Need help plz with iterative solving of equation

[sm�ller-2]

Hey, i do have a problem with the following equation. I need to solve it and find the n value.

But i have problems with the units. Can you guys help me?

Best thx 😃

[-MFra-]

Lieber Herr Stefan Müller, sollten Sie die Temperatur wie folgt festgelegt : T = 300K. Einer der Parameter der nzul Funktion nicht definiert ist. Außerdem müssen die Parameter der Funktion dimensionslos sein. Ich nehme an, dass n = 3200 eine erste Schätzung von n ist, oder nicht? Sie können zu einer physikalischen Größe nicht addieren (zB MPa) eine dimensionslose Zahl (es dieselbe Dimension haben muss, nämlich MPa). es kann nicht den Logarithmus einer physikalischen Größe zu berechnen, müssen sie dimensionslos sein.

Mit freundlichen Grüßen F. M.

Dear Mr. Stefan Muller, You should set the temperature as follows: T = 300 K. One of the parameters of the function,  , is not defined. Furthermore, the parameters of the function must be dimensionless. I suppose In addition that n = 3200 is an initial guess of n, or not? You can not add up to a physical quantity (for example MPa) a dimensionless number (it must have the same dimension, namely MPa). Mathcad can not calculate the logarithm of a physical quantity, it must be dimensionless.

Yours sincerely F. M.

[RichardJ]

Since it's an empirical equation each variable will have an expected input unit, and the result will also have some expected units. Wherever you got the equation from should specify what those units are. You have two choices. One is to specify the values of all your variables in the expected input units, but without attaching the units in Mathcad. The other is to divide every variable in the equation by the expected input units, and multiply the entire equation by the expected output units. That will give you a unit aware version of the equation that can handle any input units. Note that dividing the variable by the expected unit will only work for temperatures if the expected unit is either Kelvin or Rankine. If it's centigrade or Fahrenheit you need a more complicated expression that will return the correct numeric value for any input value. For centigrade it would be:

The unit you are using is angular degrees, and has nothing to do with temperature.

[-MFra-]

The formula is a recurrence formula. After changing all the constants dimensionless, results:

This result is acceptable?

Best regards

F. M.

[sm�ller-2]

mm im not sure it should ne an implicit equation and solved for n so that it is the same value left and right but as i see when i calculate this im not getting a zero value:

= should be then 0  ...... ?

hmm what do you mean with recurrence formula isnt it an implicit equation?

I tryed to solve with "Vorgabe and search(n) but all i get is this:

I think i Need to check my formula if there is a Problem itself ...

At the moment im clearly understand ....

I should just find the right value n so that equation is true.

I have a look on the input data and the equation itself if i did do a mistake on the input structure of the equation itself. Or misunderstood something there 😞

Thx for help so far!

[-MFra-]

To find something about it, look for the Mathcad Help "Recursive Functions". Or in calculus texts.

Bye

[sm�ller-2]

OK thx for the tip!

[-MFra-]

In my opinion, you should re-examine the issue. In what follows, I have considered the equation as a transcendental one, but the results are disappointing.

[sm�ller-2]

Thx for help!

Im going to look at the equation itself