How is flow rate related to viscosity?

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Answer 1 · 2017-05-24T20:06:35

Flow rate is inversely proportional to viscosity.

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 $F$ $F$ 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.