|Aug17-08, 06:00 PM||#1|
Solving for a constant in a power
1. The problem statement, all variables and given/known data
Hi all, this isn't exactly a homework question (I'm a law student long out of high school maths!) but has arisen in the context of some of my legal work analysing the difference in height of windspeeds re: wind turbines.
The "problem" is solve for the constant z0.
2. Relevant equations
The main formula is as follows:
vh = vref . (h/href)^(1/(ln(h/z0)), where vh = velocity at desired height, vref = velocity at measured height, h = desired height, href = measured height, z0 = aerodynamic roughness.
After inserting a known answer from a previous calculation, the formula reduces to:
(6.4/4.56) = 13.125^(1/(ln(105/z0))
3. The attempt at a solution
As I stated earlier, I'm a couple of years out of high school maths and cannot remember for the life of me how to solve for powers involving logs themselves. I can barely remember the simplest of log rules.
Any help would be much appreciated.
Many thanks all,
|Aug17-08, 06:44 PM||#2|
Let's see … 6.4/4.56 = 1.4035.
So 1.4035 = 13.125(1/(ln(105) - ln(z0)))
= e(ln(13.125))(1/(ln(105) - ln(z0)))
so ln(1.4035) = (ln(13.125))/(ln(105) - ln(z0))
so (ln(105) - ln(z0) = ln(13.125)/ln(1.4035)
so ln(z0) = ln(105) - ln(13.125)/ln(1.4035)
so z0 = 105/eln(13.125)/ln(1.4035)
|Aug17-08, 06:53 PM||#3|
You're a legend tiny tim, huge thanks
|Similar Threads for: Solving for a constant in a power|
|Solving for constant in a linear combination of vectors||Calculus & Beyond Homework||3|
|solving an ODE using a power series||Calculus & Beyond Homework||1|
|solving ODE using power series||Calculus & Beyond Homework||0|
|Solving an Equation using the Gravitational Constant...||Introductory Physics Homework||5|
|Solving xy'(x) - y(x) = x^2 Exp[x] using the power series method||Calculus & Beyond Homework||5|