Trying to calculate the radius of a bubble as it rises....

[lucas jonasch]

I am trying to predict the radius of a bubble at 0.4 m deep in a liquid.
I know:
the surface tension of the liquid (T) .002239 kg*m
the pressure outside the bubble at .5 meters depth (Po1) 394.5 kg/m^2
the pressure inside the bubble at .5 meters depth (PI1) 394.723314 kg/m^2
the radius of the bubble at .5 meters depth (R1) .001 m
the pressure outside the bubble at .4 meters depth (Po2) 315.6 kg/m^2
I do not know:
the pressure inside the bubble at .4 meters depth (PI2)
the radius of the bubble at .4 meters depth (R2)

What I tried to do was: a two-variable equation, using
PI1*(R1^3)=PI2*(R2^3) (p1v1=p2v2)
and
R2=2T/(PI2-Po2) (http://hyperphysics.phy-astr.gsu.edu/hbase/surten2.html)

I solved it and eventually got:
-Po2(R2^3)-2T(R2^2)+(PI1*(R1^3)=0

However, when I solved the equation I got a negative number, while I'd expect it to be a little bit bigger than a millimeter... I checked my math a few times and I'm pretty sure the equations I'm using make sense?? Does anyone know what's wrong??

 

[lucas jonasch]

 

[lucas jonasch]

btw, this isn't homework but I assumed this was still a good place to put it

 

[lucas jonasch]

LOL! I just realized my mistake (and it was a really DUMB one.) I entered in the data into the online cubic equation calculator keeping scientific notation for 3.94*10^-7. The three values it gave me were: -0.4294762187154887, 0.2147310149344237 + i* 0.37193321976168103, and 0.2147310149344237 - i* 0.37193321976168103.

I then tried to enter it in without scientific notation ( 0.000000394) and it gave me the right values: 0.0010720530955198526, -0.0005431209710805853 + i* 0.0009324852984662585, and -0.0005431209710805853 - i* 0.0009324852984662585.

Thank you for your help and sorry for wasting your time!