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...
