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

In summary, the conversation is discussing the problem of determining the flow rate of a fluid into a vacant cavity after a sphere is instantly removed from it. The equation Q=4pi x rsquared x v is mentioned, but it does not take into account the fluid's viscosity and density. The question is posed if anyone can derive an equation that accounts for these factors. The issue of the lack of gravity and pressure in this scenario is also brought up.
  • #1
brupenney
15
0
: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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  • #2
Why would it flow at all if there is no gravity (and presumably no pressure).
 

1. What is a flow rate equation?

A flow rate equation is a mathematical equation that calculates the rate at which a fluid (such as liquid or gas) flows through a given area or system. It takes into account various fluid properties such as viscosity, density, and pressure.

2. Why is it important to account for fluid properties in the flow rate equation?

Fluid properties have a significant impact on the behavior of fluids and how they flow through a system. By accounting for these properties in the flow rate equation, we can accurately predict and control the flow rate, which is crucial in many practical applications.

3. How is viscosity incorporated into the flow rate equation?

Viscosity, which is a measure of a fluid's resistance to flow, is incorporated into the flow rate equation through the use of the viscosity coefficient, which is a constant that represents the fluid's internal friction. The higher the viscosity coefficient, the slower the fluid will flow through a given area.

4. Does the density of the fluid affect the flow rate?

Yes, the density of the fluid has a direct impact on the flow rate. A denser fluid will flow at a slower rate compared to a less dense fluid, as it has more mass per unit volume and thus requires more force to move through a system.

5. Can the flow rate equation be used for all types of fluids?

The basic flow rate equation can be used for most fluids, but more complex equations may be required for non-Newtonian fluids (such as blood or ketchup) that do not follow the standard relationship between shear stress and shear rate. It is important to choose the appropriate flow rate equation based on the properties of the specific fluid being studied.

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