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A multiple-scales asymptotic analysis is used to describe the attenuation of a water hammer pressure wave in the Brunone model of unsteady friction. The method is applied to water hammer caused by sudden valve closure in water reservoir pipelines. The analytical results explain the parametric dependence of the Brunone unsteady friction pressure-wave attenuation. It is also found that viscous head in an extended steady friction model may provide an alternative to the unsteady friction basis for increased attenuation in cases where the attenuation has a weak spatial dependence and is primarily time-dependent. All results are numerically verified using the method of characteristics.

Analysis of water hammer attenuation in the Brunone model of unsteady friction