Poiseuille’s Law states that the volumetric flow rate ($Q$) of a Newtonian fluid through a cylindrical pipe is directly proportional to the fourth power of the pipe radius ($r$) and the pressure gradient ($\Delta P$), and inversely proportional to the viscosity ($\mu$) and the length of the pipe ($L$). Poiseuille’s Law describes the relationship between flow rate, pressure gradient, viscosity, and dimensions of the pipe in laminar flow conditions. It’s commonly used in various engineering applications, including the design of pipelines, blood flow in capillaries, and fluid dynamics in microfluidic devices. Mathematically, it can be expressed as:

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Where:

• $Q$ is the volumetric flow rate of the fluid,
• $\Delta P$ is the pressure gradient along the pipe, 
• $r$ is the radius of the pipe,
• $\mu$ is the dynamic viscosity of the fluid, 
• $L$ is the length of the pipe.