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I have always used buoyant force as acting upwards in any problem related to fluid mechanics that I have solved. Also, if we push a mug down a bucket of water. It rises up, always, not diagonally even if it is pushed diagonally inside. Does buoyant force always act upwards? If yes, how is it consistent with Newton's Third Law?

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  • $\begingroup$ What makes you thinking it may violate the Third Law? $\endgroup$
    – user115350
    May 15 '16 at 1:13
  • $\begingroup$ Sorry. I meant. If I push a mug diagonally, it comes back in upward direction, Therefore net force is acting upwards whereas my force was acting diagonally. $\endgroup$
    – Quark2
    May 15 '16 at 2:16
  • $\begingroup$ Concerning the Newton's 3rd Law part of the question. I do a demo for the students in my intro classes. I put a beaker partial full of water on a balance and adjust the weights until it balances. Then I suspend a small weight from a wire and lower it the water without letting it touch the glass. What happens is instructive. $\endgroup$ May 15 '16 at 3:08
  • $\begingroup$ I see. Carefully observing or perceiving the process, do you find it is more easy to move the mug horizontally than to move it vertically downwards? These are two components (vertical and horizontal) of the reaction force. And it does say (if nature can speak) that the reaction force is vertical, opposite to the buoyant force. $\endgroup$
    – user115350
    May 15 '16 at 4:37
  • $\begingroup$ Horizontal hydrostatic pressure force cancels out : physics.stackexchange.com/questions/196840/… $\endgroup$
    – Frobenius
    May 15 '16 at 6:32
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The buoyant force is directed against the pressure gradient, that is in the direction that the pressure decreases. If you define this direction as "upwards" then the buoyant force is due to the contact force difference between the lower (higher pressure and force) and upper (lower pressure and force) parts of the body. Regarding the third law, if the buoyant force is acting upwards on the body, the reaction is downwards in the fluid.

If your frame is accelerated this also causes a gradient of pressure. Check this video to see the diagonal buoyancy forces in action. This happens because the air inside the car has mass therefore inertia. When the car accelerate, the air gets denser in the direction contrary to the acceleration. This causes difference of pressure therefore a net force on the balloon.

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  • $\begingroup$ If my bucket was accelerated horizontally, would there be a diagonal buoyant force? $\endgroup$
    – Quark2
    May 15 '16 at 2:17
  • $\begingroup$ @Quark2 Please have another look, I tried to elaborate the answer. $\endgroup$
    – Diracology
    May 15 '16 at 2:34
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Buoyancy refers to the upward force exerted by a fluid against the weight exerted by an immersed object. The pressure difference between the top and bottom portion of the submerged object in the fluid causes this upward force. The pressure is the normal component of stress. That is, pressure is the normal force acting per unit area. Hence the force due to the net pressure acting upwards will be directed upwards through the center of gravity of the submerged object. The submerged object will have a force exerted downwards, normally, which is the weight of the body. The body displaces through the fluid for some distance until, the force on the body is balanced by the force due to the pressure acting on it upwards. At this point, the body cannot move further. When the applied force is released, there causes an unbalance on the immersed object and to counteract this, the object has to decrease the pressure by going up. Everything seems to be obeying Newton's third law.

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