However, many times the natural behavior of the model is not linear or polynomial. For example we will soon find that pressure driven flow in a pipe gives f=16/Re as an exact solution for laminar flow and f=0.079 f-.25 as an approximate relation for turbulent flow. How can we plot these?
![[Graphics:../Images/log_log_gr_11.gif]](../Images/log_log_gr_11.gif)
![[Graphics:../Images/log_log_gr_12.gif]](../Images/log_log_gr_12.gif)
We don't see any values (not too useful for reading and getting values off of, what if the range is smaller?
![[Graphics:../Images/log_log_gr_13.gif]](../Images/log_log_gr_13.gif)
![[Graphics:../Images/log_log_gr_14.gif]](../Images/log_log_gr_14.gif)
Now we can see, but this is not a nice shape.
![[Graphics:../Images/log_log_gr_15.gif]](../Images/log_log_gr_15.gif)
![[Graphics:../Images/log_log_gr_16.gif]](../Images/log_log_gr_16.gif)
For the turbulent relation, again, the plot is ugly. However, we realize that both relations are power laws. That is, the functional form involves just a product of a coefficient and the variable to some power. (often times this is all we need).
So consider the manipulation.