Real Solution of an Equation and Plot it

[ygupta]

Hello Friends,

I want to know the solution of the given below equation using Mathcad Prime 3.1.

In above equation, two variable i.e. Phi. & Zeta is given but need to find out Psi.

There is a figure given for reference which tells the relation in these variable as attache herein post.

Can anyone tell me how to calculate Psi using the given references and also if I need to plot it, then how can it be achived.

Thanks, Yogesh

[terryhendicott]

Hi,

Enclosed is Mathcad 15.  You will need to convert it to Prime 3.1

Cheers

Terry

[ygupta]

Can anyone please explain me this? I dont have any experience with Mathcad 15 and its seems to me bit difficult to understand.

Thank You @terryhendicott for your reply. 

[LucMeekes]

Explain you what? What is it that you don't understand?

[terryhendicott]

Hi,

Mathcad 15 is a predecessor to Prime 3.1.  I do not have access to Prime 3.1

Mathcad file names are *.xmcd.

Prime 3.1 file names are *.mcdx

Prime 3.1 comes with a converter that changes *.xmcd files to *.mcdx.  Use it and you get 3.1

Cheers Terry

[ygupta]

Thanks Teryy.

Although my actual problem is that I am unable to find the value of psi, wherein two variables are already given.

Apparently, I did not sepcify here that zeta value is being calculated from a equation and the output comes in unit 1/N.

In your sheets, as converter by @VladimirN (Thanks for your help), I have replaced the assumption of zeta to actual value and the function of zeta & phi gives an error of uncomp attached is the snaps from the same.

Thanks for your help.

Yogesh

[LucMeekes]

Or do like this:

(Created in Prime 4, file attached, but you cannot open that in Prime 3.1)

I suggest you recreate the sheet in your Prime 3.1.

Success!
Luc

[LucMeekes]

Alternatively:

Success!
Luc

[ygupta]

Hi @LucMeekes,

I have tried your this alternative and attached is the error.

for solve function, it says, no solution found.

any suggestion please.

thanks.

[LucMeekes]

First off: do not just post pictures. Post worksheets.

Second: I say there's an error in your definition of the F() function. In the second term one of the two phi's should be psi.

Last: did you try to reproduce my first solution? And what does it give?

Success!
Luc

P.S. Even though the function definition is wrong, a solution is still found by Mathcad 11. But the result is quite different:

I guess Prime (with mupad) is not powerful enough to solve it.

[ygupta]

Hi @LucMeekes,

Regarding your first solution, I have attached the worksheet here for your reference. My picture dont know why not appear like your does here so I have to always attached the picture.

in your first solution, psi = "Function: psi {VARIABLE}" shown.

Surely, I am making a silly mistake here but since my mathematic is not as good as your guys, please suggest.

Thanks, Yogesh

[terryhendicott]

Hi,

The value you are using is not in the range of plotting 0.1 to 1000 2.6x10^-5 check this value

   

In the function definition for "f" don't use "= 0" on the end

Don't in the next line set the function "f" = 0

Regards

Terry

[LucMeekes]

This is what you produced, with errors marked:

Do not put an =0 at the end of the definition of f().

You are mixing up the psi's and the phi's! Check your definitions, and compare to my sheet.

Finally you need to vectorize the expression to plot.

You may want to set the horizontal axis to a logarithmic scale...

Success!
Luc

P.S. You cannot just paste a picture into the text on this forum (well, you can, and it looks great, but once you submit the post, the picture is replaced by an icon).

To insert a picture in the text (like the one in this post) you HAVE to have your picture  saved as a file (.png, .jpg, or the like) and use the "Photo's" button  just above the edit window and follow the instructions.

Other than that...whenever possible always attach the Mathcad/Prime sheet.

[ygupta]

Hi,

Thanks @LucMeekes and @terryhendicott for the explanation.

I have corrected the sheet as you guys explained. Still plot is somewhat not coming in a way as expecting it to be.

Attached is the sheet for your reference. Plot is the secondary objective in my case first I need a value of psi which shall be used further on the basis of the equation. Regarding the zeta, yes this value is correct 2.567*10^-5. It is the calculated value which shall be used to calculate psi. One more issue here. I did not yet specify the actual unit of zeta that is 1/N so please we shall keep this in mind too.

We usually do this kind of equation using excel by goal seek function but Im sure there should be more advanced feature in prime to do the same/similar.

Thanks,

Yogesh

[LucMeekes]

There's something wrong with your plot, but I can't figure out what.

Delete the plot, insert a new one and make sure you vectorize the psi function for the vertical axis, as you did not do that yet.

Success!
Luc

[Werner_E]

Didn't you look at the picture here -> https://community.ptc.com/t5/PTC-Mathcad/Real-Solution-of-an-Equation-and-Plot-it/m-p/586555/highlight/true#M183918

concerning getting the value of psi with the value of zeta you provided.

Look for "Example of use".

To fix the problem with the plot you have to do three things:

1) drag the put region a bit downwards as its to high now and does not consider the definition of the function and zeta vector

2) vectorize the function call psi(zeta,phi) - that is the arrow over it (Operators menu, lower right)

3) change the plot type from "column trace" to "line trace"; change line style to solid

4) (yes, thats 4 of 3) delete the red flagged "0.1" on the ordinate

[ygupta]

Hi @Werner_E

Did exactly as you mentioned in earlier posts. Now ploting is somewhat similar to yours except the begining of the curves. My problem is that I need to use the value of psi in further equation so I need some output as well from the plot. I am new to Mathcad so dont know much about but thanks to you guys for making it easier for me.

I have attached below my problem again just to elaborate it more. 

source IEEE605

Now as per the above picture, by some formulas, I have calculate the value of zeta (in 1/N unit) & phi as mentioned in picture. Now using the equation #40, approximate value of psi shall be calculate and ploted (additionaly).

and then psi value will be used in above Ft equation with a possible result.

I hope now its clear to everyone what I actually need. Attached is my worksheet for reference in line to your suggestion.

Please suggest. Thanks

[ygupta]

Not sure whether you have access to prime 3.1 file so herein attached the snap from the worksheet with the further quation thats need to be calculated based on these variables.

If every thing done correctly, then why Ft equation does not producing the result. This is my ultimate goal for solving the psi, zeta & phi variables. Any suggestion on this please.

And just for ref. attached below is the formula, used to calculate zeta value.

Many thanks to everyone. 

[Werner_E]

psi its a function.

So in the calculation at the end which throws that error you want probably replace "psi" by "psi(2.567*10^-5, 0,396)".

Furthermore you can't simply introduce units partially.

If zeta is of unit 1/n, then the "2" ind (2+zeta) must be of the same dimension, for example. You can't add quantities of different dimensions.

What about the dimension of phi and psi? I see no simple way to make your function f dimensionwise correct.

[LucMeekes]

Yogesh,

We can all read Prime 3.1 files. We generally use a higher version of Prime: 4 or 5. The problem is that from Prime 4 or 5 we cannot save the sheet to a previous/older version, like 3.1, 3, 2 or 1.

Regarding the Unit 1/N you have a problem. In the function for f() you are adding it to the dimensionless number 2 in the second term. You cannot add apples to oranges.

I guess the function f() is emperical, that is, not based on sound physical models. If you want to work with units here, which is usually preferable, you're in for a little more challenge.

Success

Luc

[ygupta]

Hi Luc,

If I could remove the unit from zeta equation, then I will be ok with that. Is there any way to not consider the unit of a variable that is driven by multiple variables? Phi and Psi are the dimensionless variables thus doesnt have any unit but IEEE has given a formula for calculating zeta that contains multiple constant and other combination of units which yield the result in 1/N.

However, these all are the load factors so may be considered as unit less variable but no idea how to remove the unit from zeta result.

Any sugegstion on this?

Thanks

[terryhendicott]

Hi,

Cheers

[ygupta]

Hi,

As pe your snap given, I did the same but wondering its throwing an error for variable "n". However at top right, I am already defining "n" but still it says "This variable is undefined..."

Have a look at below snap:

Additionaly, calculating Ft as wihtout function of other variables, it is producing the result. Highlighted in above snap.

BTW, did you get the result of your function as you posted for example?

PS: I am not using any unit as of now for solving this example.

Thanks.

[LucMeekes]

Yogesh,

Attach the worksheet... NOT just a picture.

Luc

[Werner_E]

Don't use a numeric evaluation when you define a function!

[terryhendicott]

Hi,

If Ft is defined as a function you need to use it as a function not just put the equal sign after it

[LucMeekes]

And what if n is inbetween 1 and 2?

Luc

[terryhendicott]

Hi Luc,

n is a whole number representing the number of connectors it never should be input as a number between 1 and 2

[LucMeekes · Accepted solution]

I fired up another machine that has Prime 3.1...

You should be able to continue from here.

Prime 3.1 file attached.

Success!
Luc

[ygupta]

Hi @LucMeekes, @Werner_E,

Both of yours functions working properly now. Now I can manage the zeta with unit as well and it doesnt reproduce any error. Ploting is also pretty much similar to one shown in IEEE and I can also use the psi function in further equations as well for solving.

Attached herein sheet with both options for your reference.

Thanks to you guys and a big applaud to all of you for helping there.

Cheers !!