Bernoulli's Equation

tonyjk

Hi all,
please i would like to know physically why when the pressure increase the speed decrease and vice-versa in a flow?
Thanks

rcgldr

Think of this the other way around. Imagine you have a higher pressure zone and a lower pressure zone reasonably close to each other. The flow will accelerate away from the higher pressure zone towards the lower pressure zone. As long as there are no additional forces or work done on the flow other than the pressure zones, then Bernoulli applies and Bernoulli equation relates the increase in speed versus the decrease in pressure of the flow between the two pressure zones.

There would need to some external energy source in order to create and/or maintain those pressure zones, but Bernoulli isn't being applied to that process, only to the flow between the two pressure zones.

tonyjk

thank you.. so the pressure of the fluid is doing work(internal energy let's say) on the fluid right?

rcgldr

Yes, that is when Bernoulli applies.

Where Bernoulli doesn't apply is in the case where external work is done on a flow. For example, in the immediate vicinity of a propeller, there's a pressure jump with little or ideally, no change in speed. This the area where work is performed by the propeller, which violates Bernoulli. However Bernoulli does apply to the flow fore and aft of the propeller, assuming no other external forces are involved.

boneh3ad

Bernoulli's equation also does not apply to unsteady flows, compressible flows or flows with dissipative phenomena such as viscosity. Those are part of the assumptions used in the derivation of the equation.

arildno

For steady, non-dissipative flows with a steady state relation between pressure and density, say in form of a power-law, Bernoulli-like equations may readily be derived for such compresible cases.
they even have their uses.

MrMatt2532

Yes, these are often called "unsteady bernoulli" for unsteady flow, "compressible bernoulli" for compressible flow, or "extended bernoulli" for viscous flow. Or there is even a version of the same form that doesn't need to be applied along streamlines if your flow is irrotational.

Typically though, unless these specific forms are mentioned, bernoulli's equation means the form applied along a streamline, for steady state, imcompressible, and inviscid flow.