Partial Volume of a Cylinder Calculation

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Discussion Overview

The discussion revolves around calculating the partial volume of a cylinder, specifically focusing on the formula involved and its application in an Excel spreadsheet project. Participants seek clarification on the components of the formula, particularly the use of the cosine function.

Discussion Character

  • Technical explanation, Homework-related

Main Points Raised

  • One participant expresses uncertainty about the formula for calculating the partial volume of a cylinder, particularly the section involving R squared and cos -1.
  • Another participant provides a formula for the volume calculation, suggesting it could be implemented in Excel, although they do not use the software themselves.
  • A participant indicates that the provided formula does not work in Excel but expresses willingness to investigate further.
  • Another participant reiterates their confidence in the correctness of their formula.

Areas of Agreement / Disagreement

There is no consensus on the effectiveness of the formula in Excel, as participants express differing experiences and approaches to the calculation.

Contextual Notes

Participants have not resolved the specific mathematical steps or assumptions related to the formula, and there may be limitations in how the formula is applied in Excel.

CivCalc
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It's been a long time since I've attended school, over 33 years ago. So my question may seem basic to many here. I wish to calculate the partial volume of a cylinder for my excel spreadsheet project. The formula I've found is attached. (unable to type it)

But I do not fully understand this formula. Particulalry the R sq cos -1 section. Could somebody please explain how I use cos
Thank You

View attachment 7715
 

Attachments

  • Formula.PNG
    Formula.PNG
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Mathematics news on Phys.org
Hello, and welcome to MHB! (Wave)

I don't use Excel, but I imagine it would be something like:

Code: 
V=L*(R^2*ACOS((R-D)/R)-(R-D)*SQRT(2*R*D-D^2))
 
Thanks for response. No doesn't work on excel but that's OK, I'll investigate further
 
CivCalc said:
Thanks for response. No doesn't work on excel but that's OK, I'll investigate further

The Basic Spreadsheet
View attachment 7728
B1:B3 are the desired input values.

The formula in B5
View attachment 7729
I added a few sets of parentheses to emphasize order of operations.

You COULD name the cell ranges and refer to their meanings, rather than the cell addresses.
 

Attachments

  • Spreadsheet1.jpg
    Spreadsheet1.jpg
    8.6 KB · Views: 142
  • Spreadsheet2.jpg
    Spreadsheet2.jpg
    5.8 KB · Views: 133
Yeah, I figured what I gave was correct. :)
 

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