Fluid flow in pipes can be laminar or turbulent, depending on the Reynolds number. Laminar flow occurs at low speeds, with fluid moving in parallel layers. Turbulent flow happens at higher speeds, characterized by chaotic mixing and irregular motion.
Understanding pipe flow is crucial for designing efficient systems and analyzing fluid behavior. The Hagen-Poiseuille equation describes laminar flow, while turbulent flow requires more complex analysis using friction factors and velocity profiles.
Laminar and Turbulent Flow in Pipes
Laminar vs turbulent flow
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Fluid Dynamics – University Physics Volume 1 View original
Reynolds number (Re) dimensionless parameter characterizes flow regime in pipes Re=μρVD, ρ fluid density, V average velocity, D pipe diameter, μ dynamic viscosity
Laminar flow occurs at low Reynolds numbers (Re<2300)
Fluid particles move in parallel layers without mixing (honey, oil)
Velocity profile parabolic, maximum velocity at center, zero at pipe wall
Turbulent flow occurs at high Reynolds numbers (Re>4000)
Fluid particles exhibit irregular and chaotic motion, mixing between layers (fast-flowing rivers, blood flow in arteries)
Velocity profile flatter compared to laminar flow, more uniform distribution across pipe cross-section
Transitional flow occurs between laminar and turbulent regimes (2300<Re<4000)
Flow characteristics less predictable, can exhibit features of both laminar and turbulent flow (slow-moving rivers, blood flow in capillaries)
Hagen-Poiseuille equation applications
Hagen-Poiseuille equation describes pressure drop (ΔP) in circular pipe for laminar flow ΔP=πD4128μLQ, L pipe length, Q volumetric flow rate
Rearranging Hagen-Poiseuille equation yields expression for flow rate Q=128μLπD4ΔP