Changes between Version 25 and Version 26 of u/ehansen/RT

Timestamp:

09/14/11 13:02:26 (13 years ago)

Author:

ehansen

Comment:

—

u/ehansen/RT

@@ -36 +36 @@
 The plots were used to get a rough idea of when to calculate the growth rate.  Bear2fix was then used to actually do the calculation directly from the data.  The data does not actually need to be plotted to find the slope of a best fit line.  Essentially, this slope (the growth rate) was calculated using the method of least squares. 
 == Results ==
-It can be shown that the analytic growth rate [[latex($\lambda_a=\sqrt{A g t}$)]]
+It can be shown that the analytic growth rate [[latex($\lambda_a=\sqrt{A k g}$)]]
+Where [[latex($A$)]] is the Atwood number, [[latex($k$)]] is the spatial wave number, and [[latex($g$)]] is the acceleration due to gravity.
+The Atwood number is defined as [[latex($A=\frac{\rho_h-\rho_l}-{\rho_h+\rho_l}$)]] where [[latex($\rho_h$)]] and [[latex($\rho_l$)]] are the densities of the heavy fluid and light fluid respectively.
+For the initial conditions used here [[latex($\lambda_a=0.6472$)]]