# How is flow rate related to viscosity?

##### 1 Answer

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

#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

#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

#F = k/eta#

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