Andrew,

Do you have the performance specs for the pump?  This will tell you what the flow and pressure of the pump "will/should" be while operating.

When you dead head your pump, it should go to max PSI and shut down.

I think your pump may be under sized for what you are doing.

 I have a similar water setup for our dairy, 550 cows. Our plate cooler water goes into a 3000 gallon poly tank.  This tank is the primary source of drinking water for the milking herd, dry cows, large heifers and the parlor wash down.  If the tank level gets too low, a "make-up" valve opens to maintain a minimum water level till the next milking.  If the system fails, fresh water is supplied by one connection and 2 qtr turn valves

I have a 2 hp variable speed setup controlled by a VFD. The VFD reads the pressure to control pump speed. My pump is on the same level as the bottom of the poly tank.

Edit to add description:  The pump in the photo is a 1hp setup that was replaced. Its an upright style, multistage.  If you can zoom in, the pump is in the lower right.  My local pump supplier put this package together for me.

Bill

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