The terms absolute viscosity and dynamic viscosity are synonyms that refer to the exact same fundamental property of a fluid. This property describes a fluid’s internal resistance to flow and is often symbolized by the Greek letter mu (\(\mu\)) or sometimes eta (\(\eta\)). The use of two different terms can create confusion, but “absolute” is frequently used to make a clear distinction from the related property called kinematic viscosity. Understanding this internal friction is the starting point for analyzing how any liquid or gas moves under force.
Understanding Dynamic Viscosity
Dynamic viscosity quantifies the force required to make a fluid flow at a certain rate. This measurement represents the internal friction between adjacent layers of a fluid moving relative to one another. Liquids resist this shearing motion due to cohesive forces, while gas resistance results from the exchange of momentum between molecules.
The concept is often explained using an analogy of a fluid layer between two parallel plates. If one plate is stationary and the other moves at a constant velocity, a force is required to maintain the motion, overcoming the fluid’s internal resistance and creating shear stress.
Dynamic viscosity is mathematically defined as the ratio of the shear stress (\(\tau\)) to the shear rate (\(\dot{\gamma}\)). Shear stress is the force applied per unit area, and shear rate measures how quickly the fluid’s velocity changes across the distance between layers. For Newtonian fluids—like water and many oils—this ratio remains constant regardless of the applied shear rate.
Distinguishing Dynamic from Kinematic Viscosity
The main reason for the varied terminology is to clearly differentiate dynamic viscosity from kinematic viscosity. Kinematic viscosity, represented by the Greek letter nu (\(\nu\)), is a derived property that describes a fluid’s resistance to flow under the influence of gravity. Unlike dynamic viscosity, which involves a force, kinematic viscosity is concerned with the fluid’s motion.
Kinematic viscosity is mathematically defined as the ratio of the dynamic viscosity (\(\mu\)) to the fluid’s density (\(\rho\)), expressed by the formula \(\nu = \mu / \rho\). This means that two fluids can have similar dynamic viscosities but vastly different kinematic viscosities if their densities are not the same.
Kinematic viscosity is often interpreted as the measure of momentum diffusivity within the fluid. It determines how quickly momentum is transferred through the fluid without considering the external force required to initiate the flow. This measurement is particularly relevant when gravity is the primary driving force for the fluid’s movement, such as in drainage or open channel flow.
Measuring Viscosity and Standard Units
The measurement of dynamic and kinematic viscosity requires different approaches and instruments, leading to distinct standard units for each. Dynamic viscosity is typically measured using rotational viscometers, which determine the torque required to rotate a spindle or plate immersed in the fluid at a known speed. This measurement directly yields the shear stress, allowing for the calculation of dynamic viscosity.
Dynamic Viscosity Units
The International System of Units (SI) unit for dynamic viscosity is the Pascal-second (Pa·s), equivalent to one Newton-second per square meter (\(N \cdot s/m^2\)). In the older centimeter-gram-second (CGS) system, the unit is the Poise (P), though the centipoise (cP) is more common. One Pa·s equals 10 P or 1000 cP.
Kinematic Viscosity Units
Kinematic viscosity is most often measured using capillary viscometers, recording the time it takes for a fixed volume of fluid to flow through a calibrated tube under gravity. The SI unit for kinematic viscosity is square meters per second (\(m^2/s\)). The CGS unit is the Stokes (St), but the centistokes (cSt) is used more frequently. One \(m^2/s\) equals 10,000 St or 1,000,000 cSt.
Temperature control is important in all viscosity measurements, as small changes can cause the viscosity of many common fluids to vary significantly.