How is the amount of water for (a) toilet and (b) drinking to be carried by a flight calculated in the industry? Is there any formula or thumb rule using which we can roughly estimate the amount of water required for toilet and for drinking calculated if the aircraft type $A$ is known and the flight has $P$ passengers on board and is scheduled to fly for $H$ before its next landing?
It is going to vary according to flight mission, passenger count, season, or what part of the world the flight takes place.
Here are the capacities from a company document.
MD88/90 47USG (177.9L) MD11 250USG (946.4L) Estimated 732/733 40USG (151.2L) 737 60USG (226.8L) 747 3x 110USG = 330USG 757 66USG (249.8L)-Fill valve closes automatically at 50USG (189.3L) 762/763 120USG (453.6L)-Fill valve closes automatically at 102USG (385.5L) 763ER 160USG (600.6L) 764ER 224USG (847.9L) 772ER 300USG (1135.6L) CRJ 200/700 31.5USG (galley 8USG/30L, lavatory 5USG/19L, toilet 18.5USG/70L)
As mentioned, the term "potable" water seems to be a minor overstatement. Some companies warn employees to not uplift any potable water overseas (which means not outside the US, Canada, or UK). But based on what I've heard, I wouldn't drink it wherever it came from.
The "potable" water is usually chlorinated water, but you´ll never know about the truck or tank service overseas. Usually the galleys contain an anti-biological filter (silver ions) for the taps and coffee makers, which get changed regularly. Also the tanks will be disinfected every few weeks, normally during an A-check. Part of a C-check is to remove and test them.
On a B737, the potable water tank is in the aft cargo pit behind the last wall under the aft galley just right in front of the pressurized bulkhead. The tank itself is made out of composite materials and fiberglass. The tank is about 4 feet long and 2 feet tall. The 737s only have one potable water tank.
The B747 has three 110 gallon filament-wound fiberglass tanks attached to the forward side of the center section front spar (rear bulkhead of the forward baggage compartment). The water is moved from the tanks by pressurized air. This pressure is provided by electrically driven air compressors mounted next to the tanks. Not all operators use all three tanks and some have deleted some tanks. 747 AMM, 38-11-00, page 1, pg 2.
Passenger MD-11 hold up to four 63USG tanks, the freighter usually has all removed except for one. This water also serves for flushing the vacuum toilets if installed. The tanks sit in the utility tunnels (behind the sidewall) of the forward cargo compartment.
I used to work with the B747-400 when I was with Lufthansa. From what I can remember it had water tanks which could hold 1500kgs of water. On a long-haul flight from KUL to FRA we would generally uplift 75% so that would be 1125kgs. The selector for water quantity is on the panel next to the door 2L.
On water-source. We were required to get an external laboratory to do a water test. This involved bringing a technician to the water source at the airside where he would take a sample from each outlet and each water truck. The lab report was relayed to HQ.
When we stopped passenger flights to KUL, we still had freighters operating to KUL but these planes usually did not require water so we did not keep up our status as a water re-supply station. On one occasion a plane came in with empty water tanks and the outgoing crew insisted on uplift of water. This was not permitted because if any water from a 'non-certified' source was uplifted the tanks would need to be flushed and chemically treated when it went back to FRA base. In this case we loaded a few cartons of mineral water and the crew was happy.
It depends. Airlines have an office that is constantly looking for ways to reduce weight as every pound of reduction can save thousands in fuel costs over the year.
When it comes to water (and pretty much everything else that's not mandated) they look at historical use by route, season, load factors, and service locations to predict needed quantities and set the amount to be loaded. The goal is to carry enough with a small margin over the predicted maximum need.