Hurts my head for sure.
Thank you so much for your patience in writing your long description and the video. And thanks to the moderators for their leniency in allowing us to hijack this thread.
One moment it's all crystal clear in my head, then the next moment I'm baffled again. It's like one of these illusions where one person will insist they only ever see the witch, whereas another can see only the pretty girl, and some are lucky enough to be able to flip back and forth at will between seeing either one.
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It makes perfect sense that at some given volume of flow the pump can only lift water to a particular head height. To provide more flow and/or lift water to a greater height will require more power. Moving to different points on the curves, less flow rate means the pump's power is instead available to lift a smaller amount of water higher. Or, in the opposite direction, the pump can move more water but lift it less high. More height requires more pressure, which is a squared function i.e. lbs per
square inch, whereas more volume flow is a cubic function i.e
cubic inches. So the power required is much more sensitive to volume changes than it is to pressure changes.
Restricting the flow via the CSV increases the back pressure, i.e. increases the head height while choking the flow rate. More head height, more power required. Less flow rate, less power required. But power increased for more pressure is a squared function, while the power decreased for volume is cubic, so overall there is less power required when the flow rate is choked.
Can you give a few more details how this pump's efficiency is calculated, as shown at 1:25 in your video?
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For each of the rpm traces shown, it looks like a maximum efficiency of ~65% is achieved at about 220 gpm flow rate.
Using the 3450 rpm line, that pump can raise a column of water up to about 310 ft and hold it there with zero flow exiting out of the top of the pipe, while burning up 12hp just to hold that height. This is like waiting at a traffic light with your car's engine running, i.e. it's burning gas going nowhere, so zero percent efficiency.
At the far right end of the lines the pump is running at max horsepower to deliver its largest volume of flow rate, but the height capability has dropped way down.
At peak efficiency it's pumping to its largest combined volume x height / horsepower capability? What's the formula being used to calculate that efficiency.