Surge (Water Hammer) Quick-Check Calculator

Joukowsky transient pressure from a velocity change, the critical closure time for the line, and total pressure against the pipe's rating. The back-of-envelope for "can we just close this valve, or does it need to be slow?" Runs entirely offline; inputs persist in this browser via localStorage.

Use limits: Joukowsky is the instantaneous worst case for a single velocity change in a simple line — it doesn't model column separation and rejoinder (which can exceed Joukowsky), air pockets, pump trip dynamics, surge tanks, or relief valves. It's a screening number: if the screen fails or the system is complex (long forcemains, high spots, check valve slam history), the answer is a real transient analysis, not a bigger factor of safety on this formula.

Pipe & Flow

Pipe material (wave speed preset)

Wave speed varies with D/t ratio and restraint — presets are typical mid-range values; the design report's value governs if one exists.

Velocity change ΔV (ft/s)

For a full stoppage (valve slam, pump trip with check slam), ΔV = the flowing velocity.

Pipeline length to the reflection point (ft)

From the closing valve/pump to the nearest free surface (tank, wet well, reservoir).

Working pressure at the point of interest (psi) Pipe pressure rating / class (psi)

—

Joukowsky surge head	—
Joukowsky surge pressure	—
Total pressure (working + surge)	—
Percent of pipe rating	—
Critical closure time (2L/a)	—
Suggested minimum closure time (~10 × 2L/a)	—

How the Numbers Are Derived

The Joukowsky equation

ΔH = a · ΔV / g (feet of head) → ΔP = 0.433 · ΔH (psi)

With a = 4,000 ft/s and g = 32.2, every 1 ft/s of velocity destroyed instantly costs about 124 ft (54 psi). That's the whole reason surge control exists: velocity is cheap to create and expensive to stop.

Critical closure time — why 2L/a matters

The pressure wave travels to the nearest free surface and reflects back in t_c = 2L/a. Any closure faster than this is "instantaneous" as far as the pipe is concerned and produces the full Joukowsky rise. Closures much slower than 2L/a let the reflection relieve pressure as the valve closes, and the surge drops roughly in proportion. A practical field rule is to make controlled closures at least ~10× the critical time; the tool prints both numbers.

Note the trap: a "slow" 30-second closure on a 5-mile forcemain (t_c ≈ 13 s for DIP) is only ~2× critical — not actually slow.

Material notes

HDPE is the forgiving one twice over: low wave speed (low surge per ft/s) and its pressure ratings (PE4710) allow occasional surge to 2.0× and recurring surge to 1.5× the pressure class. That's a materially different acceptance basis than rigid pipe — check the PPI handbook and the spec.
PVC ratings are more sensitive to cyclic surge (fatigue); recurring surge on PVC forcemains is a design issue, not just a peak-pressure issue.
Negative surge matters too: the down-swing after a pump trip can pull the line below atmospheric at high points — column separation, and the rejoin slam can exceed the initial Joukowsky rise. Vacuum relief at high points exists for this.
Check valve slam is the everyday version of all this: the valve that closes after reverse flow establishes converts that reverse velocity to surge. Fast-closing or controlled checks are the fix.

References

AWWA M51 — Air Valves: Air-Release, Air/Vacuum, and Combination. https://www.awwa.org/

Plastics Pipe Institute, Handbook of Polyethylene Pipe — HDPE surge allowances. https://plasticpipe.org/

Wylie & Streeter, Fluid Transients in Systems — the real analysis when the screen fails.