The Hagen-Poiseuille equation provides a mathematical description of laminar flow in a cylindrical pipe, where the flow is smooth and orderly, with fluid particles moving in parallel layers. It shows that the volume flow rate is directly proportional to the fourth power of the pipe radius (r4), the pressure gradient ($\Delta P$), and inversely proportional to the viscosity ($\mu$) and length ($L$) of the pipe.

Where:

• $Q$ is the volume flow rate (m³/s)
• $r$ is the radius of the pipe (m)
• $\Delta P$ is the pressure difference driving the flow (Pa)
• $\mu$ is the dynamic viscosity of the fluid (Pa·s)
• $L$ is the length of the pipe (m)