Boundary Layer Characteristics
- The velocity gradients within the boundary layer and wake regions are much larger than those in the remainder of the flow fluid
- Therefore, viscous effects are confined to the boundary layer and wake regions
Transition occurs at
\[
\mathrm{Re}_{xcr}=\frac{\rho U x}{\mu}=2\times10^{5}\ \sim\ 3\times10^{6}
\]
depending on surface roughness and amount of turbulence in upstream flow
Distortion of a fluid particle as it flows within the boundary layer
Typical characteristics of boundary layer thickness and wall shear stress for laminar and turbulent boundary layers
The Navier-Stokes equations are too complicated that no analytical solution is available. However, for large Re, simplified boundary layer equations can be derived.
- The boundary layer assumption is based on the fact that the boundary layer is thin
- Physically, the flow is parallel to the plate and any fluid is convected downstream much more quickly than it is diffused across the streamlines
- For boundary layer flow over a flat plate the pressure is constant. The flow represents a balance between viscous and inertial effects, with pressure playing no role
1National Tsing Hua University OpenCourseWare(NTHU, OCW). Fluid Mechanics. WONG, SHWIN-CHUNG. Chapter 9: Flow over Immersed Bodies.
2B.R. Munson, et al. Fluid Mechanics.