Dead battery: Batteries are sold by the potential difference they maintain and by the amount of electricity (charge) they can deliver. This is equivalent to the height of water behind a dam, and the volume of water that can be released. A dead battery is thus like an empty reservoir.
Short circuit: A short circuit occurs when there is a highly electrically conductive pathway across a circuit, shortcutting current flow. The closest analogy in hydrology might be a conductive fracture, which could shortcut flow across an otherwise extremely low permeability rock.
Open circuit: An open circuit exists when electric current cannot traverse the entire circuit e.g., if there is a break in the power cord leading to a hair dryer. This would be equivalent to a truly impermeable block of material that water could not move through.
Voltmeter: A voltmeter measures a drop in electrical potential in an electric circuit. Heads are the equivalent potential term in hydrology and are measured by a water-level tape (physical or electrical), pressure transducer, a sonic device, or something similar. Of course, a voltmeter and a water-level tape aren’t entirely equivalent. A water-level tape just measures the head at one location. With electricity, we are always looking at differences in voltage. A voltmeter is the electrical equivalent of measuring the head difference between two wells. While in both cases, differences in potential are what drive flow, with heads, we can set a datum and make individual measurements relative to the datum, while with current we need to capture the voltage difference in one measurement.