Should not be possible if a river runs through the city. Why would there be a water shortage if the people can get water from the river?
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Water Shortages
- Thread starter niallmcfc
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A few animal carcasses and other filth in the upstream and you will have undrinkable water. Simple as that.
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"Water shortage" doesn't mean "no water". California is currently in a "severe drought", but they keep growing almonds. There's just much, much less water to go around.
I think in the 600+ years that siege tactics had been in use before the EU4 timeframe, it think siege engineers would have figured out how to deal with a river 
Try to visit a City in India and drink from the river running trough the city, I dare you.
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You'd probably end up drinking the remains of the people who died in the siege.