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How does viscosity change the flow rate through a narrow tube?

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differential manometer, Torricellian barometer, and siphon — fluid mechanics Figure 1: Schematic representations of (A) a differential manometer, (B) a Torricellian barometer, and (C) a siphon.

In the context of fluid mechanics, viscosity acts as a form of internal friction that opposes the movement of a fluid. When a fluid flows through a narrow tube under laminar conditions, this internal resistance directly impacts the flow rate.1234

According to the Hagen-Poiseuille equation, the flow rate through a cylindrical pipe is inversely proportional to the fluid's viscosity. This means that as the viscosity of a fluid increases, the friction opposing the flow also increases, resulting in a lower flow rate for a given pressure difference. Conversely, a fluid with lower viscosity will experience less internal resistance, allowing for a higher flow rate through the tube.256

It is important to note that this relationship applies specifically to laminar flow, where the fluid moves in smooth, regular paths. If the flow rate or pressure gradient becomes sufficiently high, the flow may transition from laminar to turbulent, at which point the simple inverse relationship defined by Poiseuille’s law no longer holds.47