[Fluid mechanics] Navier-Stokes and Hagen-Poiseuille

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The Hagen-Poiseuille equation is not applicable for free-falling fluids, as it requires a stationary solid pipe wall, which does not exist in this scenario. For vertical flows with varying diameters, the Navier-Stokes equations are more suitable to describe the behavior of viscous incompressible jets. The discussion also highlights an experiment aimed at demonstrating the limitations of the Bernoulli equation for viscous liquids compared to low-viscosity scenarios. The participants are uncertain about the appropriate viscosity to use in their calculations. Overall, the conversation emphasizes the need for a proper understanding of fluid dynamics principles when dealing with varying flow conditions.
ChaoY
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Can the Hagen-Poiseuille equation be used for a vertical flow in the water tab or any flow that has circular cross-sections with varying diameters? If not, how can the Navier-Stokes equations or any other equations be used to describe a viscous incompressible free-falling vertical jet?
 
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What are your thoughts on how to approach this problem? What is the order of magnitude of the viscosity you are considering?
 
I honestly don't know what viscosity we should use yet. We're preparing a little experiment to show that Bernoulli equation can be used to calculate velocity for liquid with low viscosity. We also want to calculate the flow rate of the jet this time with viscous liquid. The idea is to show that the Bernoulli equation becomes less effective. Now we're wondering if we could use the Hagen-Poiseuille equation to do the job instead this time considering the viscosity. Do you know if this equation still works if the circular cross section varies from two points?
 
ChaoY said:
I honestly don't know what viscosity we should use yet. We're preparing a little experiment to show that Bernoulli equation can be used to calculate velocity for liquid with low viscosity. We also want to calculate the flow rate of the jet this time with viscous liquid. The idea is to show that the Bernoulli equation becomes less effective. Now we're wondering if we could use the Hagen-Poiseuille equation to do the job instead this time considering the viscosity. Do you know if this equation still works if the circular cross section varies from two points?
If the fluid is in free fall, the hagen poiseulle equation doesn't apply because there is no stationary solid pipe wall.
 

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