The Hagen-Poiseuille equation, also known as Poiseuille’s law, describes laminar flow in a cylindrical pipe. It gives the rate of flow ($Q$) of a viscous, incompressible fluid through a pipe of constant cross-sectional area and length under a constant pressure gradient ($\Delta P$). This equation shows that the flow rate is directly proportional to the fourth power of the radius of the pipe (r4), the pressure gradient ($\Delta P$), and inversely proportional to the viscosity of the fluid ($\mu$) and the length of the pipe ($L$).The Hagen-Poiseuille equation is given by

​

Where:

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