Poiseuille flow is a type of laminar flow in which a fluid moves through a cylindrical pipe with a constant velocity and pressure gradient. It is named after the French physicist Jean-Louis Marie Poiseuille who first described it in the 19th century.
Viscosity is the measure of a fluid's resistance to flow. In Poiseuille flow, viscosity plays a crucial role in determining the rate of flow and the pressure drop along the length of the pipe. A higher viscosity will result in a slower flow and a larger pressure drop.
The formula for calculating viscosity of water in Poiseuille flow is given by: μ = (P1 - P2) * (R^4 / 8 * L * Q), where μ is the viscosity, P1 and P2 are the pressures at the two ends of the pipe, R is the radius of the pipe, L is the length of the pipe, and Q is the volumetric flow rate.
The units of viscosity in Poiseuille flow are typically in Pascals per second (Pa*s) or in centipoise (cP). In the formula, the unit of pressure (P1 and P2) is in Pascals (Pa), the unit of radius (R) is in meters (m), the unit of length (L) is in meters (m), and the unit of volumetric flow rate (Q) is in cubic meters per second (m^3/s).
The calculated viscosity of water in Poiseuille flow can be used for various purposes, such as predicting the flow rate and pressure drop in a given pipe system, designing and optimizing fluid flow systems, and understanding the behavior of fluids in pipes. It is also commonly used in industries such as engineering, chemistry, and biology.