⚡ 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.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

Transient Water Hammer & Valve Closure Surge Pressure

Fluid Mechanics

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👁️ Views 44

⚡ Solves 36

💾 Downloads 376 📦 Fortran Code 4.5 KB

📅 Released Jun 2026

⏱️ Latency < 1 ms

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⚡ Hydraulic Transient Acoustic Shockwave Propagation

Real-time visual simulation: Fast valve closure, high-pressure Joukowsky surge wave, and reservoir reflection

📝 Configuration & Presets

💧 Steel Water Main (2000m) ⚡ Hydro Penstock Trip (1.2s) 🌿 HDPE Irrigation Line 🛢️ Crude Oil Trunkline (5000m)

🧱 Pipeline Material & Fluid Medium

Pipe Material:

Fluid Medium:

📏 Pipeline Dimensions & Operating Pressure

Pipeline Length L [m]:

Pipe Inner Diameter D [mm]:

Wall Thickness e [mm]:

Static Pressure P_stat [bar]:

⏱️ Flow Rate & Valve Closure Time

Volumetric Flow Rate Q [m³/h]:

Valve Closure Time T_c [s]:

Joukowsky & Allievi Surge Formulation:
• Acoustic Wave Speed: a = √[ (K/ρ) / (1 + (K/E)(D/e)(1−ν²)) ] [m/s]
• Pipe Critical Period: T_p = 2 L / a [seconds]
• Joukowsky Maximum Surge: ΔP_max = ρ · a · V₀ [bar]
• Slow Closure Surge (T_c > T_p): ΔP = ΔP_max · (T_p / T_c)
• Peak Pipe Hoop Stress: σ_h = P_peak · D / (2 e) [MPa].

📊 Surge Pressure Results

📊 Output Summary
💾 Fortran Source

Peak Total Pipeline Surge Pressure (P_max)

45.16 bar (4.52 MPa)

Surge ΔP: +30.16 bar (+308.0 m) | Wave Speed: 1215 m/s

RAPID CLOSURE (Tc ≤ 2L/a)

Acoustic Wave Speed (a) 1215 m/s Pipe + Fluid elasticity

Pipeline Wave Period (2L/a) 1.32 s Closure Tc = 1.20 s

Pipe Wall Hoop Stress 112.9 MPa SAFE (BELOW STEEL ALLOWABLE)

Initial Flow Velocity (V₀) 2.49 m/s Q = 4500 m³/h

📈 Surge Pressure ΔP (bar) vs Valve Closure Time Tc (s)

📉 Peak Pressure Pmax (bar) vs Flow Velocity V0 (m/s)

=================================================================
 THERMOFLUIDCALC — WATER HAMMER & SURGE PRESSURE REPORT
=================================================================
Case Title                 : Hydroelectric Penstock Emergency Turbine Trip
Pipeline Material & Fluid  : Carbon Steel (E = 205 GPa, ν = 0.30) / Water (ρ = 998 kg/m³, K = 2.19 GPa)
Pipeline Dimensions        : L = 800.0 m, ID = 800.0 mm, Wall Thick e = 16.0 mm, Static Press = 15.00 bar
Flow & Closure             : Q = 4500.00 m3/h, Initial Velocity V0 = 2.49 m/s, Valve Closure Time Tc = 1.20 s
-----------------------------------------------------------------
ACOUSTIC WAVE SPEED (a)    : 1215.2 m/s
PIPELINE PERIOD (Tp = 2L/a): 1.317 seconds
CLOSURE REGIME             : RAPID CLOSURE (Tc ≤ 2L/a)
MAX JOUKOWSKY SURGE (ΔPmax): 30.16 bar (308.04 meters head)
ACTUAL SURGE PRESSURE (ΔP) : +30.16 bar
PEAK PIPELINE PRESSURE     : 45.16 bar (4.52 MPa)
Pipe Wall Hoop Stress      : 112.90 MPa
SAFETY STATUS              : SAFE (BELOW STEEL ALLOWABLE)
=================================================================

📘 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.

ThermoFluidCalc Engineering Report