How does the increase in the radius of a tube affect the laminar flow through the tube?

The relationship between the radius of a tube and laminar flow is described by the Hagen-Poiseuille equation, which states that the volumetric flow rate through a tube is proportional to the fourth power of the radius of the tube.

An increase in the radius of the tube, therefore, greatly enhances the flow rate. Specifically, when the radius is doubled, the flow rate increases by a factor of 2 to the fourth power, which calculates to 16 times the original flow rate. This means that an increase in the radius will lead to a proportional increase in flow rate that follows this exponentiation, firmly establishing that if the radius is increased, the laminar flow through the tube also increases significantly. This understanding of fluid dynamics is crucial in fields related to fluid mechanics and various applications involving pipes and tubing in engineering and biological systems.