Hydraulics2D

Flow in Pipes: Systems & Networks - Theory & Concepts - Water Hammer

Series, parallel and branching pipes, resistance formulations, equivalent systems, three-reservoir problems, Hardy Cross and nodal-head network methods, pumps, valves, demands, and hydraulic transients.

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Water Hammer Simulator

Elastic-pipe wave speed and rapid/slow valve-closure pressure rise.

Initial velocity (

V_0

)2.0 m/s

Valve closure time (

T

)0.00 s

Zero represents an ideal instantaneous closure.

Pipe length (

L

)100 m

Diameter (

D

)0.20 m

Wall thickness (

t

)10 mm

Fluid bulk modulus (

K

)2.20 GPa

Pipe elastic modulus (

E

)200 GPa

Fluid density (

\rho

)1000 kg/m³

Wave celerity (

c

)1343 m/s

Critical closure time (

T_c=2L/c

)0.149 s

Closure classificationRapid

Maximum pressure rise (

\Delta p

)2.69 MPa

Equivalent head rise (

\Delta H

)273.8 m

Normal flowCompression waveReflected low-pressure phase

Rapid closure uses the Joukowsky relation $\Delta p=\rho c\Delta V$ . For closure slower than $T_c=2L/c$ , this educational model uses the classical gradual-closure approximation $\Delta p\approx2\rho L\Delta V/T$ . Real systems may require method-of-characteristics analysis including friction, valve law, pipe restraint, entrained air, and vapor-column separation.

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Water Hammer Simulator

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