Where we have used the fact that the derivative of y with respect to y is 1. Substituting this equation for u into the expression for shear rate, we get: Where μ is the dynamic viscosity of the fluid. We can assume that the velocity profile in the fluid is linear, meaning that the velocity varies linearly with distance from the surface where the shear stress is applied. Where u is the velocity of the fluid in the x direction, and y is the distance from the surface where the shear stress is applied. Next, we can define the shear rate as the rate of change of velocity with respect to distance. Where F is the force applied to the fluid, and A is the area over which the force is applied. To derive this equation, we can start with the definition of shear stress, which is given by: This equation is the defining equation for dynamic viscosity, and it expresses the relationship between shear stress and shear rate in a fluid. This relationship is expressed mathematically as: Specifically, we assume that fluids behave as Newtonian fluids, meaning that the shear stress is directly proportional to the shear rate. To derive the formula for dynamic viscosity, we need to start with some basic assumptions about the behavior of fluids. Shampoo: The dynamic viscosity of shampoo determines its ability to flow and spread through the hair, while still providing enough resistance to create suds and clean the hair effectively.ĭynamic viscosity, represented by the symbol μ, is defined as the ratio of the shearing stress τ to the rate of deformation of a fluid (shear rate γ).The viscosity of blood is an important property in medicine, as it affects blood flow and can be used to diagnose conditions such as anemia or other blood disorders. Blood: Blood is a fluid with a relatively low dynamic viscosity compared to other fluids like honey or motor oil.For example, a high viscosity syrup will be thick and pour slowly, whereas a low viscosity sauce will be thinner and pour more easily. Syrups and sauces: The dynamic viscosity of syrups and sauces determines their texture and consistency.If the paint has too high a viscosity, it will be too thick and difficult to apply, whereas if the viscosity is too low, the paint may run or drip. Paint: Dynamic viscosity is an important property of paint, as it determines the paint’s ability to flow and spread smoothly.

The oil must be able to flow freely through the engine while still providing enough resistance to prevent metal parts from rubbing against each other and causing damage. Motor oil: The dynamic viscosity of motor oil plays an important role in lubrication of engines.Here are some examples of dynamic viscosity in daily life: Daily Life Examples of Dynamic Viscosity.s, although this can also vary depending on factors such as hematocrit (the percentage of red blood cells in the plasma) and temperature.s, although this can vary depending on the specific type of oil and the temperature at which it is tested.īlood plasma has a lower dynamic viscosity than honey or engine oil, typically ranging from 0.001 Pa.s, depending on factors such as temperature and moisture content.Įngine oil generally has a dynamic viscosity in the range of 0.05 Pa.Honey typically has a relatively high dynamic viscosity, ranging from around 2 Pa Reyn (reyn) – used for very low viscosity fluids, defined as 1 dyne Τ: Shear stress, μ: Dynamic viscosity, dv/dy: Velocity gradientĬentipoise (cP) – equal to 0.001 Poise or 0.0001 Pa It is a property of the fluid and is a measure of how thick or resistant to flow the fluid is. DefinitionĪ measure of the resistance of a fluid to flow under an applied force or stress. The unit of viscosity, accordingly, is newton-second per square meter, which is usually expressed as pascal-second in SI units. The dimensions of dynamic viscosity are (force × time) ÷ area.

Dynamic viscosity formula for air