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

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The diameter ratio of the spherical metal ball to the Falling sphere viscometer is crucial for accurate viscosity measurements. This ratio affects the annular flow area around the ball, influencing how the fluid moves as the ball descends. A larger diameter sphere decreases the flow area, which can lead to misleading viscosity readings. Using an improperly sized sphere can result in the fluid appearing either more or less viscous than its true viscosity. Understanding this relationship is essential for reliable viscosity testing in fluid dynamics.
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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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