Note for SWMM6 – this may be useful for any discussion of a Slot in SWMM6. A Preissmann Slot is used in InfoWorks ICM, XPSWMM and one of the solutions of SWMM4
The wave speed, c, is influenced by the elasticity of the pipe wall. For a pipe system with some degree of axial restraint a good approximation for the wave propagation speed is obtained using
where Ef = elastic modulus of the fluid (for water, 2.19 GN/m2, 0.05 Glb/ft2)
ρ = density of the fluid (for water, 998 kg/m3, 1.94 slug/ft3)
Ec = elastic modulus of the conduit (GN/m2, Glb/ft2)
D = pipe diameter (mm, inch)
t = pipe thickness (mm, inch)
KR = coefficient of restraint for longitudinal pipe movement.
The constant KR takes into account the type of support provided for the pipeline. Typically, three cases are recognized with KR defined for each as follows (m is the Poisson’s ratio for the pipe material):
Case a: The pipeline is anchored at the upstream end only.
KR = 1 – m / 2
Case b: The pipeline is anchored against longitudinal movement.
KR = 1 – m2
Case c: The pipeline has expansion joints throughout.
KR = 1
The following table provides physical properties of common pipe materials.
Table 3-8: Physical Properties of Common Pipe Materials
|Material||Young’s Modulus (Ec)||Poisson’s Ratio, μ|
|Asbestos Cement||23 – 24||0.53 – 0.55||–|
|Cast Iron||80 – 170||1.8 – 3.9||0.25 – 0.27|
|Concrete||14 – 30||0.32 – 0.68||0.1 – 0.15|
|Reinforced Concrete||30 – 60||0.68 – 1.4||–|
|PVC||2.4 – 3.5||0.055 – 0.08||0.46|
|Steel||200 – 207||4.57 – 4.73||0.30|