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Water Hammer (Hydraulic Surge) Simulator

Joukowsky equation: ΔP = ρ · a · ΔV. Calculates wave speed from pipe material elastic modulus and wall thickness, determines critical closure time (Tc = 2L/a), and applies rapid vs. slow closure logic. Animated pressure wave travels from valve back to reservoir and reflects.

Pipe Material

Wall Schedule / Class

Pipe Diameter (OD)6"

Pipe Length500 ft

Flow Rate400 GPM

Flow velocity: 4.54 fps

Operating Pressure80 psi

Valve Closure Time0.5 s

Critical Tc = 0.25 s

Wave Speed

4057 fps

Carbon Steel

Critical Tc

0.25 s

2L/a = 2×500/4057

Surge ΔP

122 psi

Partial (slow close)

Total Pressure

202 psi

80 + 122

Flow Velocity

4.54 fps

400 GPM in 6" pipe

Pipe Wall

0.154"

Wave Speed & Surge Comparison — All Materials (6" pipe, 400 GPM)

Material	E (psi)	Wave Speed (fps)	ΔP (psi)	Critical Tc (s)	Closure Status
Carbon Steel ✓	30,000,000	4057	122	0.25	Slow
Ductile Iron	24,000,000	4218	122	0.24	Slow
HDPE (PE4710)	115,000	506	31	1.98	Rapid
PVC (DR 18)	400,000	829	51	1.21	Rapid
Cast Iron (unlined)	19,000,000	4205	122	0.24	Slow
Copper Type L	17,000,000	2858	122	0.35	Slow
Pre-stressed Concrete	4,500,000	3901	122	0.26	Slow

Surge Protection Strategies

⏱ Slow-Closing Valves

Increase closure time > 0.2 s to move below Tc

🔧 Surge Relief Valve

Set at 88 psi (110% of operating)

🫧 Surge Tank / Air Vessel

Absorbs kinetic energy; especially for HDPE/PVC

🔄 Flexible Piping Material

HDPE/PVC have low E → lower wave speed & surge

Joukowsky (1898):ΔP = ρ · a · ΔV. Valid for instantaneous (rapid) valve closure where closure time ≤ critical time Tc = 2L/a. For slow closure (T > Tc), maximum surge ≈ ΔP_Joukowsky × Tc/T. AWWA M11 and ASCE Manual 79 recommend confirming surge pressure against allowable transient surge ratings for the pipe material and pressure class selected.