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I'm not sure which plants specifically supplies Muldraugh but 92% of Kentucky power is coal.
Anyways, it depends on whether the plant was left unattended or not. In case of utter catastrophe I imagine they would attempt to reach their families or look out for their own future survival and if for whatever reason the coal plant is no longer manned at all the reduced input would lead to reduced power within 2-4 hours and it should automatically shut down within 12-18 hours when sufficient alarms are triggered.
A nuclear plant would likely stay operational for a few days to a week before shutting itself down. Gas plant would lose pressure in 1-3 days. If there was zero effort to keep power going there'd probably be cascading failures with most of the US being without power within 24 hours.
Renewable power fares much better though, but I don't think Muldraugh has much of that and the US mostly uses hydro. Amusingly if it happened in my country I imagine we'd have thousands of surviving power sources from windmills and solar panels...
If the power plant personnel stay on their stations and does everything they can to maintain power then the limit might be that coal power plants on average have maybe 45-60 days' worth of coal on hand.
Which supports the "0-2 months" option with closer to 0 being favored (it would probably require government/military intervention to keep them manned). My last game power went out after 3 days though which seems reasonable if the government survived briefly.
Water
I think you are right that usage will be smaller, but it might get drained a lot in the final hours putting out fires and pressure will start dropping after the power fails.
However, under normal circumstances 10-30% of all water pumped by a normal utility is lost to underground pipe leaks. This produces a virtual guarantee that the towers will be empty sometime between 3 days to 15 days after the electricity goes out, even with no end-user consumption.
I guess I'd again say the "0-2 months" option, but everything depends on how soon power fails. If everything goes wrong power will be out within a day and water will be gone 3 days later.
Water will go out very shortly after the electricity, because of the dependence on electricity to move the water.
It's done that way to reduce power costs by drawing on it during the night where requirements are low. Even if they don't have a tower per se they will have some sort of reservoir.
Ideally the personnel should shut off access to the city to preserve the reservoir before they leave. It would make a decent supply for a survivor group and those few extra moments of water likely won't do anyone any good anyway. I guess that scenario might explain day zero outage.
If no pumps are running at the pumping station because there is no electricity, there is no water pressure. Period. No water pressure, nothing goes up-grade, to the distribution system.
However...
What you will have, is a small amount of water-pressure in the lines, post pump-station, in the city were the water lines are much smaller. Like 8-10" piping that's gravity/pressure fed. That won't last long at all. Water will go out very shortly after the electric grid is down. Some pumping stations will have diesel generators, but someone has to be there to man them.
Trust me, without electricity, there is no water distribution. Just residual water in the lines, but that's not going to last long as the pressure drops the water won't flow to your taps.
I think it's safe to assume in the case of small town Kentucky we are talking about a water tower, not a straight pumping station. Here's West Point's water tower: https://www.google.com/maps/place/Muldraugh,+KY/@37.996539,-85.950733,3a,75y,172h,98.89t/data=!3m4!1e1!3m2!1sN0xbofs_h7gsnicUCoUTgQ!2e0!4m2!3m1!1s0x886920e97d5031c9:0x70e1eb33a4c46c0
As for the rest, you are, of course, absolutely right. Without power there will be no fresh water coming to the tower, so the only question is how long will the tower last. Not long at all is a good generalization, but I'm interested in quantifying it somewhat.
Discovery states the size of an average water tower to be 1-1.5 million gallons: http://curiosity.discovery.com/question/how-much-water-is-stored.
USGS says average water consumption per capita in the US is 80-100 gallons: http://water.usgs.gov/edu/qa-home-percapita.html
The population of West Point, KY, as per game is approximately 4000 people. So, taking the worst numbers and running the math, we see that the town should be able to live off its tower water for 2.5 days.
Of course, zombies don't bathe or cook, so the consumption will be lower. A figure of 10-30% waste was cited by a poster above, so I'll use 25%. That means after the power shuts off, water will still run for roughly 10 days.
He mentioned that the nuclear plant could run for a few months with nobody there, but the results would be very glow in the dark.. Somehow I don't believe that to be true, Nuclear is kinda.. nuclear.. I don't think the plant really does to much except pull the "ohshi-" handle when required. Unless the cores need like constant watering like some kind of flower, But I don't know.
On the water situation, You have to take into account the people who had their faucets on ahead of time, The people that got out of the shower when they got the OMG ZOMBIES phonecall, people washing their cars with garden hoses, They aren't gonna care about turning the water off. I'd say the water might be gone in around 4 days.. But the eletricity? I'd say that's up to how you want to roleplay it in your mind, If it's like 2050 and you want to think solar panels are on every house and power is infinite, Nuclear power.. maybe 0 - 2 months.. Coal..? Maybe a week. I doubt they have that much on hand to do much more.. I'd honestly say maybe 0 - 2 days. Hydro stuff is done by letting water naturally make energy, And I hear that most dams are completely autonomous, So maybe 0 - 6 months. Maybe a rubber band broke or someone forgot to replace the Hubba Bubba in the wall. Lol
In reality I wish there was a setting where you could make the highrises/business have infinite power but the houses go for a certain set of time, Would make it a point to be in the city for the power cause most businesses have solar panels on the roof for reduced cost.
Just my 0.2 cents
Not sure where you live but I don't think it applies throughout the US and especially not in a state like Kentucky which is one of the least solar-using States. I mean in 2012 they drew 4.8 MWp vs California with 2,559.3 MWp. It's a pretty new trend so I don't think "most" businesses have it, but I could be wrong I suppose.
I do think it'd be a nice game feature if a few select houses/buildings had installed solar panels and retained power. It should also be possible to find a generator and burn your own fuel though. Eventually I suppose.