1. ## Transposition

hello my name is ben, im currenty revising to start my hnc in mechanical engineering,

i have come across a equation that im struggling to transpose and cant find any examples to help me, just wondering if anybody could help me out and show me the steps to follow? its been long time since ive done anything like this :S

D/d=√f+p/f-p for f

tanks

2. ## Re: Transposition

$\dfrac{D}{d} = \sqrt{f} + \dfrac{p}{f} - p$

$\left(\dfrac{D}{d}+p\right) f - f^{3/2} -p =0$

let $u = \sqrt{f},~\left(\dfrac{D}{d}+p\right)=a$

$a u^2 - u^3 -p=0$

This has 3 solutions. At least 1 will be real depending upon the parameters.

You'll just have to solve this with the parameters substituted in to know whether you have 1 or 3 real solutions for $u$

Given the solution(s) for $u$

$f = u^2$

3. ## Re: Transposition

If we graph $g(x)=\sqrt{x}+\frac{p}{x}$ say for $p>0$ we get

so the equation $g(x)=\frac{D}{d}+p$ has either two solutions, one double solution, or no solution

The solutions can be found using a numerical method

4. ## Re: Transposition

Originally Posted by trungdien
D/d=√f+p/f-p for f
just wondering if the original equation is actually

$\dfrac{D}{d}=\dfrac{\sqrt{f}+p}{f-p}$

... ?