# Dynamic Viscosity

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Dynamic viscosity, abbreviated as $$\mu$$ (Greek symbol mu), also called absolute viscosity, is the force required to move adjacent layers that are parallel to each other at different speeds.  The velocity and shear stress are combined to determine the dynamic viscosity.  Dynamic viscosity is a measure of a fluid's resistance to flow when subjected to an applied force or stress.  It quantifies the internal friction within a fluid as it deforms under the influence of an external force.  When a fluid flows, its molecules or particles interact with each other and create internal forces that resist the flow.  Dynamic viscosity measures the magnitude of these internal forces and their effect on the fluid's flow behavior.

Viscosity is influenced by factors such as temperature and pressure.  Generally, as temperature increases, the viscosity of most liquids decreases, while the viscosity of gases increases. Pressure typically has a minor effect on viscosity, except for highly compressible fluids.  Dynamic viscosity is an important property in various fields, including fluid dynamics, engineering, and materials science.  It plays a significant role in determining flow rates, designing fluid systems, analyzing fluid behavior in pipes or channels, and understanding the performance of lubricants and other viscoelastic materials.

## Dynamic viscosity formula

$$\large{ \mu = \frac {\tau} {\dot {\gamma}} }$$
Symbol English Metric
$$\large{ \mu }$$  (Greek symbol mu) = dynamic viscosity $$\large{\frac{lbf-sec}{ft^2}}$$ $$\large{ Pa-s }$$
$$\large{ \tau }$$  (Greek symbol tau) = shear stress $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ \dot {\gamma} }$$  (Greek symbol gamma) = shear rate $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$

## Dynamic viscosity formula

$$\large{ \mu = \frac{ \rho \; v \; l_c }{ Re } }$$
Symbol English Metric
$$\large{ \mu }$$  (Greek symbol mu) = dynamic viscosity $$\large{\frac{lbf-sec}{ft^2}}$$ $$\large{ Pa-s }$$
$$\large{ \rho }$$  (Greek symbol rho) = density of the fluid $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ v }$$ = velocity of the fluid $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ l_c }$$ = characteristic length or diameter of the fluid flow $$\large{ft}$$ $$\large{m}$$
$$\large{ Re }$$ = Reynolds number $$\large{dimensionless}$$ Tags: Viscosity Equations