Bernoulli Equation: Compressible vs Incompressible Flows

[rabbit44]

Hi, urgent question. Bernoulli's equation seems to be conservation of energy. I read that it's only for incompressible flows; but isn't the term involving pressure the energy due to the work done on a mass of air in compressing it?

Thanks

 

[stewartcs]

Hi, urgent question. Bernoulli's equation seems to be conservation of energy. I read that it's only for incompressible flows; but isn't the term involving pressure the energy due to the work done on a mass of air in compressing it?

Thanks

Bernoulli can be used for compressible flow as well.

CS

 

[Q_Goest]

Yes, it can be used for compressible flows - as long as there is no significant change in density (ie: temperature and pressure). Note also that Bernoulli's equation does not account for any energy loss such as heat transfer or irreversible, frictional losses such flow through a pipe, so Bernoulli's is very basic and needs to be applied with extreme care.

 

[rcgldr]

The Wiki article covers compressable flows:

Compressible_flow_equation.htm

 

[Redbelly98]

Hi, urgent question. Bernoulli's equation seems to be conservation of energy. I read that it's only for incompressible flows; but isn't the term involving pressure the energy due to the work done on a mass of air in compressing it?

Thanks

For incompressible fluids, the pressure term represents work done on a mass to either accelerate/decelerate it, or change it's elevation. I.e. it can change either the gravitational potential or the kinetic energy (or both).

 

[arildno]

Bernoulli's equation is merely a first integral of Newton's 2.law, as applied along a streamline. (In 2-D flow, the first integral of Newton's law as applied orthogonal to a streamline is covered by Crocco's theorem).

Thus, in principle, Bernoulli's "equation" (or, rather, the method used in deriving it!) is fully valid for ANY sort of flow.

However, only under very special conditions does something "useful" turn up in this particular decomposition of the equations of motion. (Mostly, for example in non-stationary flow, you get a nasty integral you can't simplify in any intelligent manner..)

When such usefulness occurs, we call it "Bernoulli's equation"..