Last day , when i was working on two interconnected balloons , a question was kicking my brains !!! This is the explanation of the question:

First , suppose a system that composed of two spherical membranes filled with air (two balloons have different initial volumes {means that the pressure inside which balloons are different} and the air pressure is 1 a.t.m) . We connect them with hollow tube and a valve. When we open the valve , one of them shrinks and the other one expands (It depends on their pressure) . So how can we get the velocity of the flowing air between two balloons? (Consider everything but if you have reasons for not considering one of them -for example the ratio of friction in the tube- Don't consider them and just tell me the reason)


  • $\begingroup$ Why the general relativity tag? $\endgroup$ – MBN Jan 22 '15 at 7:40

The air flow rate through a tube is approximately given by the Hagen-Poiseuille equation. If the pressure difference between the two ballons is $\Delta P$ then the HP equation gives the volumetric flow rate $Q$ as:

$$ Q = \frac{\pi r^2}{8\mu \ell} \Delta P $$

where $r$ is the radius of the pipe, $\ell$ is the pipe length and $\mu$ is the viscosity of the air. The equation actually only applies to incompressible fluids, but gives a reasonable answer even for compressible fluids like gases a long as the pressure differences aren't too high. In the case of two balloons it should be fine.

  • $\begingroup$ So ,1- Is it true if i use it for that question???? 2- How can I get the viscosity of the air???? 3- what is the relation between volumetric flow rate and velocity? $\endgroup$ – Michaele Jan 22 '15 at 7:44
  • $\begingroup$ @DavidMichaele: yes. $\endgroup$ – John Rennie Jan 22 '15 at 7:45
  • $\begingroup$ @DavidMichaele: Google for the viscosity of air. Mass flow rate = $\rho Q$, where $\rho$ is the density of the air (about 1.25kg/m$^3$). $\endgroup$ – John Rennie Jan 22 '15 at 7:50
  • $\begingroup$ And = 3- what is the relation between volumetric flow rate and velocity? $\endgroup$ – Michaele Jan 22 '15 at 7:53
  • $\begingroup$ @DavidMichaele: $Q = vA$ where $v$ is the (average) velocity in the tube and $A$ is the tube area. $\endgroup$ – John Rennie Jan 22 '15 at 7:55

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