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(OP)
Good morning. I haven't been able to get this question answered with a moderate amount of research, but it's always bothered me. When working with pumping systems, specifically wastewater lift stations, the discharge static head is generally defined as the elevation difference between the discharge liquid elevation and the centerline of the impellor. My question is, should additional head be added if the pipeline dips below the impellor level or rises above the discharge liquid level? It seems to me that things should have an effect. I've included a sketch to accompany my question. Would the discharge static head be A, B, or C? Or something else that I have not considered.

Option C.

STATIC DISCHARGE HEAD is the vertical distance in feet between the pump centerline and the point of free discharge or the surface of the liquid in the discharge tank.

Note that at startup, the pump must have enough power to lift the water to "B".

except for force mains which flow back down to the tank using gravity as shown in the sketch...

There are two options, A or C..

Try assuming static head is C.. and draw hydraulic gradient line ( Z+ P/γ ).. If the HGL does not clash with the ( above the hill ) , the assumption Z = C is correct..

If clushes, Z will be A and open channel flow will develop between high point and the reservoir.

You have to analyze the start up condition (A) and the pressurized full flow (C) condition.

Jgailla seems to be correct in case the distances are short and there is no air valve used at the curve tip location.

In case of long distances and/or there is an air valve used at top of the curve I would use A as the discharge head for start up and operation for pressurised full flow.

I actually think you have to design for two conditions (A) start-up and (C) duty. Look at your system curve for the two and size your pump accordingly. At start-up the pump must have enough power to lift the water up the the full height of the hill before it can take advantage of gravity and free-fall down the hill. I would also make sure my check valve is of sufficient size to handle a cascading back-draft of water in case of a power failure or the pump shuts down too quickly. You could also generate sizable negative (vacuum) pressures as well. Of course this all depends on the order of magnitude for elevation change and distances.

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