Kinematic viscosity is a fundamental property of fluids that describes a liquid’s resistance to flow under the influence of gravity. This measurement provides insight into how easily a fluid moves through a system without external force. The value is widely relied upon in fields such as fluid engineering, lubrication, and material science to determine a substance’s flow characteristics. Engineers use kinematic viscosity to predict pressure drops in pipelines, select appropriate pumps, and ensure lubricants perform correctly across various operating conditions.
Understanding the Required Components
Calculating kinematic viscosity requires obtaining two measurable properties: dynamic viscosity and density. Dynamic viscosity, represented by the Greek symbol \(\mu\) (mu), measures the fluid’s internal friction, or its resistance to being sheared or deformed by an applied force. It quantifies the “stickiness” of the fluid, reflecting the cohesive forces between its molecules as they move past one another. The standard SI unit for dynamic viscosity is the Pascal-second (\(\text{Pa}\cdot\text{s}\)), though the centipoise (\(\text{cP}\)) is frequently used, where 1 \(\text{cP}\) equals \(0.001 \text{ Pa}\cdot\text{s}\).
The second component is density, represented by the symbol \(\rho\) (rho), defined as the fluid’s mass per unit volume. Density measures how tightly the matter in the fluid is packed together. The standard SI unit is kilograms per cubic meter (\(\text{kg}/\text{m}^3\)), but grams per cubic centimeter (\(\text{g}/\text{cm}^3\)) is also common. Since kinematic viscosity is calculated from the ratio of these two values, any variation in dynamic viscosity or density affects the final result.
The Kinematic Viscosity Calculation
Kinematic viscosity, symbolized by \(\nu\) (nu), is calculated by dividing the dynamic viscosity (\(\mu\)) by its density (\(\rho\)). The equation is \(\nu = \mu / \rho\). This calculation removes the mass component from dynamic viscosity, resulting in a value that describes the fluid’s flow behavior under gravity. The focus shifts to how momentum diffuses within the fluid, which is why kinematic viscosity is sometimes referred to as the diffusivity of momentum.
To yield a correct result, unit consistency is necessary, typically by using SI units. Dynamic viscosity must be in Pascal-seconds (\(\text{Pa}\cdot\text{s}\)) and density must be in kilograms per cubic meter (\(\text{kg}/\text{m}^3\)). Dividing these SI units results in the SI unit for kinematic viscosity: square meters per second (\(\text{m}^2/\text{s}\)).
While \(\text{m}^2/\text{s}\) is the SI standard, common industry units, especially for petroleum products and lubricants, are the Stokes (\(\text{St}\)) and the Centistokes (\(\text{cSt}\)). One Stokes equals one square centimeter per second (\(\text{cm}^2/\text{s}\)), and one Centistokes is one hundredth of a Stokes. The conversion is straightforward: \(1 \text{ m}^2/\text{s}\) equals \(10,000 \text{ St}\), or \(1,000,000 \text{ cSt}\). The Centistokes unit is used almost universally because \(1 \text{ cSt}\) is equivalent to \(1 \text{ mm}^2/\text{s}\).
Obtaining Input Values in Practice
The required values, dynamic viscosity and density, must be determined empirically through laboratory measurement. Dynamic viscosity is measured using a viscometer, such as a rotational viscometer, which applies a force to the fluid and measures the resulting resistance. Many common capillary-type viscometers actually measure kinematic viscosity directly by timing how long a fluid takes to flow through a calibrated glass tube under gravity, with the result calculated by multiplying the flow time by a factor.
Density is measured using instruments like densitometers, which employ a vibrating-element principle to determine mass per volume. For precise calculations, especially when determining dynamic viscosity from measured kinematic viscosity, a separate density measurement is mandatory. These measurements are often carried out according to specific standards like those set by ASTM International.
A procedural constraint affecting both input values is the fluid’s temperature, as viscosity is highly dependent on this factor. To ensure comparable results, measurements must be standardized to a specific temperature. The petroleum industry often uses \(40^\circ\text{C}\) for industrial oils and \(100^\circ\text{C}\) for engine oils, as defined by the ASTM D445 standard. Precise temperature control, often to within \(\pm 0.02^\circ\text{C}\), is necessary during measurement to ensure the calculated kinematic viscosity is accurate.