwater. It tells you whether a substance floats (SG < 1) or sinks (SG > 1) in water. Mercury’s SG of 13.6 means it is 13.6 times denser than water.
What causes surface tension?
Surface tension results from the imbalance of intermolecular forces at a liquid’s surface. Molecules within the liquid are attracted equally in all directions by surrounding molecules. At the surface, molecules have no neighbours above them, creating a net inward pull that contracts the surface and makes it behave like an elastic membrane. This explains why water droplets form spheres, insects can walk on water, and meniscus curves appear in narrow tubes.