Mass flow meter
The mass flow meter does not measure the volume per unit time (e.g., cubic meters per second) passing through the device; it measures the mass per unit time (e.g., kilograms per second) flowing through the device. Volumetric flow rate is the mass flow rate divided by the fluid density. If the density is constant, then the relationship is simple. If the fluid has varying density, then the relationship is not simple. The density of the fluid may change with temperature, pressure, or composition, for example. The fluid may also be a combination of phases such as a fluid with entrained bubbles.
Actual density can be determined due to dependency of sound velocity on the controlled liquid concentration.
Viscosity
In general, the viscosity of a system depends in detail on how the molecules constituting the system interact. There are no simple but correct expressions for the viscosity of a fluid. The simplest exact expressions are the Green–Kubo relations for the linear shear viscosity or the "transient time correlation function" expressions derived by Evans and Morriss in 1985. Although these expressions are each exact, calculating the viscosity of a dense fluid using these relations currently requires the use of molecular dynamics computer simulations. On the other hand, much more progress can be made for a dilute gas. Even elementary assumptions about how gas molecules move and interact lead to a basic understanding of the molecular origins of viscosity. More sophisticated treatments can be constructed by systematically coarse-graining the equations of motion of the gas molecules. An example of such a treatment is Chapman–Enskog theory, which derives expressions for the viscosity of a dilute gas from the Boltzmann equation.