# Wondering about how to deal with a deflating balloon?

1. Feb 20, 2010

### jeebs

Hi,
Not sure if this is asked in the right section, but I am doing something which involves moving a small car, and I am trying to make predictions from an air resistance perspective. I'm trying to come up with a rough expression for the drag force on a balloon as it deflates. I've started with the general expression for the drag force $$F_d = 1/2\rho AC_dv^2$$.
To simplify things I'm assuming a spherical balloon, which has a radius rmax when it is fully inflated and a radius rmin when it is fully deflated, so it goes from having surface area A = pi(rmax)2 to pi(rmin)2. I realise the surface area of a sphere is 4pi.r2 but I need the area of the object presented to the oncoming air. I also realise that the velocity v is going to increase from zero to some maximum, but I'm ignoring that for now (perhaps unjustifiably, lol).

So assuming everything else (velocity v, air density rho and drag coefficient Cd) is kept constant, the balloon radius r determines the drag force Fd.

However, this is where I start to have problems, because I am not expecting r to decrease at a constant rate - my thinking is that, from the general spring force equation F=-kx, a balloon stretched (inflated) to the maximum is going to have a greater force trying to pull its molecules back to their original positions than if it is partially inflated. This means the rate at which air is forced out (ie. pressure decreases) falls with time.

I need to find out how r varies with time but all I can think of really is that its going to depend on the "stretchiness" of the balloon, ie. something analogous to the spring constant, k, and also the size of the hole that the air is escaping from. I'm not really sure where I should go from here, so if anyone has any ideas they think might be relevant I would love to hear them.

Thankyou.

Last edited: Feb 20, 2010