How Do Viscous Interactions Differ in Vertical and Horizontal Geometries?

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    Viscous flow
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The discussion focuses on the differences in viscous interactions in vertical versus horizontal geometries, specifically through experiments involving a sphere's motion in a fluid. The first experiment examines the ascent of a sphere in a vertical tube, measuring ascent times to calculate the viscosity coefficient. The second experiment alters the setup to analyze fluid discharge through a tube with and without the sphere, highlighting the need for lubrication theory due to the presence of viscous resistance. The conversation emphasizes the limitations of Bernoulli's equation in viscous flows and the importance of considering different flow regimes, such as creeping and turbulent flow. Overall, the analysis aims to deepen understanding of fluid dynamics under varying conditions.
  • #31
Chestermiller said:
Do you know what to do next?
I have to show the following, right?

Chestermiller said:
Let ##h_0## represent the small minimum clearance between the sphere (in our problem) and the cylinder. Let z = 0 represent the axial coordinate of the center of the sphere. Show that, for axial locations on either side of the sphere close to this center location, the clearance can be approximated by the parabolic shape $$h(z)=h_0+\frac{z^2}{2R}$$
 
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  • #32
HighPhy said:
I have to show the following, right?
yes.
 

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