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What is the impact of height, let's say being on top of a 4,000 m high mountain, on blood pressure / flow velocity given Bernoulli's Equation?

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closed as unclear what you're asking by John Rennie, alephzero, sammy gerbil, ZeroTheHero, Jon Custer Sep 27 '18 at 17:38

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    $\begingroup$ Why should Bernoulli's Equation be involved? One would think that Poiseuille's Law would be more applicable. $\endgroup$ – probably_someone Sep 26 '18 at 16:56
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    $\begingroup$ This probably has as much to do with physiology as with physics. $\endgroup$ – V.F. Sep 26 '18 at 17:26
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    $\begingroup$ Blood pressure is regulated by many factors, such as metabolic rate, stress levels (via adrenalin production,) diet (e.g. drinking alcohol lowers blood pressure), etc, etc. Some of those factors may change with altitude, but they are outside the scope of Bernoulli's equation! $\endgroup$ – alephzero Sep 26 '18 at 20:22
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Bernoulli's Equation cannot be applied in this case, because it relies on the assumption of steady flow. Flow of blood through a human circulatory system is not steady, because the pressure varies during the cycle of the heartbeat.

Also, because of the steady assumption, Bernoulli cannot be used to relate the state of a fluid system at two different points in time (i.e. before and after the ascent of a mountain). If the system has changed between those two different times, then by definition the flow cannot be steady, so again Bernoulli can't be used.

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  • $\begingroup$ There is an unsteady Bernoulli equation, and it is mentioned in the link you have attached. Unsteady flow is not a limitation for Bernoulli equation. $\endgroup$ – Deep Sep 27 '18 at 5:23
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I think you are referring the to gz term in the Bernoulli equation. You are wondering what effect this term has if the datum for z is at (say) sea level, and the flow system (in this case, a person's blood system) is located at 4000 ft. Well, it is important to notice that there are two gz terms in the Bernoulli equation, namely $gz_1$ and $gz_2$. It is the difference between these two terms that is related to the pressure variation in the flow system, not just either one of them. In other words, it is differences in elevation that are important in the Bernoulli equation, not the absolute magnitude of any one elevation.

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