Principle of Continuity and Bernoulli's Theorem

[ResidentInsomniac]

Hi All.

Please correct me if I am wrong. I am confused regarding the differences between the two and also the relationship between them, as both are mentioned whenever explaining the production of lift.


Principle of Continuity:

1) States that total mass flow in = total mass flow out
2) basically adheres to the principle of conservation of mass
3) applies to both compressible / incompressible flow

Bernoulli's Theorem:


1) States that total energy remains constant (energy and not mass?)
2) adheres to the principle of conservation of energy (both mass and energy can neither be created nor destroyed)



Keeping in mind the above points, both are basically the same, then what actually differentiates between them?

Please clarify if I missed out anything...:ugh:


Much appreciated

[Mark 1]

They are not the same. Continuity merely defines the constraint that mass flow between any two streamlines will be constant at all stations along those streamlines (in a steady state flow).

If it were not so, then mass would be accumulating somewhere along the line.
As mass flow = density * area * velocity, you can infer a velocity change due to the compression of streamlines around an airfoil.

Conservation of mass is not the same as conservation of energy.

But from the conservation of energy you can infer the change in pressure due to the change in velocity.

The lift/drag vector is derived as the surface integral of normal and tangential forces on the surface. The normal forces are due to static pressure and the tangential due to friction.

So the combination of these two principles can at least be used to derive the static pressure component.