Level 102
What is the initial value of $unknownVariable ?
Dec 6, 2022
36
Level 11
Equation with unknown in PHP
Hi guys,
I am trying to solve an equation, where I have all the results given to me in Excel, but I don't know how to get to the same results in PHP since $unknownVariable essentially is part of the calculation.
$unknownVariable = 1 / pow(2 * log(2.51 / (28294.21211 * sqrt($unknownVariable) + 0.27 * 0.0008)), 2);
// The end result should be: 0,02577574
In Excel the result is given by iterating, but how can I do the same?
Sorry for my lack of correct math terms here :D
Level 11
Hi @sinnbeck
That is what I don't know (but is trying to figure out), you can see the equation on the image below:
https://pasteboard.co/p7b9wpprAUWK.png
The php variable is basically that equation written out, minus the "missing link" of $unknownVariable
Level 102
@Reached Does it have a name ? The formula
Level 102
And im not getting the excel part? You get the results from excel? But why do you need to calculate it if you have the result already?
Level 11
@Sinnbeck There is no name for it (as far as I know anyway)
Level 11
@Sinnbeck It's because I am converting the Excel to a php-app, thus I need to convert the formulas to php :)
Sorry if that was unclear!
Level 102
@Reached Ah ok. So can you show how it is in excel ?
Level 11
@Sinnbeck Yes :)
So this is a part of the Excel sheet from which I need to calculate stuff, the derived values are calculated in other formulas, however they are not relevant to this I believe.
The formula for calculating λ is the one I pasted in the opening post, but has been substituted with the values that you see in the Excel spreadsheet here:
https://pasteboard.co/lWpgO2URebTS.png
1÷POWER(2×LOG(2,51÷(A21×SQRT(G21))+0,27×B21);2)
Where G21 is the result of the above
Level 102
@Reached And the very first row? Is the formula different ?
Level 11
@Sinnbeck I'm not quite sure what you mean? :)
Level 102
That row is probably row 22 as it checks row 21. So scroll to row 1 and see what it has there. It most likely does not have G0. Instead it probably has the starting value
Level 11
@Sinnbeck There is nothing there (as far as an initial value goes), but I asked the client about it, so hopefully I will have it soon :)
Level 102
@Reached can you show what the formula is in that cell?
Level 11
The formula for all the cells is the same as posted previously (also for the first cell). But it seems like the initial value is some kind of "guess"
Level 104
I assume you want to use recursion (assuming the $unknownVariable inside the formula is an estimate from a previous iteration)?
function calculate($previousEstimate) {
$newEstimate = 1 / pow(2 * log(2.51 / (28294.21211 * sqrt($previousEstimate) + 0.27 * 0.0008)), 2);
// check if the newEstimate is "close enough"; i.e. within N significant digits
if (abs($newEstimate - $previousEstimate) < 0.0001)
return $newEstimate;
}
return calculate($newEstimate);
}
// use some original estimate to begin your computation
calculate(1);
Level 11
@tykus Yes I believe this is very close to what I need actually. I am not sure what my initial value should be though, as it seems like no results are returned when setting it to 1 or even 0.0001
Essentially I need to calculate a whole bunch of different values depending on the user input, and then use those calculations for some other calculations, so this method will be running a loop :)
Thanks so far!
Level 104
@Reached I don't know what a original estimate might be - or how this equation might converge on its solution, so pick a reasonable original estimate.
Ultimately, because the equation needs an initial value for $unknownVariable; you must give it some matching value! How is this actually achieved in Excel; can you post the Excel formula here?
Level 11
@tykus I posted a part of the excel sheet further up in a reply to Sinnbeck :)
The Excel sheet iterated to find the value (not something I know too much about unfortunately) :/
The Excel formula is as follows:
1÷POWER(2×LOG(2,51÷(A21×SQRT(G21))+0,27×B21);2)
G21 is the result of the above
Level 104
G21 is the result of the above
Ok, so recursion is a viable solution. What does the Excel sheet do in the first row (where there is no value in the previous row) - this will be the initial estimate?
My solution takes no account of the B21 cell value(s) - is this a computed value as well? Note, you would also need to pass this into the recursive function.
Level 11
@tykus Awesome, I think we are getting there!
There are no other values of relevance above the input (all cells are empty), and I can't seem to find any other value. I will try to ask the client if they have a number I could use as the initial value
Yes B21 (0.0008) is also a computed value, based on user input. I actually already adapted the recursive function you provided to be able to swap out the relevant user-input
Level 104
@Reached but there must be something in the formula on very first row that is different from subsequent rows - there is no previous value to work with there!
Level 104
Looking at the screenshot again; this looks like a fluid dynamics problem; why is the previous result valid for different set of flow parameters? It is a long time since I was a mechanical engineer...
I wonder if recursion is the correct approach here?
Level 11
@tykus This is exactly what it is yes.
It's attempting to calculate the pressure drop in pipes given some different values, and to calculate the pressure drop, I need ƛ :D
I am sorry that I am not of more help, but I am not a mechanical engineer myself :/
I asked them for the initial number, as there is nothing to find in the Excel sheet from what I can tell
Level 104
@Reached is there a formula in the cell where the very first ƛ value appears; can you share it? Just for reference let us know what any cell references refer to.
Level 11
@tykus The formula for all the cells is the same as posted previously (also for the first cell). But it seems like the initial value is some kind of "guess"
Level 11
Level 11
Okay, so there is some news:
I was told that the starting value is always under 1, but that it's not given, so I should start with a very small number as the default value
Level 104
@Reached okay, so there is something to work with if you can make an initial guess...
The other consideration will be how you end the recursive behaviour - I suggested a "precision" value which will trigger as the estimates converge. This won't be the case in your Excel example; you will have a finite set of data to work with (different flow rates / conditions); so then iteration rather than recursion would be preferable.
Level 11
@tykus Yea, the guess is harder than it looks, hmm.. I just can't seem to find a value that will make it work
Do you mean replacing the recursive method you provided earlier with an iteration instead?
Level 11
So here is a very dumbed down version of what I've got so far:
function calculate($estimate, $reynoldsNumber, $kd) {
return 1 / pow(2 * log(2.51 / ($reynoldsNumber * sqrt($estimate) + 0.27 * $kd)), 2);
}
Route::get('calculate', function() {
$flows = [10, 15, 21, 27];
$calculated = [];
$initialValue = 0.00001;
foreach($flows as $flow) {
// Constants
$viscocity = 0.001; // ϑ /roughness
// Variables the user can change
$tubeLength = 20; // m
$tubeDiameter = 125; // mm
$kgm3 = 1000; // ƍ - kg/m3
$kd = $viscocity / $tubeDiameter;
// Calculations
$areaM2 = pi() * pow(($tubeDiameter / 2) / 1000, 2);
$speedMs = ($flow / 3600) / $areaM2;
$reynoldsNumber = $speedMs * ($tubeDiameter / 1000) * $kgm3 / $viscocity;
$calculated[] = calculate($initialValue, $reynoldsNumber, $kd);
}
return $calculated;
// $calculated:
[
0.01957545318891809,
0.01578931453909297,
0.013423221338202658,
0.011986528471523473
]
But I would expect something like this:
[
0.02577574,
0.024054954,
0.022884916,
0.022147663
]
Level 11
@tykus Another update here after having spoken to my contact person :)
The way it works in excel, is that you choose a very small starting value (basically random), and then it runs the calculation up till a 100 times (depending on your settings) on a number whenever you press "Calculate". They call it "Iterative calculation". You also set a max deviation for the calculations (something like 0.001).
I am not completely sure how to translate this to the php side. My guess is that I should use a foreach loop which runs 100 times, but I would need some way to increment the value inside the loop, otherwise the calculation will always return the same? And I would also need to check it against the deviation (sort of how you did in the recursive function)
I really appreciate your help!
Level 11
I rewrote the function a bit so that it iterates instead. However it seems to make no difference whether I use 1 or 100 iterations, so something is obviously not working the way I want it to, can anyone see any obvious mistakes?
function iterate($previousNumber, $reynoldsNumber, $kd) {
$iterations = 100;
$threshold = 0.0001;
$previousValue = $previousNumber;
$array = [];
for($i = 0; $i < $iterations; $i++) {
// Find the next value of the iteration
if(count($array)) {
$previousValue = $array[count($array) - 1];
}
$array[] = $newEstimate = 1 / pow(2 * log(2.51 / ($reynoldsNumber * sqrt($previousValue) + 0.27 * $kd)), 2);
// Check if the difference between the previous and current value is less than the threshold
if(abs($newEstimate - $previousValue) < $threshold) {
return $newEstimate;
}
}
}
// Outputs the following (regardless of number of iterations)
//0.0055242147063832
Level 75
@Reached also and just FYI there are python packages that handle this.
Level 11
@jlrdw Is this something you have any experience with? :)
Level 75
@Reached no not fluid dynamics, but I have written tube bending software. I've seen similar type questions on the freecad forum.
Level 11
@jlrdw Ah cool!
Thanks for chiming in :)
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