Editing Viscometer (section)

===Calculation of shear rate and shear stress form factors===
Rheometers and viscometers work with torque and angular velocity. Since viscosity is normally considered in terms of shear stress and shear rates, a method is needed to convert from "instrument numbers" to "rheology numbers". Each measuring system used in an instrument has its associated "form factors" to convert torque to shear stress and to convert angular velocity to shear rate.

We will call the shear stress form factor {{math|''C''<sub>1</sub>}} and the shear rate factor {{math|''C''<sub>2</sub>}}.

: shear stress = torque ÷ {{math|''C''<sub>1</sub>}}.
: shear rate = {{math|''C''<sub>2</sub>}} × angular velocity.
:: For some measuring systems such as parallel plates, the user can set the gap between the measuring systems. In this case the equation used is
::: shear rate = {{math|''C''<sub>2</sub>}} × angular velocity / gap.
: viscosity = shear stress / shear rate.

The following sections show how the form factors are calculated for each measuring system.

====Cone and plate====
: <math>\begin{align}
  C_1 &= \frac{3}{2} r^3, \\
  C_2 &= \frac{1}{\theta},
\end{align}</math>

where
: {{mvar|r}} is the radius of the cone,
: {{mvar|θ}} is the cone angle in radians.

====Parallel plates====
: <math>\begin{align}
  C_1 &= \frac{3}{2} r^3, \\
  C_2 &= \frac{3}{4} r,
\end{align}</math>

where {{mvar|r}} is the radius of the plate.

'''Note:''' The shear stress varies across the radius for a parallel plate.  The above formula refers to the 3/4 radius position if the test sample is Newtonian.

====Coaxial cylinders====
: <math>\begin{align}
  C_1 &= 2\pi r_\text{a}^2 H, \\
  C_2 &= \frac{2 r_\text{i}^2 r_\text{o}^2}{r_\text{a}^2 \left( r_\text{o}^2 - r_\text{i}^2\right)},
\end{align}</math>

where:
: {{math|''r''<sub>a</sub> {{=}} (''r''{{sub|i}} + ''r''{{sub|o}})/2}} is the average radius,
: {{math|''r''<sub>i</sub>}} is the inner radius,
: {{math|''r''<sub>o</sub>}} is the outer radius,
: {{mvar|H}} is the height of cylinder.

Note: {{math|''C''<sub>1</sub>}} takes the shear stress as that occurring at an average radius {{math|''r''<sub>a</sub>}}.