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In the case of our kit inside the barrel, the average density of the barrel has increased. The barrel will float a bit lower in the water (ie. it is now less buoyant)

In an extreme case – if I partly filled the barrel with lead, it would sink – i.e. negative buoyancy.

My guess is that this effect is not very significant if you are talking about a sleeping bag, but probably would be if you stuff the barrel with essentials like tins of beer and bottles of whisky.