Poiseuille's problem + Navier-Stokes equation PT01
Автор: Ciencia Infinita
Загружено: 2026-02-25
Просмотров: 76
Описание:
In this video, we derive and explain Poiseuille’s flow starting directly from the Navier–Stokes equations.
We show how, under appropriate assumptions (steady, incompressible, fully developed laminar flow), the Navier–Stokes equations reduce to a simple ordinary differential equation that leads to the famous parabolic velocity profile.
The physical assumptions behind Poiseuille flow
Step-by-step simplification of the Navier–Stokes equations
Derivation of the velocity profile
Expression of the pressure gradient
Wall shear stress and its physical meaning
Flow rate and volumetric discharge
Reynolds number and laminar flow condition
This problem is fundamental in fluid mechanics and appears frequently in engineering, physics, and applied mathematics courses.
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#NavierStokes
#Poiseuille
#laminarflow
#hydrodynamics
#ContinuumMechanics
#engineeringstudents
#physicslecture
#reynolds
#shearstress
#PressureGradient
#appliedmathematics
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