# Thread: how to determine a constant in a mathematical expression?

1. ## how to determine a constant in a mathematical expression?

hi fellows, i have been reviewing a paper on equation of state where i have to find a relation between pressure and density using the ideal form of
P=@*r, where P=pressure and r=density

now i have got both P and r as a function of parameter t.

r=k(sinh(t)-t)
P=1/3k (sinh(t)-8sinh(0.5t)+3t)
and i have drawn a parametric graph of p=p(r)
it's sort of a straight line as expected and what i need to do now is to find a linear or non linear relationship that best explains the pressure and density relationship. in other words finding that @ in P=@r relationship.
can you plz tell me how can i do it?
from the graph tracing the slop or from the formulas ?

2. ## Re: how to determine a constant in a mathematical expression?

Surely you know that if P= @r then @= P/r?

If you know that, at least approximately, P= @r, and want to determine @, choose any (r, P) pair and divide: @= P/r.

If P= @r exactly then it does not matter which point you use, you will get the same value for @.

If it is not exact, the value for @ will depend upon which point you choose but if "approximately", P= @r, the different values for @ will be "approximately" the same.

(Note that "P= @r" includes the point r= 0, P= 0 for any @. If r= 0, P= 0 is not given but the graph still looks like a straight line, use the more general "P= @r+ b", a straight line that, for [tex]b\ne 0[/b] does NOT go through the origin. In that case, you will need to use two points to get two equations to solve for @ and b. Geometrically, two points determine a straight line.)