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June 9th, 2014, 03:56 AM  #1 
Newbie Joined: Jun 2014 From: London Posts: 4 Thanks: 0  Help rearranging equation
Hello everyone, I'm a working engineer and it's been a long time since I had to rearrange complicated equations (complicated to me anyway!). I'd really appreciate some help  if anyone can rearrange the attached equation to make ∆pl the subject I would really appreciate it. 
June 9th, 2014, 04:24 AM  #2 
Member Joined: Feb 2012 From: Hastings, England Posts: 83 Thanks: 14 Math Focus: Problem Solving 
I may have well over simplified this, so if I have apologies, just love trying to help.i know none of these symbols, but reading it through, it seems you have : $\displaystyle Q=4(a)^{0.5} log (b)$ I would start by dividing both sides by $\displaystyle 4.log(b)$, giving $\displaystyle Q/4.log(b) = (a)^{0.5}$ square both sides gives: $\displaystyle (Q/4.log(b))^2 = a$ not just divide both sides by everything in a you don't need and shoulg give you(a rather messy looking) rearrangement. If this is totally wrong I apologise, but it all seemed logical in my head 
June 9th, 2014, 04:59 AM  #3 
Newbie Joined: Jun 2014 From: London Posts: 4 Thanks: 0 
Hi thanks for the response, but I'm still unsure of how to proceed as both a and b contain the variable I am trying to find. Getting pretty confused with the logarithms. If someone could write out the fully rearranged thing for me that would be amazing.

June 9th, 2014, 07:13 AM  #4 
Member Joined: Feb 2012 From: Hastings, England Posts: 83 Thanks: 14 Math Focus: Problem Solving 
lol woops didn't even see that was so horrible to look at I simplified too quickly. sure someone will come through for you sorry I couldn't help

June 9th, 2014, 07:53 AM  #5 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,150 Thanks: 730 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
Hi there, This looks remarkably like a formula to derive the friction factor for flow across a surface based on its roughness and the Reynolds number of the flow. Equations like this are notoriously annoying and there was a recent paper by Genic et al. (2011) reviewing and recommending various different explicit solutions to the Colebrook equation, which is the general formula for fluid flow adjacent to a rough surface. $\displaystyle \frac{1}{\sqrt{f}}=2\log\left[\frac{2.51}{Re\sqrt{f}}+\frac{\epsilon}{3.7}\right]$ The particular equation you have provided is an implicit equation, just like the Colebrook equation above, and requires a numerical method to solve for $\displaystyle \Delta_{pl}$. That is, it cannot be rearranged in the form $\displaystyle \Delta_{pl} = f(N_3,N_4,d,k_s,Q)$. The paper is on Google if you want to have a read. You may be able to find an analogous formula for the specific one you have an apply an explicit formulation to get $\displaystyle \Delta_{pl}$. 

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