wastewater pumps with shared rising main

"What would the outcome be in this situation?"

Less total flow (I.e. not the sum of each one as if the other wasn't pumping) or higher head required.

Second one.Correct

Third one Yes.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

Second one.

I think if it depends on how the pumps (or connecting pump to main pipes) are connected into the main and whatever backpressure the downstream piping may be placing at the connecting node. Think this one through with me.

If each pump were connected with check valves, then the check with the lower inlet pressure may not open, dead heading the low pressure pump. However if there were no discharge check valves, the only thing we know is that the pressure at the connecting in all pipes node must be equal. Let's say we had two pipes connecting at a header. One pipe with 100 psig at its inlet, the other with 50 psig at its inlet. The Pressure at the connection to the header of both pipes is unknown (for now). We only know that by continuity, it must be the result of the two inlet flows into the header minus the flow being taken away from the header by the downstream piping. If the downstream piping has the ability to evacuate all the flow going into the header, whatever pressure is there will not increase from whatever it is right now. If the header and downstream piping had discharge valve, currently discharging at 0 psig, and we started closing it, backpressure would be created that would make its way upstream until it came to the header inlet node. If our outlet valve added 40 psi, the outlet from the header would now be 40 psi plus flow loss in the downstream piping, say 5 psi, or 45 psig.
Now we would know that the pressure at the header inlet must be some combination of what pipe 1 could put into it at 100 psig and what pipe 2 could put into it at 50 psig. If the flow from the 100 psig pipe was very tiny, say 1/100th of the flow coming from the 50 psig pipe, pipe #1 wouldn't have much to say about the final pressure at the node. On the other hand, if the flow from the 100 psig pipe was 100 x that of the 50 psig pipe, the resulting node pressure would be very near 100 psig, unless the discharge pipeline was a very large diameter and could evacuate all the flow going into it without causing any increase over the 45 psig inlet pressure. In that case, and even if there were check valves, neither one would close and you would get flow from both.

So... I will contend that the flow from the lower pressure pump will not go to dead head 0 unless the backpresdure of the downstream piping is greater than its discharge pressure, check valves, or not. Until the backpressure of the downstream piping reaches that of the lower pressure pump, the node pressure at the connection of both pumps is the result of both pumps, which is a function of how much flow is contributed by each pump in relation to the other pump taken in combination with the evacuation rate of the downstream piping, as evidenced by its backpressure building up all the water to its inlet.

I think that makes sense. Do you see a fail in that theory?

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

I suggest modeling this system and looking at three pumping configurations (P1 only, P2 only, and P1+P2), each with maximum and minimum static lifts, so six scenarios total. That way you can know for certain how the pumps operate separately and together.

The freeware program EPANET can handle this, as can any of the commercial water modeling programs.

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"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

You could also do with checks or without.

Without check valves and pressure higher than the lowest pump discharge pressure, that pump could experience reverse flow. If you do this, a check valve located at least there, sounds like a good idea.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

Can the pump prime against a check valve with a column of water on top of it?

Wastewater pumps are installed such that the impellers stay flooded. The times I have had to resolve loss of prime on a pump like this it was due to leaking check valves letting sewage fermentation gas from downstream push the water out of the impeller casing (in other words forcing loss of prime).
The solution is venting the gas out of the system. The location where the venting gets installed depends on the specific location.

Thanks all.
These would be submersible pumps with a chaeck valve at wetwell outlet, so no need for another one at the junction

Submersible pumps so no need to prime

I have used epanet loads, but it didn't cross my mind to use it for WWPS (Doh!)