# Buoyancy and non-horizontal water

With horizontal water and downwards gravity, buoyancy pushes upwards. However, in which direction is it pushing (say a boat) when the gravity is downwards but the boat is on a non-horizontal ground with water flowing down ? Is the bouyancy still pushing in the opposite direction of the gravity or along the normal of the water plane ? (Regardless of drag forces). Thank you.

Interesting question. I think this is the answer: In the case where water is flowing downhill and the surface of the water is slanted (not perpendicular to gravity), the buoyancy force acting on the boat from the water would be perpendicular to the water surface, and not parallel with gravity. This will result in a net force on the boat in the downhill direction, so the boat (and the water) will accelerate. Eventually (assuming a finite depth of of the river or whatever is channeling the water) viscosity of the water will limit it's velocity so that it doesn't speed up forever; and the water will in turn drag on the boat, creating a balancing force that limits the boat's downhill velocity to some finite value.

• Thanks for your answer. I've tried to see what it does with the buoyancy being in the opposite direction of the gravity, and as it could be expected, the boat wasn't going down along the water plane. So I guess you're right, it should be along the normal of the water plane. Nov 23, 2017 at 9:32

Think of it this way. In a non-accelerating reference frame, gravity is the only acceleration that creates body forces that balance the pressure force of buoyancy - created by the so called 'displaced' volume - the volume that is cut off below water by the water plane.

But if the body of water that supports the vessel is in a moving, accelerating frame, that acceleration adds with gravity to create a new net acceleration - probably in a different direction. Same equilibrium applies for this new acceleration as for the first case, gravity by itself.

At static equilibrium the buoyant force vector is colinear with the body force vector that both act through the center of pressure (buoyancy) and center of mass, equal to one another but in opposite directions.

But if you roll or pitch the vessel, the forces are no longer colinear. This creates a moment that causes the ship to oscillate. If it's stable, it settles back to the equilibrium condition. If not - watch out.

• Thanks for your help. I'm coding a video game that simulates buoyancy and drag, but not water flow (that would be overkill), so the water doesn't actually flow and push the boat, it only resists to the boat movements. So my questio was only about buoyancy alone, ignoring other forces. After some experimenting it seems like the buoyancy has to push along the normal of the water plane. Nov 23, 2017 at 9:37
• That's right and the water plane at steady state aligns itself with net acceleration Nov 23, 2017 at 18:48