David,
 
So many times I have heard someone say "Lower volts causes higher amps" which totally defies Ohms Law.
 
UNLESS - your load is being controlled by something that tries to maintain speed (power) at any voltage.
 
Compressors in an air conditioner are speed controlled by the Hertz of the power supply - they have to maintain a constant speed to keep the flow of refrigerant going at the same volume. In this case when the voltage drops the compressor will still maintain the same speed, doing the same amount of work - so yes, the amperage will go up as the voltage goes down.
 
Your explanation is a bit long, but it is completely correct. Your water analogies help explain things. Some of the statements given in previous posts are implying that a loose connection will cause higher amperage. Ohms Law says this is not possible - any restriction in a circuit will always cause a voltage drop, and amps must go down.

In a message dated 10/17/2021 12:00:08 PM US Eastern Standard Time, Dave Roden writes:

Aside from the action of back EMF, when a motor is running flat out from a
battery, Ohm's law reigns.  That is, P = E * I or P = E^2 / R.