Water hammer on pump trip — the case that sets your pipeline's pressure rating

The governing case is not the one you control

In discharge-line design, the transient that makes it into the calculation report is usually the valve closure. It is the comfortable case: the maneuver time is a design variable, you pick the actuator, you write “closure in 30 s” into the specification, and the numbers work out.

The trouble is that the line will not fail on the day of the scheduled closure. It will fail on a power outage — when the pump-motor set stops by itself, within a fraction of a second, with no warning and no negotiable maneuver time. That is the case that sets the pressure class of the pipeline, and it is the one most often missing from the report.

The check has three steps, in this order: real wave speed, critical time, surge by the method that matches the regime.

Step 1 — Real wave speed (and why 1,480 m/s is wrong)

The pressure wave travels at ≈ 1,480 m/s in unconfined water. Inside a pipe it is always slower: as the wave passes, the wall deforms elastically and that added compliance damps propagation. Korteweg quantifies it:

a = sqrt( (K/ρ) / (1 + (K/E)·(D/e)·c₁) )

where K is the fluid bulk modulus, ρ the density, E the pipe material modulus of elasticity, D the internal diameter, e the wall thickness and c₁ the anchorage coefficient.

The material effect is far too large to ignore:

• Steel: typically 1,000–1,250 m/s
• Ductile iron: 1,000–1,200 m/s
• PVC: 300–500 m/s
• HDPE: 250–350 m/s

Two practical consequences. First: using 1,480 m/s on a steel line overestimates the surge by roughly 20% — a margin you pay for in pipe class. Second, and more dangerous: on a plastic line, the low wave speed reduces the positive peak but stretches the critical time, which changes entirely which maneuvers count as rapid.

Step 2 — The critical time 2L/a picks the method

Tc = 2L / a

Tc is the time the wave takes to travel to the far end and return. It is the dividing line:

• T ≤ Tc → rapid maneuver. The reflected wave has not returned by the time the maneuver ends. Full Joukowsky applies, with no attenuation.
• T > Tc → slow maneuver. The reflection arrives before the maneuver ends and relieves the peak. Michaud’s approximation applies.

This is where the pump trip parts ways with the valve closure. The stopping time of the set can be estimated with Mendiluce:

Tp = K_b + (L · V₀) / (g · Hman)

with K_b between 1 and 2 depending on the inertia of the set. On a long pipeline with a low-inertia pump, Tp lands in the same order of magnitude as Tc — or below it. In other words: the pump trip tends to fall into the rapid regime precisely on the lines where the surge is most severe.

Step 3 — The numbers, worked out

Steel pipeline, 1,200 m, water at 1.8 m/s.

Joukowsky, on the trip:

ΔP = ρ · a · ΔV = 1000 · 1236 · 1.8 ≈ 22.2 bar

Michaud, on the 4-second closure:

ΔH = (2 · L · V₀) / (g · T) = (2 · 1200 · 1.8) / (9.81 · 4) ≈ 110 m ≈ 10.8 bar

Twice as much. Same pipe run, same flow velocity — only the scenario changes. And, more to the point: those 22.2 bar add to the operating pressure. A line running at 6 bar reaches ≈ 28 bar during the transient. That does not pass on a PN-16 line, and getting this right is the difference between a pipeline that lasts 30 years and one that ruptures on the first outage of the summer.

The side almost nobody checks: the downsurge

Everything above deals with the positive peak. What follows it is the pressure drop — and that is what usually destroys pipelines.

If local pressure falls to the vapor pressure of the liquid, a cavity forms and the column separates. When that cavity collapses, the two liquid columns slam together. The resulting spike can exceed the Joukowsky value, and it happens at a location the positive-peak check was not looking at — typically the high point of the profile, far from the pump.

Signs that the risk is real: a pronounced high point in the profile, a long line, high velocity, a low-inertia pump. In those cases, checking only the positive peak gives a false sense of margin.

Checklist before signing off

1. Wave speed computed with Korteweg using the actual material and D/e ratio — never 1,480 m/s by default.
2. Tc = 2L/a computed and compared against the maneuver time of every scenario.
3. Pump trip included as a governing case, with Tp estimated (Mendiluce), not assumed slow.
4. Surge added to the operating pressure and compared against the pipe rating, with the specified margin.
5. Downsurge assessed along the line profile; where column separation is credible, size a protection device (flywheel, one-way surge tank, surge shaft, anticipating valve).

None of these five steps is hard on its own. What goes wrong in practice is the order — jumping straight to Joukowsky with free-water wave speed, or only checking the maneuver you control.

Where this is arithmetic and where it is a form

The whole sequence — Korteweg → 2L/a → regime identification → Joukowsky or Michaud, with the stopping time from Mendiluce — fits into a single form. That is exactly what the LOGOS water hammer calculator does: you enter material, geometry and velocity, and it returns the real wave speed, the critical time, the identified regime and the surge by the matching method, with the calculation report behind it.

The value is not in saving a multiplication. It is in not getting the regime wrong — which is where hand calculations slip.