Joukowsky + closure-time criteria for a single penstock / pipeline.
SI units: m, s, m/s, kg/m³, Pa.
Results
For penstock wall design, use Hmax from this tool as Hmax
in the Penstock Wall Thickness & Stress Check.
For downsurge, also check Hmin / Pmin against vapour pressure limits.
Formulas Used
Joukowsky Equation (Sudden Closure):
ΔP = ρ · a · |ΔV|
Where:
ΔP = surge pressure (Pa)
ρ = fluid density (kg/m³)
a = wave speed (m/s)
ΔV = change in velocity (m/s)
Rigid Column Approximation (Gradual Closure):
ΔP ≈ ρ · L · |ΔV| / tc
Where:
ΔP = surge pressure (Pa)
ρ = fluid density (kg/m³)
L = pipe length (m)
ΔV = change in velocity (m/s)
tc = closure time (s)
Head Change:
ΔH = ΔP / (ρ g)
Where:
ΔH = change in head (m)
ΔP = surge pressure (Pa)
ρ = fluid density (kg/m³)
g = gravitational acceleration (9.81 m/s²)