This shower thought is pretty much the basis of Archimedes principle. The upwards force of buoyancy is equal and opposite to the weight of the displaced fluid. Just imagine an empty bathtub floating in the lake. Now imagine the tub in the bathroom filled to the same level that the lake tub was submerged. The force keeping the lake tub floating and the force of the weight of the bathroom tub (including the weight of the tub) are the same.

Huh, I just went looking for stock images to show this and til that apparently historical accounts say that the principle was discovered in the bathtub.