Chapter 3 – What Causes Surge?
Surge Analysis and the Wave Plan Method
Supplementary Material: Example Problems and Solutions
Chapter 3 – Problem 3.11
3.11 The maximum pressure rise on the inlet side of the valve can be restricted to a value substantially below the full Joukowsky’s pressure rise if the valve closure time is substantially longer than one wave period (provided no cavitation or other extraneous inputs). Would it be possible to limit the pressure rise to 0 even with an abnormally long but finite valve closure time?
Solution:
Suppose the valve on a reservoir-pipeline-valve system is closed in certain time Treducing the flowrate from Q to 0.
Deceleration of flow form Q to 0 in time T leads to a change in momentum which is balanced by an increase in pressure according to the impulse-momentum principle.
Total change in momentum = L ρ Q, where L is total length of the pipeline, ρ is density of water, and Q is change in flowrate, all in standard units.
If ΔH is the uniform pressure rise and A is the pipe cross sectional area, then the associated impulse = ΔH ρg A T.
L ρ Q = ΔH ρg A T
ΔH = LQ/(gAT)
Therefore, ΔH cannot be 0 for any finite values of T.
However, ΔH approaches 0 as T -> ∞.
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