The Hagen-Poiseuille Equation describes the volumetric flow rate of an incompressible and Newtonian fluid through a long cylindrical pipe with constant circular cross-section, under laminar flow conditions. It highlights the direct proportionality of flow rate to the fourth power of the pipe's radius and the pressure difference, while inversely proportional to the fluid's viscosity and the pipe's length.

Hagen-Poiseuille Equation

Volumetric flow rate is the volume of fluid that passes through a given surface per unit time, typically measured in cubic meters per second (m³/s) or liters per minute (L/min). It is a crucial parameter in fluid dynamics, engineering, and various industrial applications, as it helps in designing systems for efficient fluid transport and management.

Volumetric Flow Rate

An incompressible fluid is a theoretical fluid with a constant density, meaning its volume does not change under pressure. This assumption simplifies the analysis of fluid flow and is often applied to liquids in fluid dynamics where density variations are negligible.

Incompressible Fluid

A Newtonian fluid is a fluid whose viscosity remains constant regardless of the stress applied to it or the rate of flow. This behavior is described by Newton's law of viscosity, which states that the shear stress between adjacent fluid layers is proportional to the velocity gradients between the two layers.

Newtonian Fluid

Long cylindrical pipe

Constant circular cross-section

Laminar flow conditions

Direct proportionality describes a linear relationship between two variables where one variable is a constant multiple of the other. This means that if one variable increases, the other increases at a consistent rate, and if one decreases, the other decreases proportionally.

Direct Proportionality

Fourth power of the pipe's radius

Pressure difference is the driving force behind fluid flow and is crucial for understanding phenomena in both natural and engineered systems. It results from variations in force exerted per unit area and is fundamental in applications ranging from meteorology to hydraulics.

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