Where 0.433 comes from
A cubic foot of water weighs about 62.4 pounds. Spread over the 144 square inches of the bottom of that cube, it presses down with 0.433 pounds on each of them. So a foot of standing water is 0.433 psi, and it does not matter whether the water is in a pipe, a tank or a lake — only the height counts.
Turn that round and 1 psi lifts water 2.31 feet. Those two numbers are the whole of this page. A ten foot storey is 4.33 psi, three storeys is 13 psi, and a shower head six and a half feet above the third floor is another 2.8 psi on top of that.
The number that is not on the gauge
With the defaults — 62 psi at a hose bib two feet up, three floors at ten feet each, a shower head six and a half feet above the top floor — the head is 24.5 feet above the gauge and 10.6 psi of the 62 has gone before anything moves. The shower sees 51.4 psi standing.
Then it opens. Twelve psi of friction through the meter, the softener, the riser and the valve, and 39.4 psi arrives. That is still a perfectly good shower. Put the same house on a street that gives 40 psi in the afternoon and the same shower gets 17.4, which is a different experience entirely, and nothing about the plumbing changed.
A reducing valve sets the pressure downstairs
A valve set to 55 psi is holding 55 at the valve, which is in the basement. It is not holding 55 at the third floor shower, which still pays the 10.6 psi of height and gets 44.4 standing. That is the trade the valve makes: it protects the fittings and appliances low down in the building, where the standing pressure is highest and where the wear actually happens, and it does so at the expense of the fixtures at the top.
It also only ever reduces. Set a valve above the incoming pressure and it sits open doing nothing. There is no setting that produces more pressure than the street is delivering, and a valve that appears to have stopped working is often a street that has dropped below the setting.
Downwards, the same column adds
Everything above runs the other way below the gauge. A basement fixture ten feet below the meter sees 4.3 psi more than the meter does. In a tall building the difference between the lowest and highest fixtures is large enough that the two ends of the same riser behave like different systems, and the fittings at the bottom lead a harder life than the ones at the top.
Questions people ask
How much pressure do I lose per floor?
A foot of height costs 0.433 psi, so a ten foot storey costs about 4.3 psi and a nine foot one about 3.9. It is subtracted whether water is moving or not, before any friction loss, and it applies to the height of the fixture rather than the height of the floor — a shower head adds another six and a half feet or so above the floor it stands on.
Why is the pressure fine downstairs and poor upstairs?
Height, and then friction on top of it. Three storeys plus a shower head is about 24 feet, which is 10.6 psi gone before the tap opens. Add the friction of getting the flow all the way up there and the difference between a ground floor tap and a top floor shower can easily be twenty psi. The gauge on the hose bib is measuring the good end.
Can a pressure reducing valve fix low pressure upstairs?
No. A reducing valve only ever takes pressure away. If it is set above the pressure arriving from the street it sits open and does nothing, and if it is set below, everything downstream including the top floor gets less. Raising the setting can recover pressure that the valve itself was removing, up to the limit of what the street supplies, and no further.
What does a reducing valve have to do with the expansion tank?
A reducing valve usually will not pass water back toward the street, which makes the plumbing a closed system. Water expands when it is heated and in a closed system that expansion has nowhere to go, so the pressure rises. Whether that needs to be dealt with, and how, comes from the adopted code and the water utility. The volume involved can be worked out separately.
What is the friction figure I am being asked for?
Everything the water loses between the gauge and the fixture while it is actually flowing: pipe friction over the developed length, fittings, the meter, and any filter, softener or backflow device in the path. It depends on the flow, so it is not one number for the whole building — it is the loss at the flow the top fixture will draw. Work it out for the actual run rather than accepting the placeholder.