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We were solving this question, then the instructor mentioned like Buoyancy force is due to pressure difference, what does pressure difference has to do with upward force?
Upward force should be the weight of the liquid displaced by object, where did pressure came from?

Edit: When someone mentions $F_B$ what should I assume? is it Buoyancy or Buoyant force?

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Upward force should be the weight of the liquid displaced by object, where did pressure came from?

Mathematically the buoyant force is equal in magnitude to the weight of the displaced fluid, but that's not the main reason for buoyancy. If you had a container of water in deep space with no gravitational influence and you put an object in the water so that it displaces the water there would actually be no buoyant force.

The pressure comes from considering the fluid in a gravitational field. The weight of fluid above pushes on fluid below, so as you go deeper into the fluid in the direction of the gravitational force the pressure becomes greater. The buoyant force on an extended object exists in a fluid in a gravitational field because the pressure at the bottom of the object is larger than the pressure on top.

One can show that because of this Archimedes principle holds, but it's just a consequence, not the reason behind the buoyant force.

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Technically, when an object is immersed in a liquid it experiences an upward force known as Buoyant Force. This phenomenon of experiencing an upward force is known as Buoyancy.

The origin of the buoyant force is actually pressure difference. Think of a cylindrical object fully submerged vertically in a liquid in a gravitational field.

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The liquid exerts pressure on the walls of the object. The force exerted by the liquid on the object is always perpendicular to the surface. The forces on the vertical surface cancel each horizontal force. But the upper and lower flat surfaces of the cylinder experience different forces due to pressure. Since the pressure in a liquid is given by $h\rho g$, greater the depth, greater the pressure. So the upper surface feels a downward force while the lower surface feels more upward force. Overall, there will be a net upward force on the object. That is what called bouyant force.

Upward force should be the weight of the liquid displaced by object

This is a special coincidence discovered by Archimedes.

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    $\begingroup$ Note that the fluid has to be in a gravitational field. $\endgroup$ Aug 27, 2021 at 11:04
  • $\begingroup$ @ACB consider this image, then can we say $F_B = (P_{N})a^2-(P_U)a^2$? since $Pressure = \frac{force}{area}$? $\endgroup$ Aug 31, 2021 at 1:40
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    $\begingroup$ @Rambalheartremo Yes, you can derive the equation for buoyant force from there. $\endgroup$
    – ACB
    Aug 31, 2021 at 2:40

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