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The performance of a combustion engine is essentially determined by the charge cycle, i.e. by the inflow of fresh air through the inlet pipe into the cylinder after a combustion cycle. The amount of air, exchanged during this process, depends on many factors, e.g. the number of revolutions per minute, the temperature, the engine and valve geometry. In order to have a tool in designing the engine one is interested in calculating this amount. The proper calculation would involve the solution of three-dimensional hydrodynamical equations governing the gas flow including chemical reactions in a complicated geometry, consisting of the cylinder, valves, inlet and outlet pipe. Since this is clearly too ambitious, we consider a simplified model.