5.1 Fluid properties and classification

Fluid mechanics studies how liquids and gases behave when forces act on them. The properties covered here (density, viscosity, and compressibility) show up constantly when you're sizing pipes, designing reactors, or analyzing heat exchangers. This section lays the groundwork by classifying fluids and understanding what controls their behavior.

Fluids, Liquids, and Gases

Defining and Differentiating Fluids, Liquids, and Gases

A fluid is any substance that continuously deforms under an applied shear stress. Both liquids and gases are fluids, meaning they flow and take the shape of their container.

What separates liquids from gases comes down to two things: compressibility and the presence of a free surface.

• Liquids have a definite volume but no fixed shape. They're nearly incompressible and form a free surface at the interface with a gas (think of the water level in a glass). Examples: water, oil.
• Gases have neither a definite volume nor a fixed shape. They're highly compressible and expand to fill whatever container they're in. There's no free surface. Examples: air, helium.

This distinction matters in engineering because you can often treat liquids as incompressible in calculations, which simplifies the math considerably. Gases require you to account for density changes with pressure and temperature.

Properties and Behavior of Fluids

The key difference between a fluid and a solid is how they respond to shear stress. A solid deforms to a fixed shape and then stops. A fluid keeps deforming for as long as the stress is applied.

Three properties govern most fluid behavior:

• Density tells you how much mass is packed into a given volume.
• Viscosity tells you how much the fluid resists flowing.
• Compressibility tells you how much the volume changes under pressure.

Fluids can also be classified as Newtonian or non-Newtonian based on how their viscosity responds to shear rate. This classification directly affects which equations you use to model flow in systems like pipelines, heat exchangers, and chemical reactors.

Density, Viscosity, and Compressibility of Fluids

Density

Density is mass per unit volume, typically in kg/m³. It measures how compact a fluid is and varies with both temperature and pressure.

$\rho = \frac{m}{V}$

The density of water at standard conditions (20°C, 1 atm) is approximately 998 kg/m³.

Density determines two things you'll use repeatedly:

• Buoyancy: Objects less dense than the surrounding fluid float; denser objects sink.
• Hydrostatic pressure: The pressure at a given depth depends on fluid density and the depth below the surface, given by $P = \rho g h$.

Viscosity

Viscosity measures a fluid's resistance to flow. It arises from internal friction between fluid layers sliding past each other.

There are two forms you need to know:

• Dynamic viscosity ($\mu$) is the ratio of shear stress to shear rate, with units of Pa·s. It represents the fluid's inherent resistance to flow. For water at 20°C, $\mu \approx 1.002 \text{ mPa·s}$.
• Kinematic viscosity ($\nu$) is dynamic viscosity divided by density, with units of m²/s. It's useful when gravitational or inertial effects matter, such as in the Reynolds number. For water at 20°C, $\nu \approx 1.004 \times 10^{-6} \text{ m}^2/\text{s}$.

$\nu = \frac{\mu}{\rho}$

Viscosity directly affects pressure drops in pipes, flow rates, and heat transfer coefficients, so getting it right is critical for equipment sizing.

Compressibility

Compressibility describes how much a fluid's volume changes when pressure changes. It's typically expressed through the bulk modulus ($K$), which is the ratio of an incremental pressure change to the resulting fractional volume change:

$K = -V \frac{\Delta P}{\Delta V}$

The negative sign is there because an increase in pressure causes a decrease in volume, so the negative keeps $K$ positive.

A high bulk modulus means the fluid is hard to compress.

• Liquids are nearly incompressible. Water has a bulk modulus of about 2.2 GPa, meaning you need enormous pressure to change its volume even slightly.
• Gases are highly compressible. Their behavior under pressure is often described by the ideal gas law: $PV = nRT$.

For most chemical engineering problems involving liquids at moderate pressures, you can assume incompressibility. For gases, or for liquids under very high pressures (think deep-sea or hydraulic systems), compressibility must be accounted for.

Newtonian vs Non-Newtonian Fluids

Newtonian Fluids

A Newtonian fluid has a constant viscosity regardless of how fast you shear it. The relationship between shear stress and shear rate is linear and follows Newton's law of viscosity:

$\tau = \mu \dot{\gamma}$

where $\tau$ is shear stress (Pa), $\mu$ is dynamic viscosity (Pa·s), and $\dot{\gamma}$ is shear rate (s$^{-1}$).

If you plot shear stress vs. shear rate for a Newtonian fluid, you get a straight line through the origin, and the slope is $\mu$.

Examples include water, air, most organic solvents, and dilute solutions. Because their behavior is linear, Newtonian fluids are straightforward to model using the Navier-Stokes equations, which makes engineering calculations much simpler.

Non-Newtonian Fluids

A non-Newtonian fluid has a viscosity that changes with the applied shear rate. The shear stress vs. shear rate relationship is no longer a straight line, so you can't use a single viscosity value.

The main types you'll encounter:

• Shear-thinning (pseudoplastic): Viscosity decreases as shear rate increases. Blood, paint, and polymer solutions behave this way. Paint is a good example: it flows easily when you brush it (high shear) but stays put on the wall (low shear).
• Shear-thickening (dilatant): Viscosity increases as shear rate increases. Cornstarch-in-water suspensions are the classic example. They resist deformation more the harder you push.
• Bingham plastic: The fluid won't flow at all until shear stress exceeds a yield stress ($\tau_0$), after which it behaves linearly like a Newtonian fluid. The model is $\tau = \tau_0 + \mu_p \dot{\gamma}$, where $\mu_p$ is the plastic viscosity. Toothpaste and mayonnaise are common examples.

Non-Newtonian fluids require specialized models like the power-law model ($\tau = K \dot{\gamma}^n$, where $n < 1$ for shear-thinning and $n > 1$ for shear-thickening), the Herschel-Bulkley model, or the Casson model to describe their flow.

Getting the classification wrong has real consequences. If you assume Newtonian behavior for a shear-thinning polymer solution, your pressure drop and flow rate calculations could be significantly off, leading to undersized pumps or poorly designed piping.

Temperature and Pressure Effects on Fluids

Temperature Effects

Temperature changes affect density, viscosity, and compressibility, sometimes in opposite directions for liquids vs. gases.

Density: Most fluids become less dense as temperature rises due to thermal expansion. This effect is much more pronounced in gases. Water decreases from about 1000 kg/m³ at 4°C to 958 kg/m³ at 100°C.

Viscosity: For liquids, viscosity decreases with increasing temperature. Higher temperatures give molecules more kinetic energy, weakening intermolecular forces and reducing resistance to flow. Water's dynamic viscosity drops from 1.787 mPa·s at 0°C to 0.282 mPa·s at 100°C. For gases, viscosity actually increases with temperature because faster-moving molecules transfer more momentum between layers.

Compressibility: Liquids become slightly more compressible at higher temperatures as molecules spread further apart. Gases become less compressible at higher temperatures because increased molecular motion resists compression.

Pressure Effects

Density: Higher pressure increases density, especially for gases. Liquids are far less affected. Air at 20°C has a density of about 1.204 kg/m³ at atmospheric pressure (101.325 kPa), but that jumps to roughly 11.21 kg/m³ at 1000 kPa.

Viscosity: Liquid viscosity generally increases with pressure because molecules are forced closer together, increasing flow resistance. Gas viscosity is relatively insensitive to pressure changes at moderate conditions.

Compressibility: All fluids become harder to compress at higher pressures, since molecules are already packed more tightly. This effect is more significant in gases. Water's bulk modulus increases from about 2.2 GPa at atmospheric pressure to about 2.6 GPa at 100 MPa.

Engineers must account for these temperature and pressure effects when designing equipment like heat exchangers, pumps, and compressors. Operating conditions can shift fluid properties enough to change equipment performance and safety margins.