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TS_103634661-Visitor
1-Visitor
July 11, 2022
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Help solving integral equilibrium problem

  • July 11, 2022
  • 4 replies
  • 2168 views

Hello,

 

I have a formula which defines water-pressure on a surface depending on depth and wavelength. 

To find the total force I have defined an integral.

 

I want to find the depth beneath the water level where the resultant is located. 

I can do this manually by guessing values but I would like the program to solve this for me. 

 

The only variable here is the depth for what I'm understanding by looking at my functions. 

Can someone help me understand what I'm missing in the attached calculation? 

 

Regards

/Tobias

Best answer by LucMeekes

Your expression with exponentials simplifies to the cosh() function.

LucMeekes_0-1657551407842.png

 

With that:

LucMeekes_0-1657546830565.png

And a Solve block is not necessary, for a simple 1 variable solution you can use the root function.

Success!
Luc

 

4 replies

V
24-Ruby III
VladimirN24-Ruby III
24-Ruby III
July 11, 2022

1. Please upload here your Mathcad Prime worksheet.

2. What version of Mathcad Prime are you using?

T
21-Topaz II
terryhendicott21-Topaz II
21-Topaz II
July 11, 2022

Capture.JPG

    L
    LucMeekes23-Emerald IVAnswer
    23-Emerald IV
    July 11, 2022

    Your expression with exponentials simplifies to the cosh() function.

    LucMeekes_0-1657551407842.png

     

    With that:

    LucMeekes_0-1657546830565.png

    And a Solve block is not necessary, for a simple 1 variable solution you can use the root function.

    Success!
    Luc

     

      T
      TS_103634661-VisitorAuthor
      1-Visitor
      July 12, 2022

      Hello,

       

      Ah this was the simplified solution I needed.

      Thanks for the help!

       

      I had problems writing out the cosh function which is why I wrote it in terms of exponentials. 

      But now I know how it's done! 🙂 

       

      Was not aware of the root-function, thanks alot! 

       

      Regards

      /Tobias

      W
      Werner_E25-Diamond I
      25-Diamond I
      July 11, 2022

      I second what Luc already wrote concerning simplifying the integrand

      Werner_E_0-1657571632642.png

      and the use of the "root" function.

      I just wanted to answer your question about

      Can someone help me understand what I'm missing in the attached calculation? 

      The problem is because you introduced three intermediate variables H, H1 and H2 in your solve block, which initially are unknown and undefined.

      Because of that you would have to solve for these variables as well and provide guess values, even though you actually are not interested in their final value. After all you have four equations in your solve block, so solving for four unknowns may work well (and it actually does):

      Werner_E_1-1657571900964.png

      But again, I won't suggest doing so.

      I am not sure if you maybe need the very same calculation multiple times and with different values for total height N (21) and height H2 (5).

      If so, you may consider using a little function with these values as argument. My suggestion uses the "root" function by providing a range (0 to N) and so is self-contained and needs no external guess values:

      Werner_E_2-1657572216375.png

      Not sure about the meaning of the "10". You may add it as a third argument to the function if necessary

       

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