# Application of Bernoulli Energy Conservation [closed]

In what cases does the static pressure decrease when the velocity increases in a flow.

And in what cases does the static pressure remain constant whilst the velocity and stagnation pressure increases?

Please answer with respect to Bernoulli's equation: Po1 = Ps1 + 0.5*rho*v1^2

For example in a closed circuit wind tunnel to what extent does the fan convert static pressure to dynamic pressure and to what extent does it just add energy by increasing the dynamic pressure.

• I'm voting to close this question as off-topic because it does not seem to be about aviation. This is a pure fluid dynamics questions, which belongs on physics.stackexchange. – Bianfable Nov 1 '19 at 11:47
• Also looks like a homework question. – CrossRoads Nov 1 '19 at 11:49
• I disagree with closure. This isn't some esoteric non-Newtonian fluid dynamics question. It is readily "applicable" to wind tunnel as mentioned in the OP. – JZYL Nov 1 '19 at 16:03
• @Bianfable, I am writing this question as I am analysing the construction of a wind tunnel. Wind tunnels perform experimental research on aviation models, and fluid dynamics makes planes fly, that was my thought train. If I posted in the wrong place, I will correct that now. Thank you for the feed back. – Von-Karmen Nov 3 '19 at 13:37
• @Von-Karmen you should edit the question to highlight what you put in your comments – Manu H Nov 4 '19 at 7:42

## 1 Answer

Bernoulli's equation holds only if there is no energy source in the system. Since the fan adds energy, Bernoulli's does not apply across the fan; in the context of 1-D flow, pressure changes discontinuously across the fan.

Due to conservation of mass (no mass source for a simple fan), airspeed cannot change discontinuously across the fan interface. Therefore, right after the fan interface, both the static pressure and the total pressure have increased.

For more information, refer to this tutorial.

• I would like to disagree with regards to the reason why Bernoulli's doesn't apply across the fan. – Von-Karmen Nov 3 '19 at 13:40
• Firstly, I would like to disagree with regards to the reason why Bernoulli's doesn't apply across the fan. Bernoulli's relies on three assumptions, the flow must be: - steady - inviscid - incompressible The fan breaks Bernoulli's because it is not inviscid or steady. It is my error to ask in terms of Bernoulli. Instead it should be the steady flow energy equation. I think I should be asking instead, what are the mechanisms by which the flow can alternate static and stagnation pressure? Perhaps that is a more esoteric physics question. – Von-Karmen Nov 3 '19 at 13:47
• @Von-Karmen No sir. Conservation of energy must hold for streamline to exist. Navier Stokes in the conservation form inherently assumes conservation of momentum and energy. If you add a source to your control volume, Bernoulli breaks down. – JZYL Nov 3 '19 at 14:11
• Yes, you are right. But that doesn't help answer the question. – Von-Karmen Nov 3 '19 at 14:14
• "If you add a source..." this is why I revised my answer to the steady flow energy equation. – Von-Karmen Nov 3 '19 at 14:20