StudySmarter: Study help & AI tools

4.5 • +22k Ratings

More than 22 Million Downloads

Free

Hagen Poiseuille Equation

Dive deep into the fascinating realm of engineering with our exploration of the Hagen Poiseuille Equation, a fundamental principle vital to our understanding of fluid dynamics. This formula, named after two eminent physicists, underpins the very foundation of engineering science. Within this comprehensive guide, you'll uncover its definition, parse through its origins and history, and gain an in-depth understanding of its elaborate mathematical representation. You'll also discover the practical applications, from real-world examples to its crucial role in articulating laminar flow and fluid mechanics. Gain invaluable insights into an equation that invariably shapes the field of engineering, anchoring key concepts and applications in fluid dynamics.

Explore our app and discover over 50 million learning materials for free.

- Design Engineering
- Engineering Fluid Mechanics
- Aerofoil
- Atmospheric Drag
- Atmospheric Pressure
- Atmospheric Waves
- Axial Flow Pump
- Bernoulli Equation
- Boat Hull
- Boundary Layer
- Boussinesq Approximation
- Buckingham Pi Theorem
- Capillarity
- Cauchy Equation
- Cavitation
- Centrifugal Pump
- Circulation in Fluid Dynamics
- Colebrook Equation
- Compressible Fluid
- Continuity Equation
- Continuous Matter
- Control Volume
- Convective Derivative
- Coriolis Force
- Couette Flow
- Density Column
- Dimensional Analysis
- Dimensional Equation
- Dimensionless Numbers in Fluid Mechanics
- Dispersion Relation
- Drag on a Sphere
- Dynamic Pump
- Dynamic Similarity
- Dynamic Viscosity
- Eddy Viscosity
- Energy Equation Fluids
- Equation of Continuity
- Euler's Equation Fluid
- Eulerian Description
- Eulerian Fluid
- Flow Over Body
- Flow Regime
- Flow Separation
- Fluid Bearing
- Fluid Density
- Fluid Dynamic Drag
- Fluid Dynamics
- Fluid Fundamentals
- Fluid Internal Energy
- Fluid Kinematics
- Fluid Mechanics Applications
- Fluid Pressure in a Column
- Fluid Pumps
- Fluid Statics
- Froude Number
- Gas Molecular Structure
- Gas Turbine
- Hagen Poiseuille Equation
- Heat Transfer Fluid
- Hydraulic Press
- Hydraulic Section
- Hydrodynamic Stability
- Hydrostatic Equation
- Hydrostatic Force
- Hydrostatic Force on Curved Surface
- Hydrostatic Force on Plane Surface
- Hydrostatics
- Impulse Turbine
- Incompressible Fluid
- Internal Flow
- Internal Waves
- Inviscid Flow
- Inviscid Fluid
- Ion Thruster
- Irrotational Flow
- Jet Propulsion
- Kinematic Viscosity
- Kutta Joukowski Theorem
- Lagrangian Description
- Lagrangian Fluid
- Laminar Flow in Pipe
- Laminar vs Turbulent Flow
- Laplace Pressure
- Lift Force
- Linear Momentum Equation
- Liquid Molecular Structure
- Mach Number
- Magnetohydrodynamics
- Manometer
- Mass Flow Rate
- Material Derivative
- Momentum Analysis of Flow Systems
- Moody Chart
- No Slip Condition
- Non Newtonian Fluid
- Nondimensionalization
- Nozzles
- Open Channel Flow
- Orifice Flow
- Pascal Principle
- Pathline
- Piezometer
- Pipe Flow
- Piping
- Pitot Tube
- Plasma
- Plasma Parameters
- Plasma Uses
- Pneumatic Pistons
- Poiseuille Flow
- Positive Displacement Pump
- Positive Displacement Turbine
- Potential Flow
- Prandtl Meyer Expansion
- Pressure Change in a Pipe
- Pressure Drag
- Pressure Field
- Pressure Head
- Pressure Measurement
- Propeller
- Pump Characteristics
- Pump Performance Curve
- Pumps in Series vs Parallel
- Reaction Turbine
- Relativistic Fluid Dynamics
- Reynolds Experiment
- Reynolds Number
- Reynolds Transport Theorem
- Rocket Propulsion
- Rotating Frame of Reference
- Rotational Flow
- Sail Aerodynamics
- Second Order Wave Equation
- Shallow Water Waves
- Shear Stress in Fluids
- Shear Stress in a Pipe
- Ship Propeller
- Shoaling
- Shock Wave
- Siphon
- Soliton
- Speed of Sound
- Steady Flow
- Steady Flow Energy Equation
- Steam Turbine
- Stokes Flow
- Streakline
- Stream Function
- Streamline Coordinates
- Streamlines
- Streamlining
- Strouhal Number
- Superfluid
- Supersonic Flow
- Surface Tension
- Surface Waves
- Timeline
- Tokamaks
- Torricelli's Law
- Turbine
- Turbomachinery
- Turbulence
- Turbulent Flow in Pipes
- Turbulent Shear Stress
- Uniform Flow
- Unsteady Bernoulli Equation
- Unsteady Flow
- Ursell Number
- Varied Flow
- Velocity Field
- Velocity Potential
- Velocity Profile
- Velocity Profile For Turbulent Flow
- Velocity Profile in a Pipe
- Venturi Effect
- Venturi Meter
- Venturi Tube
- Viscosity
- Viscous Liquid
- Volumetric Flow Rate
- Vorticity
- Wind Tunnel
- Wind Turbine
- Wing Aerodynamics
- Womersley Number
- Engineering Mathematics
- Engineering Thermodynamics
- Materials Engineering
- Professional Engineering
- Solid Mechanics
- What is Engineering

Lerne mit deinen Freunden und bleibe auf dem richtigen Kurs mit deinen persönlichen Lernstatistiken

Jetzt kostenlos anmeldenNie wieder prokastinieren mit unseren Lernerinnerungen.

Jetzt kostenlos anmeldenDive deep into the fascinating realm of engineering with our exploration of the Hagen Poiseuille Equation, a fundamental principle vital to our understanding of fluid dynamics. This formula, named after two eminent physicists, underpins the very foundation of engineering science. Within this comprehensive guide, you'll uncover its definition, parse through its origins and history, and gain an in-depth understanding of its elaborate mathematical representation. You'll also discover the practical applications, from real-world examples to its crucial role in articulating laminar flow and fluid mechanics. Gain invaluable insights into an equation that invariably shapes the field of engineering, anchoring key concepts and applications in fluid dynamics.

The Hagen Poiseuille Equation is a mathematical formula used in the field of fluid dynamics. It describes the relation between the pressure drop along a pipe, the length and diameter of the pipe, and the flow rate of the fluid.

- \(Q\) represents the flow rate,
- \(d\) is the diameter of the pipe,
- \(Δp\) is the pressure drop along the pipe,
- \(μ\) is the dynamic viscosity of the fluid, and
- \(L\) is the length of the pipe.

Note that the Hagen Poiseuille Equation is applicable under certain conditions, including steady, laminar flow and negligible gravitational effects.

- Hagen, a German hydraulic engineer, first published his theoretical results on fluid flow in 1839. Interestingly, his work was largely ignored, maybe due to the fact that he published in an obscure journal.
- Poiseuille, a French physicist and physiologist, derived the same result independently; his primary interest was in the flow of blood through the human body's small vessels. His findings were published in 1846, hence most of the Western world refers to the formula as Poiseuille's law.

Suppose you're tasked with determining the flow rate of water through a long garden hose. Given the hose's length and diameter, the water's viscosity, and the pressure difference from one end to the other, you could apply the Hagen Poiseuille Equation to calculate this.

Notation | Variable | Typical Units (SI) |

\(Q\) | Flow rate | \(m^3/s\) |

\(d\) | Diameter of the pipe | \(m\) |

\(Δp\) | Pressure difference | \(Pa\) or \(N/m^2\) |

\(μ\) | Dynamic viscosity | \(Pa \cdot s\) or \(N \cdot s/m^2\) |

\(L\) | Length of the pipe | \(m\) |

In industrial applications, the understanding of the Hagen Poiseuille Equation aids in the design and operational efficiencies of numerous systems. It can help optimise the diameter and length of pipelines for minimal pressure drops, thus conserving pump energy in fluid transport processes.

In the petroleum industry, the equation can determine the optimal pipe size for transporting oil, bearing in mind that larger diameters reduce frictional losses but at a higher cost due to material needs.

In intravenous drug delivery, the controlled dosage rate can be accurately calculated using this equation, considering the drug's viscosity, the catheter diameter, and the pressure.

Laminar flow, also known as streamline flow, occurs when a fluid flows in parallel layers with no disruption between them. In other words, there is no transverse mixing, only longitudinal diffusion.

An interesting yet counter-intuitive point to note is the concept of entrance length in flow through pipes. Even though the Hagen Poiseuille Equation assumes fully developed flow (i.e., the velocity profile is fully established), in the real world, the flow needs an ‘entrance length’ to fully develop from the pipe inlet. This length depends on the Reynolds number, which signifies whether the flow is laminar or turbulent.

- The Hagen Poiseuille Equation, a fundamental principle in fluid dynamics, describes the relationship between pressure drop along a pipe, the length and diameter of the pipe, and the flow rate of the fluid.
- The equation states that the volumetric flow rate of a fluid through a pipe is directly proportional to the fourth power of the diameter and the pressure difference, and inversely proportional to the pipe length and the fluid's dynamic viscosity.
- The equation's applicability is subject to conditions such as steady, laminar flow and negligible gravitational effects.
- Two scientists, Gotthilf Hagen and Jean Léonard Marie Poiseuille, contributed to the development of this equation, which finds its applications in various fields like biomedical applications and industrial fluid transport.
- The understanding and interpretation of the units involved in the Hagen Poiseuille Equation are crucial for practical applications and accurate calculations.

The Hagen-Poiseuille equation is a physical law that describes the flow rate of a viscous fluid through a long, cylindrical pipe. It states that this rate is proportional to the fourth power of the radius, the pressure gradient along the pipe, and inversely proportional to the fluid's viscosity.

No, the Darcy Weisbach equation and the Hagen Poiseuille Equation are not the same. The former is used to calculate head loss due to friction in fluid flow, whereas the latter describes laminar flow through a circular pipe. Both serve different applications in the field of engineering.

The Hagen-Poiseuille equation cannot be used for turbulent flow because the equation assumes laminar flow in the system, which is characterised by smooth, parallel layers of fluid. Turbulent flow, with its irregular, chaotic movement, violates these assumptions and hence does not align with the equation's limitations.

The Hagen-Poiseuille equation describes fluid flow through a pipe. An example could be calculating the flow rate of blood through a capillary or the flow of water through a household pipe, as the equation takes into account viscosity, pipe length and radius, and pressure difference.

The Hagen-Poiseuille equation is used in engineering to calculate the flow rate of a fluid through a pipe. It specifically deals with laminar flow conditions, providing precise predictions about pressure drop, pipe diameter, fluid viscosity, and pipe length.

What does the Hagen-Poiseuille equation describe?

The Hagen-Poiseuille equation describes the flow of viscous fluids through long cylindrical pipes, taking into account parameters such as pipe radius, pressure difference, fluid viscosity, and pipe length.

What are the parameters that influence the flow rate in the Hagen-Poiseuille equation?

The parameters are the radius of the pipe, the pressure difference, the fluid viscosity, and the length of the pipe.

How is the Hagen-Poiseuille equation used in various fields of engineering?

It's used in Civil and Environmental Engineering for designing water systems, in Mechanical Engineering for predicting coolant flow, and in Biomedical Engineering for understanding blood flow through arteries.

How does the radius of the pipe influence the flow rate in the Hagen-Poiseuille equation?

As the radius increases, the flow rate dramatically increases, quadrupling each time the radius doubles.

What does the Hagen Poiseuille equation describe?

The Hagen Poiseuille equation describes the rate of viscous flow in a cylindrical pipe when the liquid entirely fills the pipe and flows under a steady-state condition.

What are the steps involved in deriving the Hagen Poiseuille equation?

The steps involve considering a pipe of length and radius, initializing the Navier-Stokes equation, simplifying the equation under Hagen Poiseuille flow assumptions, using integration to solve the simplified equation, and finally integrating the velocity over the cross-section area.

Already have an account? Log in

Open in App
More about Hagen Poiseuille Equation

The first learning app that truly has everything you need to ace your exams in one place

- Flashcards & Quizzes
- AI Study Assistant
- Study Planner
- Mock-Exams
- Smart Note-Taking

Sign up to highlight and take notes. It’s 100% free.

Save explanations to your personalised space and access them anytime, anywhere!

Sign up with Email Sign up with AppleBy signing up, you agree to the Terms and Conditions and the Privacy Policy of StudySmarter.

Already have an account? Log in