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Home > News & Articles > Poiseuille's Law: Definition, Statement, Laminar Flow, Viscosity, Derivation and Formula
Updated on 05th August, 2023 , 10 min read
You may wonder how fluid flows through a pipe or tube. The complete explanation lies in Poiseuille's law. As an engineer or student of fluid dynamics, understanding this fundamental law of fluid flow is essential. Poiseuille's law describes the pressure-driven flow of an incompressible fluid through a pipe with constant circular cross-section. It relates the flow rate, viscosity, and pressure difference between two points. With Poiseuille's law, you can calculate the flow rate and pressure loss in a pipe for any fluid. This article provides a comprehensive overview of Poiseuille's law, including the equation, variables, and applications. You will learn how to apply this important law in calculations and understand the factors affecting fluid flow in pipes.
Poiseuille's Law describes the relationship between the factors that affect the flow of fluid through a pipe. According to this law, the flow rate of an incompressible fluid through a pipe is directly proportional to the pressure difference across the pipe and the fourth power of the pipe's radius. It is inversely proportional to the length of the pipe and the viscosity of the fluid.
Mathematically, Poiseuille's Law can be expressed as:
Q = (πr4ΔP)/(8ηL)
Where Q is the volumetric flow rate, r is the radius of the pipe, ΔP is the pressure difference across the pipe, η is the dynamic viscosity of the fluid, and L is the length of the pipe.
This law shows that flow rate can be increased by increasing the pressure difference, increasing the radius of the pipe, decreasing the length of the pipe, or decreasing the viscosity of the fluid. It highlights how even small changes in these parameters can have a significant impact on flow rate due to the radius being raised to the fourth power.
Poiseuille's Law applies to laminar flow of incompressible fluids in long pipes of constant circular cross-section. It provides an important theoretical basis for understanding fluid flow and has many applications in mechanical and biomedical engineering.
Poiseuille's Law describes the relationship between the pressure drop (ΔP) and flow rate (Q) of an incompressible fluid through a pipe. The equation is:
ΔP = 8μLQ/πr^4
Where,
This equation demonstrates that flow rate is directly proportional to the pressure drop along a pipe and inversely proportional to both fluid viscosity and pipe length. Flow rate increases with higher pressure drop, lower viscosity, and shorter pipe length.
Conversely, as pipe radius increases, flow rate also increases due to a decrease in resistance. Resistance is inversely proportional to the fourth power of the pipe radius. So, doubling the radius results in a 16-fold decrease in resistance.
A laminar flow refers to the smooth, steady flow of a fluid in parallel layers with no disruption between the layers. In a laminar flow, the fluid particles move in smooth paths parallel to each other. The flow velocity remains constant with no mixing of fluid across the layers. Laminar flow occurs at lower velocities, where the viscous forces in the fluid dominate the inertial forces. The Reynolds number, which is the ratio of inertial forces to viscous forces, is less than 2000 for laminar flow.
Some key characteristics of laminar flow are:
Laminar flow is highly ordered and predictable. It allows for simplified analysis using Poiseuille's law. In contrast, turbulent flow is chaotic, irregular, and difficult to predict or model mathematically. Understanding the difference between laminar and turbulent flow is crucial in the study of fluid dynamics and applications like the Poiseuille's law.
Viscosity refers to a fluid's resistance to flow. In other words, it is a measure of a fluid's thickness or internal friction. The more viscous a fluid is, the more slowly it flows. Viscosity depends on the strength of intermolecular forces in a fluid which determine how easily its molecules slide past each other.
Some factors that affect a fluid's viscosity include:
The viscosity of a fluid is measured using a viscometer and is reported in units of poise (P) or centipoise (cP) where 1 P = 0.1 Pa∙s. Water has a viscosity of 1 cP at room temperature while honey can have a viscosity of 10,000 cP or higher. Understanding how viscosity varies with different factors and materials is important for applications like lubrication, transport, and coating flows.
Poiseuille's Law states the flow rate of an incompressible fluid in a pipe is directly related to the pressure difference and the fourth power of the pipe's radius while being inversely related to pipe length and fluid viscosity.
Equation: Q = (πr^4ΔP) / 8μL
Where,
Flow rate (Q) can be increased by:
Flow rate sensitivity to changes in pipe radius:
In summary, Poiseuille's Law quantitatively relates the physical properties of a fluid flowing through a pipe to its flow rate. It enables the calculation of laminar flow when relevant values are known and input into the formula.
In summary, Poiseuille's Law quantitatively relates the physical properties of a fluid flowing through a pipe to its flow rate. It enables the calculation of laminar flow when relevant values are known and input into the formula.
Poiseuille's law shows the relationship between flow rate (Q), pressure difference (ΔP), fluid viscosity (μ), and tube radius (r) and length (l). It can be expressed mathematically as:
Q = (πr4ΔP) / (8μl)
Consider a horizontal, cylindrical pipe through which an incompressible fluid is flowing steadily under a constant pressure difference between the two ends of the pipe. We want to find an expression for the flow rate of the fluid through the pipe.
This is the final form of Poiseuille's Law, which describes the relationship between the flow rate (Q) of an incompressible fluid through a pipe and the pressure difference (ΔP), pipe radius (r), pipe length (L), and dynamic viscosity of the fluid (μ).
Poiseuille's law formula relates the flow rate (F) of an incompressible fluid through a pipe to factors like pressure difference (ΔP), pipe radius (r), pipe length (l), and fluid viscosity (η). The equation is:
F = (πr4ΔP) / (8ηl)
Where π is the mathematical constant (approximately 3.14), r is the radius of the pipe, ΔP is the pressure difference between the two ends of the pipe, η is the dynamic viscosity of the fluid, and l is the length of the pipe.
This law states that the flow rate is directly proportional to the pressure difference and the fourth power of the radius, but inversely proportional to the length of the pipe and the viscosity of the fluid. In other words, increasing the pressure difference, the radius of the pipe, or decreasing the length of the pipe or the viscosity of the fluid will increase the flow rate.
Some key points about Poiseuille’s law:
Poiseuille’s law is a fundamental principle in fluid dynamics with many practical applications. Understanding this concept is important for optimizing flow systems and calculating pressure drops in pipes or tubes.
According to Poiseuille's law, several factors affect the flow of fluid through a pipe:
Practical Applications of Poiseuille's Law:
Understanding Blood Flow: Poiseuille's Law is essential in the medical field to comprehend blood flow through the circulatory system.
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By - Nikita Parmar 2023-08-25 09:48:44 , 11 min readFlow rate is directly proportional to the fourth power of the tube's radius. This means even a small increase in radius can lead to a large increase in flow rate. Widening the tube allows more fluid to pass through at once.
Flow rate is inversely proportional to tube length. The longer the tube, the slower the flow rate. This is because friction between the fluid and tube walls causes resistance, slowing the fluid. Shorter tubes minimize this effect.
More viscous fluids flow at a slower rate. Their thickness makes them more resistant to flow, so a higher pressure difference is required to achieve the same flow rate as a less viscous fluid. Viscosity and flow rate are inversely related.
According to Poiseuille's law, if pressure difference doubles, flow rate will also double. Pressure difference is directly proportional to flow rate. Higher pressure will push the fluid through the tube faster.
Poiseuille's Law, also known as Hagen-Poiseuille Law, describes the flow of a Newtonian fluid (liquid or gas) through a cylindrical pipe or vessel. It relates the flow rate to factors such as the viscosity of the fluid, the length, and radius of the pipe.
Poiseuille's Law is named after the French physician Jean-Louis-Marie Poiseuille, who formulated it in 1838. However, it is essential to note that Gotthilf Heinrich Ludwig Hagen had also independently derived a similar law a few years earlier, and therefore, it is sometimes referred to as Hagen-Poiseuille Law.
Poiseuille's Law is valid only for laminar flow, where the fluid moves smoothly in layers with minimal disruption. In laminar flow, the relationship between flow rate and pressure difference is linear. For turbulent flow, where the fluid's motion becomes chaotic and irregular, Poiseuille's Law does not apply.
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