Question

How is flow rate related to viscosity?

Answer 1

Flow rate is inversely proportional to viscosity.

Explanation:

The relation is called Poiseuille's law, which describes the smooth flow of a fluid along a tube.

The flow rate `F` is proportional to the pressure drop `Δp = p_1 – p_2` divided by `R`, the resistance to flow.

`color(blue)(bar(ul(|color(white)(a/a) F = (Δp)/R = (p_1 – p_2)/R color(white)(a/a)|)))`

The resistance to flow in turn is directly proportional to the viscosity `eta`.

`color(blue)(bar(ul(|color(white)(a/a) R = (8etaL)/(πr^4)color(white)(a/a)|)))" "`

Combining the two formulas gives Poiseuille's law:

`color(blue)(bar(ul(|color(white)(a/a)F = (πr^4Δp)/(8etaL)color(white)(a/a)|)))" "`

If `r, Δp`, and `L` are constant, we can write

`F = k/eta`

Thus, the flow rate is inversely proportional to the viscosity.