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

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SUMMARY

The discussion centers on deriving a flow rate equation for a sphere in a fluid characterized by viscosity (n) and density (p), without the influence of gravity. The initial equation presented, Q=Av, simplifies to Q=4πr²v, but fails to incorporate the effects of fluid properties on velocity. Participants are tasked with creating a more comprehensive equation that factors in these properties to accurately describe the flow rate as the fluid rushes into the cavity left by the sphere.

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

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