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Questions and Answers
Who were the scientists who experimentally derived the Hagen–Poiseuille equation?
Who were the scientists who experimentally derived the Hagen–Poiseuille equation?
Jean Léonard Marie Poiseuille and Gotthilf Heinrich Ludwig Hagen were the scientists who experimentally derived the Hagen–Poiseuille equation.
Explain the assumptions of the Hagen–Poiseuille equation.
Explain the assumptions of the Hagen–Poiseuille equation.
The assumptions of the Hagen–Poiseuille equation are: 1. The fluid is incompressible and Newtonian, 2. The flow is laminar through a pipe of constant circular cross-section that is substantially longer than its diameter, and 3. There is no acceleration of fluid in the pipe.
Who provided the theoretical justification of the Poiseuille law?
Who provided the theoretical justification of the Poiseuille law?
George Stokes provided the theoretical justification of the Poiseuille law.
In what type of flow can the Hagen–Poiseuille equation be successfully applied?
In what type of flow can the Hagen–Poiseuille equation be successfully applied?
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What kind of fluid does the Hagen–Poiseuille equation apply to?
What kind of fluid does the Hagen–Poiseuille equation apply to?
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Study Notes
Scientists Involved
- Hagen–Poiseuille equation derived experimentally by Georg Simon Ohm, Jean Léonard Marie Poiseuille, and Heinrich Hagen.
- Poiseuille is credited with providing significant early insights into fluid dynamics related to viscosity and flow rate.
Assumptions of the Hagen–Poiseuille Equation
- Applies to incompressible, Newtonian fluids, meaning viscosity remains constant regardless of the flow conditions.
- Assumes laminar flow, indicating orderly and smooth fluid movement without turbulence.
- Flow occurs through a cylindrical pipe of constant radius and length.
- Neglects effects of gravity, temperature variations, and fluid interactions with the pipe wall (no slip condition).
Theoretical Justification
- Theoretical framework of the Poiseuille law was provided by Ludwig Prandtl, who extended the principles of fluid dynamics, leading to a deeper understanding of viscous flow.
Application of Hagen–Poiseuille Equation
- Successfully applied only in laminar flow situations, typically when the Reynolds number is below a critical threshold (approximately 2000).
- Ideal for scenarios involving slow-moving fluids in narrow pipes.
Fluid Type for Application
- The Hagen–Poiseuille equation specifically applies to viscous fluids, which exhibit resistance to flow due to internal friction.
- Examples include water, oils, and other common fluids under low flow conditions.
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Description
Test your knowledge of fluid dynamics with this quiz on the Hagen-Poiseuille equation. Explore the principles behind pressure drop in incompressible and Newtonian fluids in laminar flow through cylindrical pipes. Learn about its application in various scenarios, from lung alveoli to drinking straws.
