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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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