Solving equation

1. Jul 9, 2010

Hello there,

I am a mechanical engineer and am attempting to build an Excel document for calculations purposes.

Currently I am stuck on orifice plate calculations.

I was wondering if someone could help me solve the following equation for d2?

$$\alpha$$ = $$\pi$$(d2/2)2 $$\sqrt{}$$1/1-(d2/d1)4

Any help would be appreciated.

(Apologies if I have posted this in the wrong place)

Matt

2. Jul 9, 2010

Mentallic

Sure thing,

$$\alpha = \pi\left(\frac{d_2}{2}\right)^2\sqrt{\frac{1}{1-\left(\frac{d_2}{d_1}\right)^4}}$$

square the entire equation to rid yourself of the square root:

$$\alpha^2 = \pi^2\left(\frac{d_2}{2}\right)^4\left(\frac{1}{1-\left(\frac{d_2}{d_1}\right)^4}\right)$$

Multiply through by that denominator:

$$\alpha^2\left(1-\left(\frac{d_2}{d_1}\right)^4}\right) = \pi^2\left(\frac{d_2}{2}\right)^4$$

Expand the left side, and move the right to the left side:

$$\alpha^2-\alpha^2\left(\frac{d_2}{d_1}\right)^4} -\pi^2\left(\frac{d_2}{2}\right)^4=0$$

This can be more easily visualized as:

$$\alpha^2-d_2^4\frac{\alpha^2}{d_1^4} -d_2^4\frac{\pi^2}{16}=0$$

Factorize out the required variable:

$$\alpha^2-d_2^4\left(\frac{\alpha^2}{d_1^4} +\frac{\pi^2}{16}\right)=0$$

Well you can probably finish it from here, and you might want to manipulate some things so you don't have fractions in fractions.

3. Jul 9, 2010

Gerenuk

Check if it's
$$d_2=\frac{1}{\sqrt[4]{\left(\frac{\pi}{4\alpha}\right)^2+\frac{1}{d_1^4}}}$$

4. Jul 9, 2010

Thankyou both for yor prompt reply.

I have tested the two formulas based on existing figures and Mentallic's formula/equation gives the desired result.

Gerenuk, you equation gives d1, not d2.

Thank you very much for your assistance.

Matt

5. Jul 9, 2010

Mentallic

You're welcome