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June 9th, 2014, 03:56 AM   #1
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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.
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June 9th, 2014, 04:24 AM   #2
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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
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June 9th, 2014, 04:59 AM   #3
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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.
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June 9th, 2014, 07:13 AM   #4
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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
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June 9th, 2014, 07:53 AM   #5
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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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