Why Does Ball-to-Viscometer Diameter Ratio Matter in Viscosity Measurements?

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SUMMARY

The diameter ratio of a spherical metal ball to the diameter of a Falling Sphere Viscometer is crucial for accurate viscosity measurements. This ratio affects the annular flow area around the ball, influencing the velocity of the ball as it drops through the fluid. An improper diameter can lead to misleading viscosity readings, making it essential to maintain the correct ball-to-viscometer diameter ratio for reliable experimental results.

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We had a experiment on a metal ball dropped on a Falling sphere viscometer containing a certain liquid(I forgot what was it). I just don't know why our professor asked us to get the ratio of the spherical metal ball's diameter and the diameter of the Falling sphere viscometer and plot the velocity of the spherical metal ball vs. this ratio. I hope someone can help me...
 
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The key to think about is the area of the annulus created by the ball being in the tube. That annulus is the flow area that the fluid has to get around the sphere. Just using your intuition, what do you think should happen if that area were to decrease, i.e. use a larger diameter sphere?

The test correlates a fluid's viscosity to the rate at which the sphere drops. If you were to use an improper sized sphere, the fluid would seem either more or less viscous than it really is.
 

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