Can bernoulli's theorem applied to inside a boundary layer?

Answer 1

In the case of large Re, the velocity fields of the fluid in most real cases have a velocity potential, which makes calculations of the pressure and velocity much easier. This is referred to as potential flow, which is an area with well-developed numerical tools. The potential flow theory is very sensitive to turbulence, and therefore the above mentioned boundary layeris important. All bodies in fluids are surrounded by boundary layers. Outside of this, we have potential flow with no turbulence or compression. Inside the boundary layer, we have large effects from viscosity due to adhesion of the fluid to the body. In the case of potential flow, a good way to visualize the flow pattern are streamlines. These are lines in the flow with equal velocity, and these are waht you usually see in schematical drawings of the flow around aircraft wings, for instance. Streamlines are always parallel to the boundary of an object in the steam.

Answer 2

Bernoulli's theorem assumes inviscid flow conditions, so it cannot be directly applied inside a boundary layer where viscous effects are significant. However, modifications like the boundary layer approximation or using the Bernoulli equation in conjunction with the boundary layer equations can provide useful insights into flow behavior near solid surfaces.