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Math Help - Help rearranging an equation - need to find K

  1. #1
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    Help rearranging an equation - need to find K

    Ok, maths is not my strongest point... so I need your help...

    Topic is hydrogeology, I need to rearrange this to isolate K.

    Hx^2=h1^2 - x/L (h1^2- h2^2) + Nx/K (L-x)

    Please explain your workings, as I need to understand this...

    Help!!
    Last edited by neilforrow; October 20th 2010 at 02:06 AM. Reason: html code probs
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Hx^2={h1}^2 - \frac{x}{L ({h1}^2- {h2}^2)} + \frac{Nx}{K(L-x)}

    Hx^2(L-x)={h1}^2(L-x)-\frac{x(L-x)}{L ({h1}^2- {h2}^2)}+\frac{Nx}{K}

    \frac{Hx^2(L-x)}{Nx}=\frac{{h1}^2}{Nx}-\frac{x}{L ({h1}^2- {h2}^2)Nx}+\frac{1}{K}

    \frac{Hx^2(L-x)}{Nx}-\frac{{h1}^2}{Nx}+\frac{x}{L ({h1}^2- {h2}^2)Nx}=\frac{1}{K}

    K=\frac{1}{\frac{Hx^2(L-x)}{Nx}-\frac{{h1}^2}{Nx}+\frac{x}{L ({h1}^2- {h2}^2)Nx}}
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  3. #3
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    Zarathustra - thanks for the help

    appologies for the basic maths help here, but I need to fully understand this:

    so you:
    multiplied by (L-x) to isolate k
    divided by Nx to give 1/k

    thisis where I get a bit confused

    subtracted Hx^2(L-x) / Nx to isolate 1/k

    divide by 1 to give k = .......

    I have got values for h1, h2, L x and N. I will plug them in and see what I get.

    Thanks again for the help.
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  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
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    Hmmm... for the part where you confused a bit...

    Imagine ( ) that \frac{Hx^2(L-x)}{Nx}-\frac{{h1}^2}{Nx}+\frac{x}{L ({h1}^2- {h2}^2)Nx}=M

    Hence:

    M=\frac{1}{K}

    KM=1

    K=\frac{1}{M}
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