Problem

Propane at $25$oC is flowing in the parallel pipe system shown. calculate the pressure difference PA$$P$$ by following the steps outlined below, do NOT make any assumptions.

$$ The volumetric flow at A is in L$/$min and is equal to $169.$

$$ The lower branch has a total length of $45$ m$.$ The significant minor losses in the lower branch are the standard $90$ elbows $(3$ of them$)$ and the valve. All other sources of minor loss can be ignored.

$$ All pipes are commercial steel with dimensions as shown in the diagram.

$$ A and B are at the same elevation $($ZA $=$ ZB$)$