The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part II—model development, calibration and verification

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Unsteady friction and visco-elasticity in pipe fluid transients (2010, methodology): “(7) is (Covas et al. 2005) ∂1 ∂t = ∑N k=1 Jk jk F(x, t) − 1k(x, t) jk ( ) (11) where Jk ¼ 1/Ek is the creep compliance, k the element number of the discrete Kelvin–Voigt model, Ek the modulus of elasticity, jk ¼ hk/Ek the retardation time, hk the creep viscosity, N the total number of Kelvin–Voigt…”
Fluid-structure interaction with pipe-wall viscoelasticity during water hammer (2011, methodology): “The MOC numerical results (including standard quasi-steady friction) for the heads at locations 1, 5 and 8 corresponding to dis ances from the upstream end of 271 m, 197 m and 116.5 m, respectively, are compared with the numerical and experimental results of Covas et al. (2005) in Fig.”
The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part I—experimental analysis and creep characterization (2004, methodology): “Given the viscoelastic nature of PE, the facility was used to collect pressure and strain data for the analysis of the mechanical behaviour of the pipe, as well as for the calibration and validation of the hydraulic transient solver developed in the companion paper (Covas et al., 2004a).”