I was taught that the relative velocity of all fluid particles directly in contact with the boundary in a fluid flow is zero. In other words, that the relative velocity of fluid particles in the boundary layer decreases as the distance from the body decreases, from the relative velocity of the fluid outside the boundary layer, to zero at the surface of the body.

Bernoulli principle says that the total pressure in a non-compressible fluid flow must remain constant everywhere, and that therefore, the pressure normal to the surface of a body is decreased when the pressure parallel top the surface increases (when relative velocity increases). If this is true, the natural assumption is that the pressure normal to the surface must always be equal to the total pressure, i.e., constant, and lift due to decreased normal pressure is impossible.

This is clearly not the case, as anyone using an atomizer, or blowing across the top of a curved piece of paper can attest. Is the Bernoulli principle not applicable, or invalid, inside the boundary layer? Or is some other phenomenon or factor at work here?

Can anyone explain this?


1 Answer 1


Bernoulli is a statement of conservation of energy in a fluid flow. As such, it is only valid for inviscid flows. It is still useful for real fluids because in the interior of the flow viscous effects may be small. But that is clearly not the case in a boundary layer.

As a second point, even in the inviscid case, Bernoulli only applies along streamlines in general. In order to be constant throughout the fluid, the flow must be irrotational (which it isn’t in a boundary layer).

  • $\begingroup$ I believe this is the right answer, however, 1. What is an "inviscid flow" (I know what viscosity is.) Clearly you do not just simply mean "flow of a inviscid fluid", as that would imply that Bernoulli does not apply to the flow of any real fluid, as all real fluids have some viscosity. 2. If Bernoulli does not apply in Boundary Layer then it must be the case that at the surface of a body, the normal pressure being applied is in fact lower than the pressure outside the Boundary Layer? $\endgroup$ Commented Jan 24, 2018 at 15:59
  • $\begingroup$ 1. Yes, that's what I mean. Strictly, Bernoulli's relation does not apply when there is viscosity, as shear then causes dissipation. However, in many real flows, the effects of viscosity are minor so can be ignored without giving poor results. 2. I don't follow. The boundary layer is not accelerating, so must have equal pressure from each side. $\endgroup$
    – Ben51
    Commented Jan 24, 2018 at 16:03
  • $\begingroup$ I mean the pressure the fluid is pushing on the surface of the body with. The force, per unit area, of the molecules hitting and rebounding from the surface of the body. That is, general,y where Bernoulli is applied , to imply that since total pressure must remain constant, when the fluid is in motion, there is dynamic pressure (from velocity) parallel to the surface and so the normal pressure must be sufficiently lower to keep the total pressure constant. $\endgroup$ Commented Jan 24, 2018 at 18:15
  • $\begingroup$ By Newton's third law, the force with which the fluid pushes on the body (microscopically it's caused by molecular rebounds, macroscopically it's called pressure) is the same as the force with which the body pushes on the fluid. If there is no acceleration, there is no net force. So the pressure just outside the boundary layer must equal the pressure at the surface. No? $\endgroup$
    – Ben51
    Commented Jan 24, 2018 at 18:20
  • $\begingroup$ Yes, although, to be precise, we don't know if there is any acceleration or not. Whether the body in question is going to accelerate is the result of the vector sum integral (surface integral) of all the point forces pushing on the body, from all directions. it does not include any force the body is exerting on the air molecules. That would be relevant if we are calculating the acceleration of the air molecules, not the acceleration of the body. $\endgroup$ Commented Jan 24, 2018 at 18:25

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