So if you have a valve and oil flowing through it... then you shut off the valve... I assume that most of the oil will stop flowing and the pressure will basically be 0 at the valve and atmosphere at the end of the pipe...

so if from left to right you had a shutoff valve then a 5' hor. run then 10' vert. rise then 10' hor. run then a 15' vert. drop and then a 15' hor. run then there is essentially open end pipe into a furnace

oh and its 1/2" steel pipe

so do you think the atmospheric pressure will hold in most of the oil? I set this up with rubber hose and tried it... it wasnt the same size and it was rubber and water, but most of the water stayed in the line...

maybe the original velocity of the fluid will create a siphon or something I'm not thinking about? Maybe the oil will leak out over a long amount of time?

Trying to use my memory of 1 semester of fluid mechanics here... hopefully someone with more experience can help...

Given enough time (probably a few minutes, depending on the oil viscosity) the 10' hor run, the 15' vert drop and the 15' hor run will drain into the furnace. Air will have to flow from the open end into the pipe to replace the volume of the drained oil. If the valve is shut tight no siphon can form.

The pressure upstream of the closed valve/Balance Valves will be the supply pressure, plus or minus any changes in static head from the source of pressure.  The pressure downstream of the valve will be 10' of your oil.

Do not worry about the friction in the pipe.  Friction is only a factor when there is flow.  At the very slow rate at which the oil will leak out of the pipe the friction will be nothing.

The two important forces are gravity and surface tension.  If you take a drinking straw, with a diameter of about 1/8", fill it with water and hold it vertically with your finger closing the upper end the water will not run out.  Gravity is trying to pull the water out of the bottom of the drinking straw and surface tension is holding it in the pipe.  With the small diameter surface tension wins.

If you try the drinking straw experiment with a 6" pipe (imagine the top is closed with a blank flange - fingers aren't that big!) the water will not be held in the pipe.  The weight of the water is too much for the surface tension.  Somewhere between 1/8" and 6" there is a point where the switch occurs.  I don't know for sure which side of the switch your 1/2" pipe with oil will be, but I suspect it will be more like the 6" pipe.

If the pipe/straw is horizontal there is less head for gravity to operate on and the point where gravity wins over surface tension will probably occur at a larger diameter than for a vertical pipe.

The oil is not leaking through the closed valve.  It drips out of the open pipe (assuming gravity wins over surface tension) and air flows into the pipe to replace the lost oil.

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