Help wanted in solving this equation

  • Context: Undergrad 
  • Thread starter Thread starter paula1980
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Discussion Overview

The discussion revolves around solving an equation involving the variable hc, which appears on both sides of the equation. Participants explore methods for finding the value of hc using tools like MathCad and Excel, discussing iterative approaches and numerical methods.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant struggles to solve an equation for hc, which is present on both sides, and seeks assistance.
  • Another suggests using iteration to guess a value for hc and check if it satisfies the equation.
  • A different participant mentions that hc = 0 is a solution found by inspection, and speculates about the possibility of expressing other solutions in terms of the Lambert-W function.
  • One participant expresses uncertainty about their implementation of the suggested methods and requests feedback on their Excel model.
  • Another participant claims to have found a solution of hc = 1.585, but this is later contested as being incorrect based on a reference paper suggesting a value in the range of 25-30.
  • Another suggestion includes using Newton's Method or the bisection method for finding solutions.
  • A participant reports finding a value of hc around 18, while noting that a referenced paper states a value closer to 25, indicating discrepancies in results.

Areas of Agreement / Disagreement

Participants express differing views on the correct value of hc, with some proposing specific numerical solutions while others challenge these values based on external references. The discussion remains unresolved regarding the exact value of hc.

Contextual Notes

Participants mention various methods for solving the equation, but there are indications of uncertainty and potential errors in calculations. The discussion includes references to different values of hc that are not aligned, suggesting a need for further verification.

paula1980
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Hello:

I have been trying to solve the following equation on MathCad or Excel, however its been quite a struggle :(

Can anyone please able to help me?

As you can see in the equation below, I have to plot the value of hc but its located on both right and left side of the equation. All other variable (ao, f and v etc.) are constants.

http://s9.postimage.org/cvr73gwel/help.png

Any help is REALLY appreciated. Thank you for your time and help.
 

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Instead of plotting hc, try to solve your equation by iteration. Guess a value of hc, plug it into the RHS, and see how close you are so that LHS = RHS.

Alternately, you can rearrange your original expression so that RHS - LHS = 0 = y.

Then you can plot a curve of hc versus y to find out the value of hc which satisfies the original equation.
 
Well, there's one solution of the equation that can be found by inspection of the equation itself: ##h_c = 0##.

For any others (I suspect there's only one more real one from a quick plot of x - ln|x+1|), it's possible to express the solution in terms of the Lambert-W function it looks like, but it's probably easiest to just do as SteamKing advised.
 
Thanks Steamking and Mute for your prompt responses! Do appreciate it.

I have tried following steamking's advice but still have a sense of unsurity if I did this correctly.
Please have a look at the attached Excel file, where I have tried modelling this and, if possible, provide a feedback.

I am finding it a little tricky to grasp how one can have LHS = RHS in this equation. FYI, I have attached the equation also in the spreadsheet..its presented in a slightly different manner but is same equation as before.

Thanks.
 

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This situation occurs frequently.

Using your spreadsheet, another value which satisfies the relation is hc = 1.585
 
SteamKing said:
This situation occurs frequently.

Using your spreadsheet, another value which satisfies the relation is hc = 1.585

That answer is not close to correct. According to the paper I am reading it should be near 25-30 range. Again its possible I may have made a mistake somewhere but thanks for your help!
 
Try something like Newton's Method. Or maybe a bisection method.
 
I found the answer...please see the attachment. I simply needed to substrate Hc-Hc...when the difference is close to zero, that value of Hc corresponds to the answer I was seeking which was around 18 (although in the paper it states around 25) but with my variables I am obtained 18.

Thanks everyone for your help particularly SteamKing.
 

Attachments

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