Note for Mathematica 3 users: The log-log plot labeling problem mare arise here.
![[Graphics:../Images/lubricatedflow_gr_168.gif]](../Images/lubricatedflow_gr_168.gif)
![[Graphics:../Images/lubricatedflow_gr_169.gif]](../Images/lubricatedflow_gr_169.gif)
We see that increasing q2, the outside fluid flow rate decreases the pressure drop for quite a range. This is not what is expected for a single fluid flow.
Just check h so that we are sure it is OK
Note for Mathematica 3 users: This one does not work very well. You need to change the [[5]] to [[1]] to pick out the first root, but some of the values are the wrong root.
![[Graphics:../Images/lubricatedflow_gr_170.gif]](../Images/lubricatedflow_gr_170.gif)
![[Graphics:../Images/lubricatedflow_gr_171.gif]](../Images/lubricatedflow_gr_171.gif)
![[Graphics:../Images/lubricatedflow_gr_173.gif]](../Images/lubricatedflow_gr_173.gif)
![[Graphics:../Images/lubricatedflow_gr_174.gif]](../Images/lubricatedflow_gr_174.gif)
The minimum pressure drop occurs when h ≃ 1.5. This makes sense because h is supposed to be about 30% of D/2 (= 1.5 for this calculation) for the most efficient flow.