## Expert?

Posted by ragknot on October 23, 2012 – 9:34 pm

Someone ask me to POST this on ToM for some info on “LinkedIn”.

I think it is easy to solve this, but he want to know who can solve this to verify it can be solved.

I laughed at his question, but I know that some can do it.

Find the exact value of F to at least 10 decimal places, more if possible.

F=ABS(2*LOG(0.00001*F+0.0022))

October 24th, 2012 at 7:16 pm

It isn’t possible to give the exact value as it’s irrational.

If the log is base 10, then F = 5.29449882524305…

If the log is base e, then F = 12.1312450833841…

October 24th, 2012 at 10:33 pm

5.29449882524305 is accurate!

Irrational? Well maybe, but I knew you could get the right answer to many decimal places. Irrational is right. But irrational things may or may not be OK for use. I like to think about it like using pi to compute something like the circumference of my tire. Since my tire will change on air pressure, and how worn out rubber using pi to 4 decimal places will be OK.

But using the number you gave for accuracy depends on this… Is it more accurate than other variables used for a specific computation?

What if I said the number you gave has been needed for years and years, but engineers had to settle for 3 decimal places because published approximations could only be 3 decimals in accuracy.

I hope the fellow that asked me to post this will speak to you.

Hint: the number to be used will be …

=1 / (5.29449882524305)^2

or 0.035673875099635

Does that hint help you remember something?

October 25th, 2012 at 3:57 am

It reminded me of the Colebrook-White equation.

In view of the empirical nature of the CW equation, four significant figures is more than sufficient.

If F were allowed to be negative, then -5.33648352117219 is another solution (assuming log base 10). If it had been base e then we’d have got -12.3541832818553

October 25th, 2012 at 5:43 am

I knew you would get that, Chris, but now, figure out the third guy who asked me to post it here?

Maybe he can log on here.

October 28th, 2012 at 9:12 pm

Chris,

The guy who asked me to post this on ToM, used to be on here often, but I have not seen a comment or a “post” in a long time. But he can log on when he wants.

Hey, he has his photo on this website!

We are LinkIn friends.

December 15th, 2012 at 12:39 pm

Can anyone give a detailed step to reach the solution?

December 15th, 2012 at 8:45 pm

Hi Jacky. The trick is to “guess” an initial value for F. I probably used F = 1. Stick that into the right hand side of the equation to get a new value for F. Then stick that value into the equation. You’ll find that F converges to a definite value.

If we’d been unlucky, F might not have converged. Then inverting the equation might give an equation where the trick works.