How to make derivative terms nondimensional

Using the chain rule for derivatives


[Graphics:../Images/dimensionless_gr_1.gif]= [Graphics:../Images/dimensionless_gr_2.gif][Graphics:../Images/dimensionless_gr_3.gif]= [Graphics:../Images/dimensionless_gr_4.gif][Graphics:../Images/dimensionless_gr_5.gif]
[Graphics:../Images/dimensionless_gr_6.gif]= [Graphics:../Images/dimensionless_gr_7.gif][Graphics:../Images/dimensionless_gr_8.gif]= [Graphics:../Images/dimensionless_gr_9.gif][Graphics:../Images/dimensionless_gr_10.gif]

and making the substitutions:

s= r/R,
[Graphics:../Images/dimensionless_gr_11.gif]= [Graphics:../Images/dimensionless_gr_12.gif]/U,
[Graphics:../Images/dimensionless_gr_13.gif]= [Graphics:../Images/dimensionless_gr_14.gif]/U

Converted by Mathematica      November 6, 2000