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Bernoulli’s equation and reference frames

Sometimes in train, when setting behind opening window, I can feel strong gale blowing in. The closer to the window the stronger wind be.

Let $o$ denote a point outer and $i$ denote a point inner which is a distance from the window but in the same streamline of $o$. Then by Bernoulli's principle

$$\frac{1}{2}\rho_o v_o^2+\rho_o g z_o+p_o=\frac{1}{2}\rho_i v_i^2+\rho_i g z_i+p_i$$

$o$ and $i$ seems almost in the same plane, hence they are same in $\rho,z$ and $p$

But $v_o>v_i$, that makes the equation not hold... So does Bernoulli's principle also hold in moving reference frames?

Update

According to this paper, we know that Bernoulli's Equation is frame-dependent in newtonian mechanics.

However if we talk about it in the Special Theory of Relativity, is it frame-independent? Or it may contradict to the Principle of Relativity.

Update According to this paper, Bernoulli's Equation seems relativistically frame-dependent.

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    $\begingroup$ Why do you think that $\rho$ and $p$ are the same? Surely if the window may be a discontinuty for $v$, it may do the same for $\rho,p$, right? Otherwise an open window is needed but the equation is designed exactly for such situations and yes, it holds in any inertial frame, like any classical physics principle. $\endgroup$
    – Luboš Motl
    Commented Dec 22, 2012 at 14:18
  • $\begingroup$ @LubošMotl if point $i$ is far from the window enough, then $v_i=0$, $\rho_i$ and $p_i$ seems same like the train is static. $\endgroup$
    – Popopo
    Commented Dec 22, 2012 at 15:21
  • $\begingroup$ @VijayMurthy if you think a post is a duplicate, flag it as such. (Or vote to close if you have enough reputation) Just posting a comment does very little. $\endgroup$
    – David Z
    Commented Dec 22, 2012 at 22:46

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