Consider a solid sphere (capable of withstanding full vacuum) of 3m diameter filled completely with water resting at sea level. It has a 10cm hole at the bottom with a cork on it. If you open the cork, what is the time taken for water to completely drain out.
What happens for higher diameter spheres?
let a be the area of the drainage hole and v be the velocity of water out of that hole, then av is the rate at which the water is leaving the sphere and V be the volume of the sphere then
now when the sphere is filled to hight h the volume is equal to
now using (1), (2), and the chain rule
v(h)=Sqrt(2*g*h) where g is acceleration due to gravity on earth (9.8m/s^2)
100*h*(3-h)/Sqrt[2*g*h] dh = -Dt
when t=0 h=3
now the sphere is empty when h=0 thus we can find how long it takes to drain by setting h=0 in (3) and solving for t thus
or about 31.2984 seconds
now that seems a little quick for that much water to be able to drain so I think I may have made a mistake somewhere, if someone could please point it out I would be greatly appreciate it :-D
Posted by Daniel
on 2006-07-14 01:41:54