Editing Boundary layer (section)

== Predicting transient boundary layer thickness in a cylinder using dimensional analysis ==

By using the transient and viscous force equations for a cylindrical flow you can predict the transient boundary layer thickness by finding the Womersley Number (<math> N_w </math>).

Transient Force = <math> \rho v w </math>

Viscous Force = <math> {\mu v\over\delta_1^2} </math>

Setting them equal to each other gives:

:<math> \rho v w={\mu v\over\delta_1^2} </math>

Solving for delta gives:

:<math> \delta_1=\sqrt{\mu\over\rho w}=\sqrt{\ v\over\ w} </math>

In dimensionless form:

:<math> {L\over\delta_1}={L\sqrt{w\over\ v}}=N_w </math>

where <math> N_w </math> = Womersley Number; <math> \rho </math> = density; <math> v </math> = velocity; <math>w=</math> ?; <math> \delta_1 </math> = length of transient boundary layer; <math> \mu </math> = viscosity; <math> L </math> = characteristic length.