# Expanding root term

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• Sep 2nd 2007, 03:09 PM
pjb11001010
Expanding root term
Hi all,

This may not quite be an advanced algebraic problem but has been puzzling me for ages now, so though i'd seek help.

So here goes:

I have the equation:

Q = C * ( sqrt ( P1 - P2 ) )

C is constant, P1 and P2 are inputs

Is there a way of rearranging as to seperate P1 and P2 so that the sqrt operation occurs afterwards. The reason for this being that they are pressure inputs into a state space system (simplified - dynamics are there).

Many thanks for any replies in advance
• Sep 2nd 2007, 03:27 PM
pjb11001010
addition comment to previous question
Sorry, just an addition to the original problem:

I had thought that the equivilent would be:

Q^2 = (C^2* P1) - (C^2*P2),

However, as it is part of a state space matrix, is there a way to manipulate Q further (in output eq'n y = Cx or otherwise)?

Kind regards, and many thanks in advance again.
• Sep 2nd 2007, 03:32 PM
Jhevon
Quote:

Originally Posted by pjb11001010
Hi all,

This may not quite be an advanced algebraic problem but has been puzzling me for ages now, so though i'd seek help.

So here goes:

I have the equation:

Q = C * ( sqrt ( P1 - P2 ) )

C is constant, P1 and P2 are inputs

Is there a way of rearranging as to seperate P1 and P2 so that the sqrt operation occurs afterwards. The reason for this being that they are pressure inputs into a state space system (simplified - dynamics are there).

Many thanks for any replies in advance

what about this?

$\displaystyle Q = C \sqrt {P_1 - P_2}$

$\displaystyle \Rightarrow \frac {Q}{C} = \sqrt {P_1 - P_2}$

$\displaystyle \Rightarrow \frac {Q^2}{C^2} = P_1 - P_2$

$\displaystyle \Rightarrow \boxed { P_1 = P_2 + \frac {Q^2}{C^2}}$

or

$\displaystyle \boxed { P_1 = P_2 + \left( \frac {Q}{C} \right)^2 }$