What is Poiseuille's law: Definition and 13 Discussions

In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section.
It can be successfully applied to air flow in lung alveoli, or the flow through a drinking straw or through a hypodermic needle. It was experimentally derived independently by Jean Léonard Marie Poiseuille in 1838 and Gotthilf Heinrich Ludwig Hagen, and published by Poiseuille in 1840–41 and 1846. The theoretical justification of the Poiseuille law was given by George Stokes in 1845.The assumptions of the equation are that the fluid is incompressible and Newtonian; the flow is laminar through a pipe of constant circular cross-section that is substantially longer than its diameter; and there is no acceleration of fluid in the pipe. For velocities and pipe diameters above a threshold, actual fluid flow is not laminar but turbulent, leading to larger pressure drops than calculated by the Hagen–Poiseuille equation.
Poiseuille's Equation describes the pressure drop due to the viscosity of the fluid; Other types of pressure drops may still occur in a fluid (see a demonstration here). For example, the pressure needed to drive a viscous fluid up against gravity would contain both that as needed in Poiseuille's Law plus that as needed in Bernoulli's equation, such that any point in the flow would have a pressure greater than zero (otherwise no flow would happen).
Another example is when blood flows into a narrower constriction, its speed will be greater than in a larger diameter (due to continuity of volumetric flow rate), and its pressure will be lower than in a larger diameter (due to Bernoulli's equation). However, the viscosity of blood will cause additional pressure drop along the direction of flow, which is proportional to length traveled (as per Poiseuille's Law). Both effects contribute to the actual pressure drop.

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  1. DadoNoah

    Calculating force on a syringe plunger for a viscous fluid?

    I'm currently working on a precise glue/resin dispenser, and I'm trying to derive an equation for the force one must exert on a syringe plunger as a function of the desired flow rate Q, and also accounting for the fluid viscosity and the syringe barrel and needle geometry. I've attached a scan...
  2. G

    Does Poiseuille's Law apply for vertical motion of fluids down a tube?

    I investigated the flow rate of differing dilutions of glycerol through an orifice of a vertical tube and obtained the following: I'm looking for a way to quantify these results so looked to Poiseuille's Law; I'm pretty sure my graph does not show inverse proportion? Could anyone advise me as...
  3. WhiteWolf98

    Determining the coefficient of viscosity of water (Graph Problem)

    Homework Statement So, the question is based around an experiment to determine the coefficient of viscosity for water (by capillary flow). Part of the experiment involved producing a graph of Q against h. This graph is supposed to be linear, and is supposed to pass through the origin. As can be...
  4. A

    Theoretical Pipe Flow: Understanding Poiseuille's Law

    Hey guys, I am doing an internship and I have had some thoughts about fluid flow that have come up and I am having trouble fully grasping some concepts due to no one being able to thoroughly explain any answer that they might come up with. So I have a crude understanding of some fluid dynamics...
  5. Z

    Calculate Flow Rate of a Syringe: Poiseuille's & Bernoulli's Laws

    I am trying to come up with a mathematical model so that, when the displacement of the plunger of a syringe is know, I can calculate the amount of a specific liquid in the barrel. Or the relationship between the speed of the plunger and flow rate at the tip of the needle (Again assuming that the...
  6. D

    Calculating something wrong with Poiseuille's Law

    Homework Statement At resting, can you breath sufficient air through a tube of 100 cm length and 2 cm radius? normal resting respiration rate: 10 - 20 breaths per minute (3 - 6 seconds per breath) normal resting respiration volume: 0.5 L normal pressure difference in respiration = 1 mmHg =...
  7. D

    Use dimensional analysis to derive Poiseuille's Law

    Homework Statement Using dimensional analysis deduce the relationship between the pressure drop per unit length along a cylindrical pipe of radius r, and the radius of the pipe, the viscosity of the fluid in the pipe, η, and the volume flow rate, V ̇ . Homework Equations Δp/l = 8ηV...
  8. W

    Role of Pipe Length in Poiseuille's Law

    I can't figure out why the length the a pipe (L) increases the change in driving pressure with respect to this law: Delta P = (8*mu*L*Q)/(pi*(r^4)) I would think that delta P wouldn't change because the fluid is incompressible. Does anyone have a conceptual explanation for the simple...
  9. I

    Poiseuille's law - Need help determining pressure difference

    Homework Statement The problem is if i have a barrel of water, and at the bottom there is a pipe sticking out going horizontally (leading to an open end), how do i determine the pressure difference?. I think I am right in saying the pressure at the end of the pipe would be pressure from the...
  10. S

    Exploring Poiseuille's Law: Pressure, Flow, and Resistance in Blood Vessels

    Ok first of all before I get to this I have one question, What does loss of hydrosatic pressure due to resistance mean in this equation. What happens to the molecules when they lose hydrostatic pressure, do they stop moving and accumulate? Poiseuille's Law says that if you decrease the...
  11. J

    Poiseuille's Law question

    The pulmonary artery, which connects the heart to the lungs, has an inner radius of 2.8 mm and is 8.5 cm long. If the pressure drop between the heart and lungs is 400 Pa, what is the average speed of blood in the pulmonary artery? I am using the equation pi*r^4(p1-p2)/(8*viscosity*length)...
  12. R

    Solving Poiseuille's Law Flow Rate Problem | Help Needed

    I'm having difficulty with a question and would appreciate a point in the right direction. The question is, "What is the flow rate of a tube that consists of two sections, the first with length 20cm and radius 0.15cm and the second part with length 1.0 cm and .05cm radius. The pressure...
  13. R

    Solving Poiseuille's Law Trouble - Flow Rate Calculation

    Trouble with a problem. What is the flow rate if a tube consists of two sections, the first with a length of 20cm and radius 0.15cm and the second part with length 1.0cm radius 0.05? with a pressure difference across the entire tube of 3cmHg (p1-p3). (viscosity = 0.801 cP) I've tried this...
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