Pressure surge (Joukowsky) When a valve closes quickly or a pump fails, a pressure wave travels through the pipeline. Joukowsky gives the maximum value; the closing time decides whether it takes full effect.
Input (Technical book, chap. 3.7.2)
GPa
GPa
mm
mm
m/s
Applied wave propagation speed a
– m/s
m/s
m
s
kg/m³
Result
Pressure change according to Joukowsky Δp
– bar
| Head change Δh | – m WS |
| Reflection time TR | – s |
| Critical closing time 20 · TR | – s |
| Reduced surge pressure (Michaud) | – bar |
–
Δp = ρ · a · Δv (Joukowsky)TR = 2 · L / a (Reflection time)Δp ≈ 2 · ρ · L · Δv / ts (Michaud, ts > TR)a = √( K / ( ρ · (1 + K · dm / (ER · s)) ) ) (Korteweg)
| Reference | Technical book, chap. 3.7.2 · Physical principles |
|---|---|
| Assessment | Chap. 3.7.5 · A safety-relevant pressure surge is to be expected if t_s < 20 · T_R |
| Limits | Approximation for rapid closure. Does not replace a surge simulation for detailed design. Pump failure, air vessels, check valves, high points and partially filled pipes require a more detailed analysis. With cavitation (column separation), the surge can significantly exceed the Joukowsky value. |
Guide values for wave speed by pipe material (Tab. 3.7-2)
| Pipe material | a [m/s] |
|---|---|
| Steel | 1000 – 1200 |
| Ductile cast iron | 1000 – 1100 |
| Concrete / reinforced concrete | 900 – 1200 |
| PE-HD | 300 – 400 |
| PVC | 400 – 500 |
| GFK | 400 – 600 |
Influence of gas content (Tab. 3.7-3)
| Gas content [vol. %] | a [m/s] |
|---|---|
| 0 (pure water) | ca. 1250 |
| 0,2 | ca. 450 |
| 0,4 | ca. 300 |
| 1,0 | ca. 240 |
Dissolved and free gases in wastewater reduce a considerably (values at approx. 3 bar). As the gas content fluctuates during operation, the design must be based on the worst case: minimum gas content, highest wave speed, largest pressure surge. The calculator therefore uses the value without gas reduction.