# Hardcore re-arrangement help

by 3123marriott
Tags: hardcore, rearrangement
 P: 688 I'd try the following (if there is no gross mistake in what follows): multiply up and down the right-hand side by ${\sqrt g}$, and pass $g \, C_0 A_{pipe} \sqrt 2$ multiplying to the left; then take $A_{tank} \sqrt{Z_{full}}$ as common factors on the right and pass them dividing to the left:$$\frac {g T C_0 A_{pipe}} {A_{tank}} \sqrt {\frac 2 {Z_{full}}} = 2 \sqrt g - \sqrt{\frac{C_f L P}{A_{pipe}}}$$Now substitute $B^2 = A_{pipe}$, and multiply through by one more $B$:$$\frac {g T C_0} {A_{tank}} \sqrt {\frac 2 {Z_{full}}} B^3 - 2 \sqrt g B + \sqrt{C_f L P} = 0$$ That's a cubic equation in $B$, which should have at least one real solution (or maybe three): http://en.wikipedia.org/wiki/Cubic_f...cubic_function For each non-negative solution, take $A_{pipe} = \sqrt B$ as a solution to your original problem. P.S.: Oh well, that's what chiro was saying all along...