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With 9 blades that are in a slanting axis so that they roughly follows a spiral around the center, would this device be similar to a pump, and turn (rotate) and gently pump the water down along the central axis as it contracts and squeezes itself together?

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If it is primed so there is a stablished flow of water down with enough momentum, yes it will rotate while contracting and expanding acting like a fish swimming and will generate either pressure down to pump a central flux of water or will start to move up if free to move.

A fish swinging its tail to left and right, or up and down, creates propulsion and moves forward, by riding its own wake, as opposed to steering.

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