To all the Math/Physic nerds of SEN...
I'm in a program named "Math's Integration". Over all, we choose a subject at start and work on it all through the year, handing about 2-3 pages of calculations per week (obligatory!).
My subject: What will be the distance travelled by a
balloon having 'x' litres of 'x' fuel (taking in count the initial elevation from the ground and the arrival's fuel used).
'x' being a value we just haven't decided yet, so if you want to calculate stuff, just set a constant as 'x' and you'll be fine.
The thing is... I can't get to figure out how to apply the Buoyancy equations on this situation...
I'm trying to start with an extremely simplified situation, though I still fail to apply the equation: I'm not counting any friction, wind, balloon deformation due to pressure changes, non-uniform air density inside the balloon due to the heat not being spread equally and instantly, etc.
B = -p*V*g
If I set heights, find approximated values of the air density, and apply the equation, I'm fine, but this really won't get me anywhere.
I do understand the balloon will eventually reach an equilibrium state... but how to calculate its height?
Am I supposed to find what is the density that makes the Buoyancy equal to the negative force that represents the gravity and then find a table that permits me to evaluate an approximate height based on this air density?
I'm really, really lost!
Please, please, intelligent people, help me!
EDIT: PARTIALLY SOLVED: http://www.staredit.net/261831/EDIT:
COMPLETELY SOLVED:
http://www.staredit.net/271126/Get my final report of 30 pages right there:
http://www.mediafire.com/?r7mkbub7xa8i9s1