Use Bernoulli to find the pressure distribution around the cylinder.
If the geometry is very long and thin (like a microchannel), use the Lubrication Approximation to simplify the equations. Check for Irrotationality: If , you can use the Velocity Potential ( advanced fluid mechanics problems and solutions
Integrate the pressure component in the vertical direction. Result: Kutta-Joukowski Theorem : L′=ρUΓcap L prime equals rho cap U cap gamma Use Bernoulli to find the pressure distribution around
Always start by identifying the Reynolds Number ( ), Mach Number ( ), and Froude Number ( Mach Number ( )
). They tell you which terms in the Navier-Stokes equations you can safely ignore.
The boundary layer thickness grows with the square root of the distance: