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Help wanted in solving this equation 
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#1
Nov2512, 03:35 PM

P: 5

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. 


#2
Nov2512, 03:51 PM

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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. 


#3
Nov2512, 05:22 PM

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P: 1,391

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  lnx+1), it's possible to express the solution in terms of the LambertW function it looks like, but it's probably easiest to just do as SteamKing advised. 


#4
Nov2512, 05:59 PM

P: 5

Help wanted in solving this equation
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. 


#5
Nov2512, 06:23 PM

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


#6
Nov2512, 06:39 PM

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#7
Nov2512, 07:39 PM

P: 828

Try something like Newton's Method. Or maybe a bisection method.



#8
Nov2612, 06:53 AM

P: 5

I found the answer...please see the attachment. I simply needed to substrate HcHc...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. 


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