Effect of Radius Reduction on Blood Flow Rate

In a clinical setting, a research team is studying the flow of blood through a narrowed artery, using a model that simulates a cylindrical tube filled with a viscous liquid. They create a scenario where the radius of the artery is reduced by half. According to the principles of fluid mechanics, particularly Poiseuille's Law, which describes the laminar flow of incompressible fluids, how does the reduced radius affect the volumetric flow rate of the blood through the artery?

Consider the following variables:

• Q: Volumetric flow rate
• r: Radius of the tube
• ΔP: Pressure difference across the tube
• η: Dynamic viscosity of the fluid

Given that Q is directly proportional to r^4 and the other factors remain constant, what can be concluded about the effect of reducing the radius by half on the flow rate?