โก Transient Water Hammer & Valve Closure Surge Pressure
Calculate pipeline water hammer surge pressure (Joukowsky & Allievi): acoustic wave speed in elastic pipes (a), pipeline wave period (2L/a), maximum pressure surge (bar), and pipe wall hoop stress.
โก Fortran 90 Engine
Double Precision (IEEE 754)
โ ISO / ASME Validated
Fluid Mechanics
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Released
Jun 2026
โฑ๏ธ Latency
< 1 ms
๐ก
Hardware & Sizing Partner: Need to size a control valve or check ASME flange bolt torque for this line?
โก Hydraulic Transient Acoustic Shockwave Propagation
Real-time visual simulation: Fast valve closure, high-pressure Joukowsky surge wave, and reservoir reflection๐ Configuration & Presets
๐ง Steel Water Main (2000m)
โก Hydro Penstock Trip (1.2s)
๐ฟ HDPE Irrigation Line
๐ข๏ธ Crude Oil Trunkline (5000m)
Joukowsky & Allievi Surge Formulation:
โข Acoustic Wave Speed: a = โ[ (K/ฯ) / (1 + (K/E)(D/e)(1โฮฝยฒ)) ] [m/s]
โข Pipe Critical Period: Tp = 2 L / a [seconds]
โข Joukowsky Maximum Surge: ฮPmax = ฯ ยท a ยท Vโ [bar]
โข Slow Closure Surge (Tc > Tp): ฮP = ฮPmax ยท (Tp / Tc)
โข Peak Pipe Hoop Stress: ฯh = Ppeak ยท D / (2 e) [MPa].
โข Acoustic Wave Speed: a = โ[ (K/ฯ) / (1 + (K/E)(D/e)(1โฮฝยฒ)) ] [m/s]
โข Pipe Critical Period: Tp = 2 L / a [seconds]
โข Joukowsky Maximum Surge: ฮPmax = ฯ ยท a ยท Vโ [bar]
โข Slow Closure Surge (Tc > Tp): ฮP = ฮPmax ยท (Tp / Tc)
โข Peak Pipe Hoop Stress: ฯh = Ppeak ยท D / (2 e) [MPa].
๐ Surge Pressure Results
Configure inputs and click Compute to view results.
๐ Calculation Methodology & Water Hammer Standards
Joukowsky Equation & Elastic Wave Speed
Calculates peak potential surge $\Delta P_{max} = \rho a \Delta V$ when valve closure occurs faster than one acoustic round-trip ($T_c \le 2L/a$).
Allievi Slow Closure Mitigation
Extending valve closure duration ($T_c > 2L/a$) allows reflected relief waves from the upstream reservoir to attenuate peak transient pressure proportionally.
Key Engineering Assumptions
- Elastic pipe wall deformation (Korteweg / Halliwell wave speed formulation).
- Linear or standard valve effective closure characteristic.
- Applicable to municipal water mains, hydro penstocks, fire mains, and oil trunklines.