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From the Bernoulli equation

$$\frac{p}{\rho} + \frac{v^2}{2} + gh = \mathrm{const.}$$

along streamlines, it seems that there should be an ultimate limit to the height of an 'inflatable dancer' when fully inflated. What is it?

Assuming constant cross-section, conservation of material, and the assumption that pressure at height is negligible (actually that p_max/rho_1>>p_2/rho_2) leads me to

$$h=\frac{1}{g}(\frac{p_{max}}{\rho_1} + v_1^2(\frac{1}{2} + \frac{\rho_1^2}{\rho_2^2}))$$

where p_max is pressure at ground (max bursting pressure for some reasonable material) and rho_1, rho_2 are the densities at ground, height - anyone see a way to kill another variable? Ideal gas can eliminate one rho at the cost of adding T...

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  • $\begingroup$ What means "fully inflated"? Surely you could make it arbitrarily stiff by putting in more pressure. $\endgroup$
    – Mike Dunlavey
    Commented Jan 20, 2020 at 1:47
  • $\begingroup$ assuming one is using flexible material that exists today, which has some max pressure p_max $\endgroup$
    – jeremy_rutman
    Commented Jan 22, 2020 at 7:17
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    $\begingroup$ Why is the height dependent on the flow parameters and not say the actual length of the inflatable? $\endgroup$
    – Kyle Kanos
    Commented Apr 5, 2023 at 19:07
  • $\begingroup$ The length of the inflatable is whatever you want, as long as it stays inflated - the question is how high can one of these go and actually 'work' given infinite supplies . What is the top height any part of such a device can reach $\endgroup$
    – jeremy_rutman
    Commented Apr 9, 2023 at 21:03
  • $\begingroup$ I see. So your question is more akin to, "For a given motor/fan, what is the largest inflatable that could be stood fully erect?" than "how high can the inflatable go?" that you've posted? $\endgroup$
    – Kyle Kanos
    Commented Apr 12, 2023 at 22:15

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