Where the pressure comes from
Water in a pipe has momentum. When a valve shuts, the water immediately behind it has to stop, and it stops by compressing slightly and stretching the pipe. That compression is a pressure rise, and it travels back up the pipe as a wave at the speed of sound in that pipe and its water — roughly 4,400 feet per second in copper, and much slower in plastic because the pipe wall gives.
The Joukowsky relation puts a number on it: the pressure rise equals the density of the water times the wave speed times the change in velocity. In the units plumbing works in, that comes out at about 59 psi for every foot per second of velocity destroyed, in copper, for a closure fast enough to count as instantaneous. Five gallons a minute through a half inch bore is about 6.9 feet per second, so stopping it dead is a surge of roughly 400 psi arriving on top of whatever the system was already at.
Note what is not in that formula. Not the length of the pipe, not the pressure it was at, not the pipe diameter except through its effect on velocity. Length and pressure matter for other reasons, but the height of the spike is set by velocity and wave speed alone.
Why closing time changes everything
The full surge only develops if the valve closes before the wave has had time to travel to the nearest open end and back. That round trip takes twice the length divided by the wave speed, and on short branches it is very short indeed: twenty-two feet of copper is about ten thousandths of a second. A solenoid in a washing machine closes in a couple of hundredths, which is slower than the round trip but the same order, so most of the surge develops. A lever faucet takes several tenths of a second, twenty or thirty round trips, and the wave is reflected and relieved so many times during the closure that only a fraction of the surge builds.
That single ratio explains the pattern every plumber knows. Appliances bang and hand-operated taps do not, on the same pipe, at similar flows. It is not the appliance being violent; it is a solenoid closing in a hundredth of a second on a run whose round trip time is a hundredth of a second.
Reading the numbers this page gives you
| What it is | What it is good for | What it is not |
|---|---|---|
| Velocity in ft/s | Ranking fixtures, and a general check on branch sizing | A substitute for measuring the actual flow |
| Instantaneous surge | The ceiling — what the closure could produce at worst | What your system sees, unless the valve is genuinely that fast |
| Closing-time adjusted figure | Comparing fixtures on the same system | A design pressure for selecting components |
| Peak on top of standing pressure | Seeing why a high static pressure makes hammer worse | A measured transient — those need a gauge that captures peaks |
Every one of those is an order of magnitude estimate from a model that assumes a rigid straight pipe with no air in it and one clean closure. Real plumbing has entrained air that softens the wave dramatically, flexible connectors that absorb it, tees and elbows that reflect it, and occasionally geometry where two reflections arrive together and add. The right use of these figures is to work out which branch to deal with first and to understand the mechanism, not to specify anything.
Arrestors, air chambers and the thing that stopped working
An arrestor gives the stopping water somewhere to go. A sealed chamber with a piston or a bladder over a cushion of gas absorbs the momentum over a few hundredths of a second instead of a few thousandths, which is the whole trick. Because it works by being close to the event, placement matters: on the branch the quick-closing valve serves, as near the valve as the piping allows, ahead of it. Put it back at the manifold and a length of water column is still free to slam before the arrestor is involved.
The older approach was a capped vertical stub of pipe left full of air. It works when installed and stops working within months, because the air dissolves into the water and the stub fills. That is the classic house where the banging came back — the air chambers waterlogged. Draining the system down refills them and buys another few months. Sealed devices exist because the air chamber was a consumable that nobody serviced.
An appliance valve closes on both hot and cold, so the usual arrangement at a washing machine is a pair rather than one. And a system that developed hammer suddenly, having been quiet for years, is often telling you about something other than the valve: a failed pressure reducing valve, a waterlogged expansion tank, or a pressure that has risen. Those live at the water service and are licensed work.
What else the bang could be
Not every noise in a wall is hammer, and the distinction is diagnostic rather than academic. A single sharp bang the instant a valve shuts is hammer. A rhythmic ticking that starts when hot water runs and fades after is thermal movement, and the pipe expansion calculator covers how far the pipe is actually moving. A shudder or chatter while water is running, rather than when it stops, is usually a loose washer or a valve on the edge of cavitation. A rumble that builds as a fill valve closes is that valve throttling, not a transient. And a bang followed by running water is not a plumbing noise problem at all.
If the velocities on this page are coming out above roughly eight feet per second, the branch is running fast enough that hammer is a symptom rather than the disease, and the sizing is worth revisiting — the pressure drop calculator covers what that velocity is costing in friction, and the fixture unit calculator covers the demand the branch was sized for in the first place.
Questions people ask
What causes the banging noise when a tap or appliance shuts off?
A moving column of water being stopped faster than it can decelerate smoothly. The momentum has to go somewhere, and it goes into a pressure spike that travels back up the pipe as a wave at roughly the speed of sound in the pipe. In copper that is about 4,400 feet per second, and the spike is around 59 psi for every foot per second of velocity destroyed. A washing machine solenoid stopping five gallons a minute in a half inch line is stopping about seven feet per second, which is several hundred psi arriving in a few thousandths of a second. The noise is that wave reflecting up and down the branch and shaking the pipe against the structure.
Why do appliances cause water hammer but hand taps do not?
Closing time against the round trip time of the branch. The full surge only develops if the valve shuts before the pressure wave can travel to the nearest open end and back, which on a twenty foot copper branch is about a hundredth of a second. An appliance solenoid closes in that order of time. A lever faucet takes a few tenths, which is twenty or thirty round trips, and during that time the wave is repeatedly reflected and relieved so only a fraction of the surge ever builds. Same pipe, same flow, completely different noise, purely because of how fast the valve moves.
Where should a water hammer arrestor be installed?
On the branch serving the quick-closing valve, as close to that valve as the piping allows, ahead of it. The arrestor works by giving the stopping water somewhere to go within a few thousandths of a second, so distance between it and the valve is water column that is still free to slam before the device is involved. An appliance valve closes on both hot and cold, so a pair is the normal arrangement. Beyond that, whether an arrestor is required, what size it should be and how it is supported are questions that depend on the fixture, the product and your local requirements, and anything cut into live supply piping is plumbing work.
Are the pressures this calculator shows what my pipes actually see?
No, and they are not meant to be. The Joukowsky relation assumes a rigid straight pipe, water with no entrained air, and one clean instantaneous closure, and real plumbing violates all three. Air in the water softens the wave dramatically. Flexible connectors, branches, elbows and fittings absorb and reflect it. A pressure reducing valve or an expansion tank takes some of it. Occasionally two reflections arrive together and the peak is briefly higher than the simple figure. What these numbers are genuinely useful for is ranking the fixtures on your system against each other and understanding the mechanism. A real transient peak is measured with a gauge that captures peaks, not calculated on a web page.
My house was quiet for years and now it bangs — what changed?
Usually not the fixture. The classic cause is air chambers waterlogging: an older system relied on capped vertical stubs of pipe holding a cushion of air, the air gradually dissolved into the water, and the stubs filled. Draining the system down refills them and the quiet comes back for a few months, which is a good diagnostic even if it is a poor fix. The other common causes all live near the water service — a pressure reducing valve that has failed or drifted upward, a supply pressure that has risen, or a thermal expansion tank that has lost its precharge and is now full of water. Higher static pressure raises every surge peak by the same amount. All three are at or near the service entry and are licensed work.