Why is the kinematic viscosity unit m²/s when you only measure the time it passes a certain distance through a capillary rheometer?

Question

Why did the scientists who designed the kin.viscosity measurement using a capillary rheometer setup decide to express the results in m²/s when all you measure is the time: the less viscous (faster flowing) a fluid is, the faster it will cover the fixed distance in a capillary rheometer. Kin. viscosity = the time for the distance covered in seconds (or minutes) x the rheometer constant = less m²/s for a faster flowing fluid. So the unit doesn't make sense either.

Answer 1

Because the kinematic viscosity unit is the division of dynamic viscosity $ μ =\text{ absolute or dynamic viscosity (N s/m^2)}$ by the $density$.

$$ν = \frac{ μ}{ ρ}$$

• $μ = \text{absolute or dynamic viscosity (N s/m^2)}$
• $ρ = density \ (kg/m3)$
• $ν = kinematic\ viscosity\ (m^2/s)$

The m^2 in the dynamic viscosity comes from Newton's definition of tangential force per unit area required to move one horizontal plane with respect to another plane - at a unit velocity - when maintaining a unit distance apart in the fluid. It is the area of the layer being considered. see here.

Edit

To obtain kinematic viscosity (v = ny), we multiply the capillary measured flow time (tf) by the so-called capillary constant (KC). This constant needs to be determined for each capillary by calibrating the capillary, i.e. by measuring a reference liquid of known viscosity. [source][2]

$$v = K _{C} {\cdot} t _{f} $$

[2]: https://wiki.anton-paar.com/us-en/how-to-measure-viscosity/#:~:text=To%20obtain%20kinematic%20viscosity%20(v,reference%20liquid%20of%20known%20viscosity.