Fluids mechanics homework, feel like I have messed up the equations

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Discussion Overview

The discussion revolves around a homework problem related to fluid mechanics, specifically focusing on the equations governing viscosity and the application of these equations to a practical scenario involving the motion of a ball through a fluid. Participants are seeking clarification on how to correctly interpret and apply the equations provided in their homework.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how to find the coefficient of viscosity and mentions the general understanding that syrup has high viscosity while water has low viscosity, but lacks the specific equation to determine actual values.
  • The same participant questions whether to use only the first part of equation 3 to find dynamic viscosity or if both sides of the equation need to be combined, indicating uncertainty about the correct approach.
  • Another participant points out a potential typo in equation 3, suggesting that it incorrectly includes dynamic viscosity in the denominator and provides a link to Stokes' law for reference.
  • The initial poster acknowledges the typo and expresses surprise at having missed it, indicating a willingness to correct their understanding based on feedback.

Areas of Agreement / Disagreement

There is no clear consensus on the correct interpretation of the equations, as one participant identifies a typo that may affect the understanding of the problem. The initial poster is uncertain about the correct approach to solving the problem, indicating that the discussion remains unresolved.

Contextual Notes

The discussion includes references to specific images and values related to the homework problem, but the limitations of these images and the assumptions made in the calculations are not fully explored. The exact definitions and context of the variables involved are not clarified, which may affect the understanding of the equations.

Meckii
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Homework Statement
Confused with trying to find the values in the equation although I feel like im just messing up the equation in my head.
Relevant Equations
Equation 3: Coefficient of viscosity = 4 x pi x r^3 × g / 3 x 6 x pi x coefficient of visc x mean velocity of ball
(Ps - P1) = (2/9) x r^2 x g ((ps - p1) / u)

Equation 5: v = dynamic viscosity / density
Edit: So I have written out equation 3 again and taken a picture to show my working out, the 2 things that I am confused about is how do I find the coefficient of viscosity? I know that syrup is high viscosity and water is low viscosity but I don't know the equation to get the actual value. The 2nd issue I have is when I have the coefficient of viscosity value, do I just use the 1st part of equation 3 to find the Dynamic Viscosity or do I have to somehow combine both sides of the equation? If it is the latter I do not have a clue how to work out both together. The last 2 images are what I have worked out just.

I have attempted my solution on the images attached, the first 3 images show the equations needed for the questions while the last 4 or 5 images show my working out and the way I tried attempting the questions.

The 4th pic shows the practical work done showing the specific gravity, s and the Density, p. While the 6th page shows my attempt at the equation 3 and equation 5, the final page shows equation 5 questions at the top also. While in the 5th pic the times that the ball took to travel a certain distance is shown at the top.

All I really ask is a little bit of guidance as it has stumped me quite a bit and I am unsure how to progress with the correct values/answers.

Values achieved,
s = shown in the first table
Density, p = shown in the 2nd table
u = mean average is shown in last pic
g = 9.81
Ps = 7.850 (I am assuming this is correct, density of steel which I looked up)
P1 = given in the density table on page 4, all 4 values
r = the radius which is known as 1.59mm, 2.38mm and 3.175mm
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Last edited:
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Lnewqban said:
Equation #3 has a typo, as it incorrectly includes the dynamic viscosity (μ) in the denominator.
Please, see:
https://en.m.wikipedia.org/wiki/Stokes'_law

Welcome, Meckii :cool:
Lnewqban said:
Equation #3 has a typo, as it incorrectly includes the dynamic viscosity (μ) in the denominator.
Please, see:
https://en.m.wikipedia.org/wiki/Stokes'_law

Welcome, Meckii :cool:
Updated, surprised i missed that, thanks for letting me know though, ended up forgetting to add the pics also
 
Edit: I pictures 4-6 are the first pictures added, pictures 7-8 are the new pictures I have added which I just wrote out.
 

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