At the end of last week there was a problem with the water supply to part of the science buildings here at The University of Waikato. Today, there's been work going on to fix the problems. As a result, we have a very much reduced water pressure. The tea-room on the first floor is still supplying water, at a reduced flow rate, but on the third floor, where I have my office, it's a different story. Turn on a tap and there's some gurgling and, if you're lucky, after several seconds some water splurges out. Just a little, mind you. Then it's back to the gurgling.
The pressure in a water supply reduces with height. The higher one needs to lift a column of water (e.g. to the third floor, rather than the first), the more pressure is required. The relationship is encompassed as part of Bernouilli's principle . The pressure change with height, assuming no water flow, is just the density of the water (1000 kg per metre cubed) times the acceleration due to gravity (about 10 metres per second squared) times the height. Three floors up is maybe about 9 metres in this building – so that comes to about 90 000 pascals pressure.
We can compare that to atmospheric pressure, which is about 100 000 pascals. So the water pressure up on the third floor is approximately 'one atmosphere' lower than that on the ground, assuming it's all fed by the same supply. Domestic water pressure varies considerably from place to place, but a few atmospheres would be typical. But today, with the water work going on, it's clearly a lot less than this, and the supply we have is struggling to maintain and significant pressure up here at the top of the building,
Water pressure also reduces with increased flow rate (again, from Bernouilli's principle). Given that people are probably opening up the taps for longer in a desparate attempt to get enough water out to wash the soap off their hands, that's not going to help the situation.