# Dynamic Shear Viscosity

on . Posted in Fluid Dynamics

Dynamic shear viscosity, abbreviated as $$\mu$$ (Greek symbol mu), is a measure of a fluid's resistance to flow under shear stress when the applied stress varies with time.  It characterizing the flow behavior of fluids, and it describes how easily a fluid deforms under the influence of an applied shear force.  When a fluid is subjected to shear stress, it undergoes deformation, with one layer of fluid moving relative to another layer.  Dynamic shear viscosity quantifies the magnitude of this internal resistance to flow.  The higher the dynamic shear viscosity, the greater the resistance to flow, and the more viscous the fluid is considered to be.

The dynamic shear viscosity of a fluid depends on factors such as temperature, pressure, composition, and flow conditions.  It is commonly measured using rheometers or viscometers under controlled conditions.

Dynamic shear viscosity is used in various engineering applications, including fluid dynamics, lubrication, polymer processing, and chemical engineering.  Understanding the dynamic shear viscosity of fluids is usedl for designing processes, predicting flow behavior, and selecting appropriate materials for specific applications.

### Dynamic Shear Viscosity Formula

$$\mu = F_a \; y \;/\; A \; u$$     (Dynamic Shear Viscosity)

$$F_a = \mu \; A \; u \;/\; y$$

$$y = \mu \; A \; u \;/\; F_a$$

$$A = F_a \; y \;/\; \mu \; u$$

$$u = F_a \; y \;/\; \mu \; A$$

Symbol English Metric
$$\mu$$  (Greek symbol mu) = dynamic shear viscosity $$lbf-sec \;/\; ft^2$$ $$Pa-s$$
$$F_a$$ = applied force $$lbf$$ $$N$$
$$y$$ = separation distance $$ft$$ $$m$$
$$A$$ = area of each plate $$ft^2$$ $$m^2$$
$$u$$ = speed of movement $$ft \;/\; sec$$ $$m \;/\; s$$

Tags: Viscosity Fluid