Poiseuille’s Law

When you pour a glass of juice for yourself, the liquid flows easily and fast. When the syrup is poured on top of your pancakes, the syrup trickles down very slowly and flows around the vessel. The difference is because of the force of viscosity, both within the fluid and between the surroundings and the fluid. This fluid attribute is known as viscosity. 

The viscosity of juice is low, but that of syrup is high. This module will teach you about the ideal fluids with low or no viscosity. This article will tell us about how various parameters, such as viscosity, impact fluid flow rate, laminar flow, the basic flow of fluids and various other fluid-based concepts work and rely on.

Poiseuille’s Law was experimentally proved and derived by Sir Gotthilf Heinrich Ludwig Hagen in 1839 and Sir Jean Léonard Marie Poiseuille in 1838, who then published the Poiseuille’s Law in the year 1840.

What is a laminar flow?

A laminar flow is a type of flow in a fluid such as a gas or a liquid that flows in which the fluid travels in regular paths or smoothly.

What do you mean by viscosity?

Viscosity is the resistance of a liquid or gas (any fluid) to a change in the movement or shape of the nearby portions relative to one another. Viscosity also indicates the opposition to flow.

Viscosity, a fluid’s resistance to change in form or movement of adjoining sections concerning one another viscosity, signifies resistance to flow. The reciprocal viscosity is defined as fluidity, and it measures how easily a substance flows. 

Molasses, for example, has a viscosity higher than water. Because a component of a fluid that is compelled to move carries along neighbouring sections to some extent, the viscosity may be thought of as internal friction between molecules; this friction resists the development of velocity disparities within a fluid. When fluids are employed in lubrication and carried in pipelines, viscosity is crucial in determining the forces that must be overcome.

The divergent, or shearing, stress that induces flow in many fluids is equal to the shear strain rate or deformation rate. In other words, for a given fluid at a certain temperature, the shear stress divided by the shear strain rate is constant. This constant is referred to as the dynamic, or absolute, viscosity, or simply the viscosity.

Poiseuille’s Law statement

In a few cases of a laminar flow or a smooth flow, the volume rate of flow of a substance is denoted by the difference in the pressure divided by the resistance provided by the viscosity. This resistance completely depends upon the nature of viscosity and the length; the fourth power depends on the radius and is slightly different. Poiseuille’s law reasonably agrees with experiments for uniform liquids such as Newtonian fluids. These fluids obey all the laws of Newton if there is less or zero turbulence present.

Poiseuille’s Law states that the velocity of the flow of a fluid that is steady through a narrow blood vessel or a tube differs directly as the pressure and the fourth power of the tube’s radius and inversely proportional to the length of the tube as well as the coefficient of viscosity.

In fluid dynamics, the Hagen-Poiseuille equation is also commonly called the Hagen-Poiseuille law; Poiseuille’s law is a law in Physics that gives the pressure drop in a fluid flowing through a long cylindrical pipe.

This law can be successfully applied to airflow inside alveoli of a lung or the flow of fluid through plastic, paper or any kind of straw, etc.