How is flow rate related to viscosity?

1 Answer
May 24, 2017

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.

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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.