Viscosity is a fundamental property of fluids that describes their internal resistance to flow. This characteristic determines how easily a fluid moves or deforms when subjected to an outside influence. The way scientists and engineers quantify this resistance has led to the development of two distinct, yet related, measurements: dynamic viscosity and kinematic viscosity. The distinction lies in whether the measurement accounts solely for the internal friction of the fluid or if it also incorporates the fluid’s density.
Defining Viscosity as Fluid Resistance
Viscosity can be thought of as the thickness or stickiness of a fluid. A simple way to understand this property is to compare a fluid like molasses to water; the molasses resists movement much more strongly. This resistance stems from internal friction caused by the cohesive forces between the fluid’s molecules. When a fluid flows, different layers move at different speeds, and the friction between these layers creates a drag that slows the motion.
Dynamic Viscosity and Internal Friction
Dynamic viscosity, also referred to as absolute viscosity, measures the force required to overcome the fluid’s internal friction and induce flow at a specific rate. It quantifies the fluid’s resistance to shear stress, which is the force applied parallel to a surface that causes layers of the fluid to slide over one another. Imagine placing a layer of fluid between two parallel plates and trying to drag the top plate; dynamic viscosity describes the amount of force needed to maintain that sliding motion. This measurement is directly tied to the concept of Newton’s Law of Viscosity, which states that the shear stress is directly proportional to the rate of shear strain, with dynamic viscosity serving as the proportionality constant.
This property is a measure of the fluid’s inherent stickiness, independent of its mass or weight. The standard International System of Units (SI) unit for dynamic viscosity is the Pascal-second (\(\text{Pa}\cdot\text{s}\)). The older CGS unit is the Poise (P), though the centipoise (cP) is often used in practice. Measuring dynamic viscosity is particularly useful when analyzing systems where an external force, like a pump or mixer, is actively driving the flow.
Kinematic Viscosity and Momentum Diffusion
Kinematic viscosity is a derived property that focuses on how readily momentum is transferred through a fluid, rather than the force required to move it. It is calculated by taking the dynamic viscosity of the fluid and dividing it by the fluid’s mass density. This division by density mathematically removes the force component from the measurement, leaving a value that describes the fluid’s inherent mobility. Kinematic viscosity is sometimes described as the momentum diffusivity of the fluid.
The unit of kinematic viscosity in the SI system is square meters per second (\(\text{m}^2/\text{s}\)). In the CGS system, the unit is the Stokes (St), with the centistoke (cSt) being a frequently encountered unit. This measurement is especially relevant when the only external force acting on the fluid is gravity. Since gravity acts on the mass of the fluid, the density of the fluid becomes a necessary factor in determining its flow characteristics. Fluids with the same dynamic viscosity will have different kinematic viscosities if their densities are not equal, leading to different flow behaviors under gravity.
Relating Dynamic and Kinematic Measurements
Density is the sole factor differentiating the two values for any given fluid. The practical implication is that the choice between dynamic and kinematic viscosity depends entirely on the forces dominating the fluid’s motion in a specific application.
Dynamic viscosity is the preferred measurement when dealing with applications involving external pressures and shear forces, such as in the design of pumping systems, mixing equipment, or when assessing the sheer resistance of lubricating oil between moving parts in an engine. Conversely, kinematic viscosity is used predominantly in gravity-driven flow systems, like calculating how fast a liquid will drain or flow in an open channel.
The petroleum industry, for instance, frequently uses kinematic viscosity to grade motor oils, as the oil’s flow under the force of gravity within the engine is a primary concern. Ultimately, dynamic viscosity is a purer measure of fluid friction, while kinematic viscosity is a measure of that friction relative to the fluid’s inertia.