Flow around a reducing bend - effect on pumping work
On my race vehicle, one part I am looking at is reducing the pipe losses within the modified oil lubrication system (now dry sump). The main area in question is a 120 degree bend that the engines lubrication pump is pulling oil into the oil storage tank. This has been reduced in ID from 16mm (-12JIC) to 13mm (-10JIC). Naturally I aim keen to reduce the radii difference, however I am struggling to put to words the reasoning for why.
In short, could cavitation be an issue? Since for around 0.5m the pipework is 16mm then round the inlet to the pump 13mm and expanding into a larger pump housing (around 20mm inlet)?
Could I characterise this issue using Q = (Pi*(R^4)*P)/8*L*n, since Q is the same (positive displacement pump), as are L/n/Pi we are left with:
R1^4*(P1)=R2^4*(P2) ---->>> (16E-3)^4*P1=(13E-3)^4*P2 ------>>> 2.3P1=P2, meaning that a 2.3 x greater input energy would be required to turn the pump specific to this situation?
Any input appreciated!