Why Does Sigma(s) Cause Complex Roots in My Equation?

[dscot]

Hi,

I've been having some problems trying to re-arrange this equation for a few days now, the problem is that sigma(s) appears twice in the equation: http://screencast.com/t/dlDwH4eIcp

The problem seems to be that I always end up with complex roots rather than a single equation for sigma(s).

Note the exponential should not be under the square root.

Thank you :)

 

[f95toli]

Not sure what you are trying to do...

It is pretty obvious from looking at the equation, that an expression for sigma_s will be multi-valued, and will only be real for certain values of theta and sigma_l.

 

[dscot]

Hi f95toli,

Thank you for taking the time to respond to my question.

Thats what I was afraid, I'm basically carrying out this experiment in the lab and have all the other values but couldn't get this equation solved for sigma(s).

I'm not too sure what to do if there's no way the equation can be solved?

 

[f95toli]

Of course it can be solved. Assuming the other parameters are in the right range you can easily find the real roots by solving it numerically (I am here assuming that there are physical reasons for why sigma_s can't be complex).

Perhaps there are other constraints that will allow you to discard one of the solutions?