![]() ![]() The relationship between the shear stress and the velocity gradient can also be obtained by considering two plates closely spaced apart at a distance y, and separated by a homogeneous substance. Non-Newtonian fluids exhibit a more complicated relationship between shear stress and velocity gradient than simple linearity. Many fluids, such as water and most gases, satisfy Newton's criterion and are known as Newtonian fluids. Here, the constant η is known as the coefficient of viscosity, the viscosity, the dynamic viscosity, or the Newtonian viscosity. Isaac Newton postulated that, for straight, parallel and uniform flow, the shear stress, τ, between layers is proportional to the velocity gradient, ∂ u/∂ y, in the direction perpendicular to the layers. In general, in any flow, layers move at different velocities and the fluid's viscosity arises from the shear stress between the layers that ultimately opposes any applied force. ![]() Volume viscosity is essential for Acoustics in fluids, see Stokes' law (sound attenuation) Newton's theory Extensional viscosity is widely used for characterizing polymers. For example, at "room temperature", water has a nominal viscosity of 1.0 × 10 -3 Pa∙s and motor oil has a nominal apparent viscosity of 250 × 10 -3 Pa∙s. Simply put, this quantity is the ratio between the pressure exerted on the surface of a fluid, in the lateral or horizontal direction, to the change in velocity of the fluid as you move down in the fluid (this is what is referred to as a velocity gradient). That is why they are often referred to as simply viscosity. Shear viscosity and dynamic viscosity are much better known than the others.
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