Sizeing the under current or power for pump protection

Well, there are two ways, Captain, depending on what you have available.

One of the ways is with an underload detector. What this does is measure the phase angle between the voltage wave and the current wave within the equipment. If the phase angle difference is low, then the motor is loaded. If the angle increases, then it is running unloaded, and this condition can be used as a signal to turn off the motor, blow a whistle, or whatever.

The other way is to look at the load current. One the motor unloads, the current drops away towards the no load current, and a suitable comparator can be used to make a signal that turns off the motor, blows a raspberry, etc.

Now, you may find, if your motor is fed from one of those new-fangled inverter drive things, that these functions are provided in the inverter controls themselves as some sort of parameter, in which case you have to sit with the motor and adjust them until the thing behaves correctly.

You can get self-contained phase angle comparators and undercurrent trips as stand-alone items, if you want to.

Things have moved on a bit since 1942.

As to sizing them, well, it depends upon what space you have available as to what you go for, as in all things.

I feel, you can set to about 15% of rated current with a time delay of about 3 seconds.

General rule of thumb - take 25% of the best efficiency point on your pump curve. Read off the Power at that flow rate. Calculate the amperage for that power and set your low current trip at that amperage.

On the assumption that the pump will not damage immediatly it runs dry, why not let it run dry with an ammeter connected. Then you can set your under power trip.

Bear in mind that the pump may pull more current when it is truly dry rather than wet but unloaded.

Chas