- #1

joshmccraney

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## Homework Statement

Consider the process of blowing up a spherical balloon. Measurements indicate that the “surface tension” of the balloon material is ##k## (assumed constant here with units of force per unit length). Assuming that an air compressor used to blow up the balloon can deliver a constant mass flow rate of air of ##\dot{m}## , plot the balloon radius, ##r_b##, as a function of time assuming ##r_b(t) = 0##.

## Homework Equations

Conservation of Mass

## The Attempt at a Solution

I know the answer is $$\frac{4 \pi}{3} \left. r_b' \right.^2(2+r_b') = t'\\

r_b'=r_b\frac{\rho_{atm} r T}{k}\\

t' = t \frac{\dot{m}}{\rho_{atm}}\left(\frac{\rho_{atm} R T}{}k\right)^3$$

But I'm not sure how to arrive there. I was thinking $$m = \rho V = \rho \frac{4}{3}\pi r^3 \implies \dot{m} = \rho 4 \pi r^2 \frac{dr}{dt}$$. Any ideas?