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Not too sure how to approach this equation - fluids mechanics

Engineering Asked by Mecki95 on April 11, 2021

Apologies if anything has been left out.

Ok, so there is just 1 equation which I am struggling to understand, I have made an attempt and also written out the full equation in 2 parts, but I dont know whether I need to use just the 1st half of the equation to get the dynamic viscosity or use both halves of the equation and if I need to use both halves, I am unsure how to.

My main course is the electrical and electronic side, so we dont usually see much or so far I havent seen much of the combining side where youd usually use P1 and P2. If its just using the first part of the equation then its something id be able to do.

My last question is about the coefficient of viscosity, how exactly would I obtain this value? I understand the basic knowledge that in my position, Syrup is high viscosity while water is low viscosity. So the higher the density the higher the viscosity, but how do I get the actual coefficient value? Id assume its not a simple google search of, coefficient of viscosity of water, as it comes up with the dynamic visc, which is something I need to work out for the table or is it that simple? I was given no information on how to work the value out.

Any guidance would be appreciated.
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Images 6 and 7 werent exactly needed but I thought id show what I did beforehand, it isnt shown on the image but page 7s velocity values were fixed afterwards to have the true mean average value, so I have the values ready for the equation, along with water actually being on my main copy, but I just dont have access to my pc to retake a picture.

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One Answer

What this boils down to is using the force balance of the ball falling through the liquid and Stokes law to determine the dynamic viscosity. The drag from viscosity and buoyancy force oppose the gravitational force of the falling ball as shown in the diagram in the posted picture. Equation 3 is an algebraic manipulation of the force balance to obtain dynamic viscosity. The kinematic viscosity is related to the dynamic viscosity via the fluid density (equation 5). If you have one viscosity and the density, you can determine the other viscosity. I have not personally heard of the coefficient of viscosity, however, this NASA chart refers to the dynamic viscosity as the coefficient of dynamic viscosity (https://www.grc.nasa.gov/WWW/BGH/viscosity.html). Solar Mike is correct, higher density does not necessarily mean higher viscosity. Viscosity is a measure of a fluid resistance to flow while density is mass per unit volume. Does this clarify things at all for you?

Answered by mechcad on April 11, 2021

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