Editing Dimensional analysis (section)

==== Quantity of matter ====
In Huntley's second approach, he holds that it is sometimes useful (e.g., in fluid mechanics and thermodynamics) to distinguish between mass as a measure of inertia (''inertial mass''), and mass as a measure of the quantity of matter. '''Quantity of matter''' is defined by Huntley as a quantity only {{em|proportional}} to inertial mass, while not implicating inertial properties. No further restrictions are added to its definition.

For example, consider the derivation of [[Poiseuille's Law]]. We wish to find the rate of mass flow of a viscous fluid through a circular pipe. Without drawing distinctions between inertial and substantial mass, we may choose as the relevant variables:
{| class="wikitable"
! Symbol !! Variable !! Dimension
|-
| <math>\dot{m}</math> || mass flow rate || T<sup>−1</sup>M
|-
| <math>p_\text{x}</math> || pressure gradient along the pipe || T<sup>−2</sup>L<sup>−2</sup>M
|-
| {{mvar|ρ}} || density || L<sup>−3</sup>M
|-
| {{mvar|η}} || dynamic fluid viscosity || T<sup>−1</sup>L<sup>−1</sup>M
|-
| {{mvar|r}} || radius of the pipe || L
|}

There are three fundamental variables, so the above five equations will yield two independent dimensionless variables:
: <math>\pi_1 = \frac{\dot{m}}{\eta r}</math>
: <math>\pi_2 = \frac{p_\mathrm{x}\rho r^5}{\dot{m}^2}</math>

If we distinguish between inertial mass with dimension <math>M_\text{i}</math> and quantity of matter with dimension <math>M_\text{m}</math>, then mass flow rate and density will use quantity of matter as the mass parameter, while the pressure gradient and coefficient of viscosity will use inertial mass. We now have four fundamental parameters, and one dimensionless constant, so that the dimensional equation may be written:
: <math>C = \frac{p_\mathrm{x}\rho r^4}{\eta \dot{m}}</math>

where now only {{mvar|C}} is an undetermined constant (found to be equal to <math>\pi/8</math> by methods outside of dimensional analysis). This equation may be solved for the mass flow rate to yield [[Poiseuille's law]].

Huntley's recognition of quantity of matter as an independent quantity dimension is evidently successful in the problems where it is applicable, but his definition of quantity of matter is open to interpretation, as it lacks specificity beyond the two requirements he postulated for it. For a given substance, the SI dimension [[amount of substance]], with unit [[Mole (unit)|mole]], does satisfy Huntley's two requirements as a measure of quantity of matter, and could be used as a quantity of matter in any problem of dimensional analysis where Huntley's concept is applicable.