How fast a bubble will rise in water, say a 55 gal drum?
Answer:
It depends on the size of the bubble. Bigger bubbles rise more quickly. You can estimate the speed by assuming a spherical bubble and balancing the drag and buoyancy forces. A bubble of diameter D has a volume:
V = (Pi * D^3)/6
And a projected frontal area of: A = (Pi D^2)/4
The buoyancy force is the product of density of water (r = 1 gram/cm^3), the volume, and gravity (g = 9.8 m/sec^2)
Fb = V*g*r
The drag force is:
Fd = s^2 * r * A * C / 2
Where s is the speed and C is the drag coefficient (1.0 for a sphere).
Balancing the forces:
V*g*r = s^2 * r * A * C / 2
V*g = s^2 * A * C / 2
s = sqrt(2*V*g/(A*C))
But V/A = (2/3) * D and C = 1 so:
s = sqrt(4 D * g/3)
I've ignored viscous drag here. This will slow the bubble. In water the effect is not too big but in viscous stuff (e.g., honey, glycerin, syrup) viscous effects will dominate.
This says a 1 cm bubble rises at 36 cm/sec. Make some bubbles and see if this is close to right.
The answers post by the user, for information only, FunQA.com does not guarantee the right.
More Questions and Answers: