Derive a flow rate equation that accounts for the fluid properties?

[brupenney]

Hi
I have been wrestling with this situation for a while, trying to derive an equation for it...A sphere is placed in a fluid of viscosity n and density p, outside any gravity. The sphere is instantly beamed out (perhaps by Capt Kirk?). At what volume rate will the fluid rush into the vacant cavity, taking into account p and n? The familiar Q=Av (flow rate = Area times velocity) yeilds Q=4pi x rsquared x v, but doesn't take the other factors influencing the velocity into account.

Can anyone here derive a flow rate equation that accounts for the fluid properties?

Thanks a lot

 

[Chestermiller]

Why would it flow at all if there is no gravity (and presumably no pressure).