Basic Concepts

Abstract

The viscosity η is defined as the ratio of the shear stress σ₂₁ and the shear rate γ̇

$$ \eta = \frac{{{\sigma _{21}}}}{{\dot \gamma }} $$

((2.1))

The shear stress σ₂₁, as can be seen in Fig. 2.1, is the force F [N] that is exerted on the surface element A [m²] parallel to the direction of the flow:

$${\sigma _{21}} = \frac{F}{A}$$

((2.2))

The shear stress has the unit [Pa], which is the same as for a pressure. In former times, the unit [dyn/cm²] was often used:

$$1Pa = 1N/{m^2} = 10dyn/c{m^2} = 1kg/\left( {m/{s^2}} \right) $$

((2.3))

The shear rate γ̇ describes how fast the fluid layers move in respect to one another in a laminar flow profile. It is described as the ratio of the velocity difference Δv [m/s] of two fluid layers and the distance Δh between them.