# Water Hammer Modeling for Water Networks via Hyperbolic PDEs and Switched DAEs

## Abstract

In water distribution network, instantaneous changes in valve and pump settings introduce jumps and sometimes impulses. In particular, a particular impulsive phenomenon which occurs due to sudden closing of valve is the so-called water hammer. It is classically modeled as a system of hyperbolic partial differential equations (PDEs). We observed that under some suitable assumptions the PDEs usually used to describe water flows can be simplified to differential algebraic equations (DAEs). The idea is to model water hammer phenomenon in the switched DAEs framework due to its special feature of studying such impulsive effects. To compare these two modeling techniques, a system of hyperbolic PDE model and the switched DAE model for a simple setup consisting of two reservoirs, six pipes, and three valves is presented. The aim of this contribution is to present results of both models as motivation for the claim that a switched DAE modeling framework is suitable for describing a water hammer.

## Keywords

Water hammer Solution theory Switched system Dirac impulse## Notes

### Acknowledgement

We are thankful to Jochen Kall for fruitful discussions concerning the PDE simulations of earlier versions of this work.

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