To determine the viscosity of a fluid, you need to get into the field of viscosity measurement, which is a broader field of science known as rheology. Rheology deals with the flow behavior and deformation of materials.
Imagine that all materials are classified on a virtual scale from solid to liquid. Scientists point out that solid materials are elastic and liquids are viscous. In our daily life, we mostly come across viscoelastic materials. That is, a substance that is neither perfectly elastic nor completely viscous. Depending on the properties of the material, we classify it as a viscoelastic solid (like a sweet jelly) or a viscoelastic liquid (like a yogurt drink or body wash).
The specific field of viscosity measurement covers desirable viscous fluids and - taking into account certain limitations - also viscoelastic liquids, ie viscous fluids containing elastic moieties. Flowing fluids tend to exhibit low resistance to deformation. They are low viscosity fluids. High viscosity fluid resists deformation. Therefore, they are not easy to flow.
two flat models
The two-plate model provides a mathematical description of viscosity. Think of a sandwich [1] : There are two plates in between. Correct calculation of viscosity-related parameters depends on two criteria:
Liquid does not slide along the plate, but makes good contact with it. Scientifically speaking, there is an adhesive force between the fluid and the plate.
The flow is laminar. It forms infinitely small thin layers and does not undergo turbulence (ie, eddies). You can map laminar flow as a stack of paper (or a beer mat).
The lower board does not move. The upper plate moves very slowly and subjects the fluid to a stress parallel to its surface: the shear stress (τ). The force (in Newtons) applied to the upper plate divided by the area of the plate (in square meters) determines the shear stress. The unit of force/area is N/m², named pascal [Pa ] after Blaise Pascal [2] .
$$\tau = {F\over{A}} \left[N\over{m^2}\right]$$
Equation 1: Shear Stress
The two-plate model allows calculation of another parameter: the shear rate (γ-point or D).
The shear rate is the velocity of the upper plate (in meters per second) divided by the distance between the two plates (in meters). Its unit is [1/s] or countdown seconds [s -1 ].
$$\dot{\gamma}=(D=){v\over{h}}\left[{m\over{s\cdot m}}\right]\left[{1\over{s}}\ right] = [s ^ {-1}] $$
Equation 2: Shear Rate
According to Newton's law [3] , the shear stress is the viscosity multiplied by the shear rate. Thus, viscosity η is the shear stress divided by the shear rate. This simple relationship can only describe Newtonian fluids.
$$ \tta \{\eta}{\cdot} \dot{\gamma} \rightarrow{\eta} = {\tau \over \dot {\gamma}} [Pa \cdot{s}] = \left [ {Pa \ over {1 \ over s}} \ right] $$
Equation 3: Reformulating Newton's Law: Dynamic viscosity is the shear stress divided by the shear rate.
