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อัปเดต 2026-09-07
Wave speed & Joukowsky
surge magnitude
The wave speed a sets how fast pressure waves travel and, with the Joukowsky relation ΔH = a·Δv/g, the peak surge from a sudden velocity change.
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The wave speed a comes from the fluid bulk modulus and the pipe’s elastic give (or you enter it); the Joukowsky relation then gives the peak surge from a sudden velocity change, and the round-trip time 4L/a sets the reflection period. The engine echoes the wave speed it actually used in the honesty notes.
สมการ
Joukowsky surge
Head rise from an instantaneous velocity change Δv — the upper bound for a fast closure.
Wave speed
K = fluid bulk modulus, E = pipe elastic modulus, e = wall thickness, c₁ = restraint factor. A rigid pipe (E→∞) recovers √(K/ρ).
Reflection period
A closure faster than 2L/a produces the full Joukowsky head.
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