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Product(s): |
HAMMER |
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Version(s): |
CONNECT Edition, V8i |
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Area: |
Calculations |
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Problem
What equation does HAMMER use to calculate Wave Speed in the Wave Speed Calculator Tool?
Solution
HAMMER uses the following equation developed by Korteweg. This is generally considered valid for thin-walled pipelines (D/e > 40) so if your pipe is not thin-walled (for example HDPE pipes may be too thick) or if you do not want to use the Korteweg equation, use another method such as ModelBuilder import as described here: Entering Pipe Wave Speed for a Transient Simulation
Note also that this equation does not account for viscoelastic effects that can be significant for example in plastics such as PVC and polyethylene (PE). Covas et al. (2002) showed that these effects, including creep, can affect wave speed in pipes and must be accounted for if highly accurate results are desired. They proposed methods that account for such effects in both the continuity and momentum equations. However, using the standard Korteweg equation used by HAMMER's Wave Speed Calculator tool may be a good enough approximation for the purposes of transient simulations. One option to consider is a sensitivity analysis - try a range of values higher and lower than the values suggested by the wave speed calculator and compare the transient results to see if it is significantly impacted by the wave speed. If not, then this may indicate that you do not need to worry about accounting for viscoelastic effects.
For more information, see page 586 of Advanced Water Distribution Modeling and Management.
Where:
a = Wave speed (ft/s, m/s)
Ev = Bulk modulus of Elasticity (lbf/ft^2, Pa)
p = liquid density (slugs/ft^3, kg/m^3) (1.94 slugs/ft^3 for Water @4C with specific gravity of 1.0)
D = Diameter (in, mm)
e = wall thickness (in, mm)
E = Young's Modulus (lbf/ft^2 / Pa)
ψ = pipeline support factor (depends on the selected method, see below)
- Pipe is anchored throughout against axial movement: ψ = 1 - µ2 , where µ is Poisson's ratio
- Pipe is equipped with functioning expansion joints throughout: ψ = 1
- Pipe is supported only at one end and allowed to undergo stress and strain both laterally and longitudinally: ψ = 5/4 - µ (ASCE, 1975)
See Also
Advanced Water Distribution Modeling and Management.