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Gas in European pipeline systems is measured in kWh (not in m³ or kg), because it's the energy in the gas that we're after. Hence the funny unit.

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Sure, but they why kWh/h instead of kW? If you're inclined to measure the quantity of gas in terms of its energy, why not measure its flow in terms of power? (of course kWh/h _is_ power, but why denote it so strangely?)

This conveys the state of the mind, what's important. A more clear example is car mileage, which is expressed in l/(100 km), but can be shortened to area unit like mm² (and it even has a physical interpretation: https://what-if.xkcd.com/11/), but that's not what we need to know (how much mm² of petrol your car burns?).

Similarly, we don't need power of the transfer of the gas, we need to know how much gas gets exchanged, because it's priced per kWh, so removing h from each side actually makes things harder in another equation.

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