January 13th, 2018, 08:23 AM  #1 
Newbie Joined: Jan 2018 From: iran Posts: 1 Thanks: 0  determining equations parameter
Hi, I'm new to this forum, maybe I should post my problem in some other topics. I have problem in determining K and D in following Equation, it's experimental equation and I have 10 answer for "f" and "t", "s" and "v" are defined quantity S=4.3589 , V=6.8557 F=[0.022081745 0.039747141 0.079494282 0.125865947 0.183278484 0.20094388 0.214192927 0.304728081 0.359932444 0.388638713 ]; t=[0.083333333 0.291666667 1 2 3 4 5 19 47 90 ]; Can anyone helping me to determine D and K? It's really important to me and I am in hurry, I will attach equation. I really appreciate. Thanks. Last edited by skipjack; January 13th, 2018 at 10:52 AM. 
January 13th, 2018, 11:16 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,966 Thanks: 807 
You have $f= \left(\frac{S}{V}\right)\sqrt{\frac{D}{K}}\left[\left(kt + \frac{1}{2}\right)\text{erf}(\sqrt{kt}) + \sqrt{\frac{kt}{\pi}}\exp(kt)\right]$. Dividing both sides by $\left(\frac{S}{V}\right)$ and $\left(kt + \frac{1}{2}\right)\text{erf}(\sqrt{kt}) + \sqrt{\frac{kt}{\pi}}\exp(kt)$, that becomes $\displaystyle \sqrt{\frac{D}{K}} = \frac{Vf}{S\left[\left(kt + \frac{1}{2}\right)\text{erf}(\sqrt{kt})+ \sqrt{\frac{kt}{\pi}}\exp(kt)\right]}$. Squaring both sides, $\displaystyle \frac{D}{K} = \frac{V^2f^2}{S^2\left[\left(kt+ \frac{1}{2}\right)\text{erf}(\sqrt{kt})+ \sqrt{\frac{kt}{\pi}}\exp(kt)\right]^2}$. Of course, you can't solve for both S and D from only one equation. Last edited by skipjack; January 18th, 2018 at 07:33 PM. 
January 13th, 2018, 11:46 AM  #3  
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 922  Quote:
 
January 18th, 2018, 04:01 PM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,966 Thanks: 807 
Thank you.

January 18th, 2018, 07:25 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,704 Thanks: 1529 
Hi Alirezap and welcome to the forum. In your equation, do you know the value (or values) of $k$, or was the use of $k$ a typo? Also, are $S$ and $V$ in your equation intended to be upper case? 

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