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We assume static pressure of a fluid coming out of a pipe or nozzle of gas turbine with high temperature and velocity is equal to atmospheric pressure, which confuses me for some point.

Does it mean that a fluid in atmosphere can not have more or less static pressure than atmospheric pressure?

For instance,

There is stationary air in room. It has no kinetic energy, so no dynamic pressure. It has only static pressure which is equal to atmospheric pressure.

Now, we suddenly add kinetic energy to it by turning a big fan on.

Its previous condition: enter link description here

Its current condition: enter link description here

Is static pressure in condition 2 equal to Patm or less than Patm?

I think total pressure in condition 1 and 2 can't be equal to each other, since we add extra energy. So, static pressure in condition 2 should be still equal to Patm.

When this fluid comes to a rest by hitting the wall, its static pressure will be its total pressure and be more than Patm.

Do you agree?

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  • $\begingroup$ A good text covering static and dynamic pressure: See Engineering Thermodynamics, Work and Heat Transfer by Rogers & Mayhew $\endgroup$
    – Solar Mike
    Apr 13, 2023 at 20:03

3 Answers 3

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You are forgeting a very important law and a very important equation, namely the Bernoulli equation. The Bernoulli equation is essentially an equation of conservation of energy. It goes:

$p_{s} + p_{d} + p_{h} = C$

meaning that the static pressure, the dinamic pressure and the hydrostatic pressure (which we will not take in consideration here) have to be constant, C is just some constant number. You can look at this like a pendulum that exchanges its potential and kinetic energy with each swing, but the constant energy in the system remains constant.

So when you bring more kinetic energy in the system (in your case that is the dinamic pressure) the static pressure must diminish. Thus in your case the $P_{t2}$ the static pressure will be have to decrease and be lower than the atmospheric pressure!

Here is a link to the Bernoulli equation on the Wiki. An very important equation, a form of conservation of energy for fluids.

https://en.wikipedia.org/wiki/Bernoulli%27s_principle

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The Bernoulli equation applies to conservative flow, meaning there is no added head or energy midstream. If there is a source or sink midway, it has to be accounted for.

You are right. If you add energy by placing a fan in the stream, the pressure is the sum of static and dynamic pressure. The same thing happens in a turbocharged carborator, a jet engine, and so on. The reverse of this is also true. The static pressure of air drops after passing through a windmill.

Here is the Wikipedia image of an axial fan flow diagram.

  • C is speed
  • P pressure

'

wiki

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  • $\begingroup$ So static pressure in condition 1 and 2 is the same and equal to atmospheric pressure. The difference between them is dynamic energy added. However, total pressure in condition 2 is higher than condition 1. When air after moving by blade hits wall, its static pressure will be higher than atmospheric pressure since all dynamic pressure will be converted to static pressure. Am I right here too? $\endgroup$
    – Jawel7
    Apr 13, 2023 at 22:11
  • $\begingroup$ yes. it is called stagnation pressure. Stagnation pressure is compared to static pressure in airplanes via Pitot tube and they use the same formula $p= v^2 \rho/2$ to calculate airspeed. Or in structural engineering, the wind load is stagnation pressure, multiplied by code factors. $\endgroup$
    – kamran
    Apr 13, 2023 at 23:03
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Of course it can, this is the nature of airfoils. Furthermore, atmospheric pressure changes across the world - a barometer is used to measure this. The result of different atmospheric pressures? Wind.

In general, "the atmosphere" is treated like a plenum, which is generally defined as a place where everything has the same pressure. But as you dig in its easy to find exceptions.

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  • $\begingroup$ What about my static pressure question regarding kinetic energy addition to air? $\endgroup$
    – Jawel7
    Apr 13, 2023 at 21:39

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