Allievi Penstock Water Hammer Calculator

Hydraulic Transients: Compute acoustic wave speed, Joukowsky rapid surge, Allievi slow valve closure, and maximum head rise.

Penstock Length $L$ (m):

Inside Diameter $D$ (m):

Wall Thickness $e$ (mm):

Static Head $H_0$ (m):

Initial Flow Velocity $V_0$ (m/s):

Valve Closure Time $T_c$ (s):

Penstock Elastic Modulus $E$ (GPa):

Water Bulk Modulus $K$ (GPa):

Wave Speed ($a$)

-- m/s

Closure Regime

Max Head Rise ($\Delta H$)

-- m

Max Total Pressure

-- bar

• Pipeline Reflection Time ($T_r = 2L/a$): -- s

• Allievi Pipe Parameter ($\rho_0 = a V_0 / 2g H_0$): --

• Relative Closure Time ($\theta = T_c / T_r$): --

• Joukowsky Instantaneous Limit ($\Delta H_J$): -- m

• Peak Total Head ($H_{max} = H_0 + \Delta H$): -- m

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