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I have learned that for fluids and gases $P_\text{total}=P_\text{dynamic} + P_\text{static}$.

Suppose we have a closed circular tube in a form of ring filled with air under some pressure. In this case I believe the following is true.

$P_t = P_s$ as $P_d=0$.

No suppose some kind of propeller starts to move the air, so it circulates within the tube. Now what will happen?

  1. $P_t$ will stay constant $P_s$ will go down and $P_d$ will go up.
  2. $P_s$ will stay constant and $P_t$ will go up due to increase in $P_d$.
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Assuming the system with the propeller is isentropic (which is a pretty bad assumption), then $P_t$ is conserved which means that $P_s$ must decrease and $P_d$ must increase.

If the propeller is not isentropic, then $P_t$ may change and then you can't really say what happens to $P_s$ or $P_d$ without more information.

So the answer depends on whether Bernoulli's equation is a good assumption or not. That's up to you to decide.

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