Poiseuille's Equation for Pressure Drop is a mathematical formula that describes the relationship between the pressure drop in a fluid flowing through a cylindrical pipe and the fluid's viscosity, flow rate, and pipe diameter. It was developed by French physicist Jean Léonard Marie Poiseuille in the 19th century.
Poiseuille's Equation is derived from the Navier-Stokes equations, which describe the motion of a viscous fluid. By making certain assumptions and simplifications, Poiseuille was able to derive a simpler equation that relates pressure drop to fluid properties and pipe geometry.
Poiseuille's Equation assumes that the fluid is incompressible, the flow is laminar (smooth and non-turbulent), and the pipe is long and straight with a constant cross-sectional area. It also assumes that the fluid has a constant viscosity and that there are no external forces acting on the fluid.
Poiseuille's Equation is commonly used in the fields of fluid mechanics and engineering to calculate pressure drops in various systems, such as pipes, blood vessels, and ventilation systems. It is also used in the design and optimization of fluid flow systems, such as in chemical and petroleum industries.
Yes, Poiseuille's Equation is only valid for laminar flow and does not account for the effects of turbulence. It also assumes a constant viscosity, which may not hold true for all fluids. Additionally, it does not take into account the compressibility of the fluid, which may be significant in certain applications.