Editing Newtonian fluid (section)

== Newton's law of viscosity ==
The following equation illustrates the relation between shear rate and shear stress '''for a fluid with laminar flow only in the direction x''':
<math display="block">\tau_{xy} = \mu \frac{ \mathrm{d} v_x }{ \mathrm{d} y },</math>
where:
* <math>\tau_{xy}</math> is the shear stress in the components x and y, i.e. the force component on the direction x per unit surface that is normal to the direction y (so it is parallel to the direction x)
* <math>\mu</math> is the dynamic viscosity, and
* <math display="inline">\frac{ \mathrm{d} v_x }{ \mathrm{d} y }</math> is the flow velocity gradient along the direction y, that is normal to the flow velocity <math>v_x</math>.
If viscosity <math>\mu</math> does not vary with rate of deformation the fluid is Newtonian.

=== Power law model ===
[[File:Dilatant-pseudoplastic.svg|thumb|In blue a Newtonian fluid compared to the dilatant and the pseudoplastic, angle depends on the viscosity.]]
The power law model is used to display the behavior of Newtonian and non-Newtonian fluids and measures shear stress as a function of strain rate.

The relationship between shear stress, strain rate and the velocity gradient for the power law model are:
<math display="block">\tau_{xy} = -m\left| \dot{\gamma} \right|^{n-1} \frac{dv_x}{dy},</math>
where
*<math>\left| \dot{\gamma} \right|^{n-1} </math> is the absolute value of the strain rate to the (''n''−1) power;
* <math display="inline">\frac{dv_x}{dy}</math> is the velocity gradient;
* ''n'' is the power law index.

If
* ''n'' < 1 then the fluid is a pseudoplastic.
* ''n'' = 1 then the fluid is a Newtonian fluid.
* ''n'' > 1 then the fluid is a dilatant.

=== Fluid model ===
The relationship between the shear stress and shear rate in a casson fluid model is defined as follows:
<math display="block">\sqrt{\tau} = \sqrt{\tau _0} + S\sqrt{{dV \over dy}}  </math>
where ''τ''<sub>0</sub> is the yield stress and
<math display="block">S = \sqrt{\frac{\mu}{(1-H)^\alpha}},</math>
where ''α'' depends on protein composition and ''H'' is the [[Hematocrit]] number.