# Will buoyant force change if the container is accelerated up or down?

If we have a fluid which is in a container that is accelerated, say, upward by $$a$$. Then, what will be the buoyant force on an object with volume $$V$$, Density of liquid, $$\rho$$?

I believe it will be $$V \rho(g+a).$$ Am I right, or have I confused it with pseudo force? Can you please give a suitable explanation?

Archimedes' principle tells us that the upthrust on a body immersed in a fluid is equal to the weight of the fluid displaced, where the weight is the force given by $F = ma$ i.e. the mass of fluid displaced, $m$, multiplied by the acceleration, $a$, experienced by the fluid.

In this context there is no difference between gravitational acceleration and inertial acceleration - this is one example of Einstein's equivalence principle - so:

$$a = a_{gravity} + a_{inertial}$$

And the upthrust is therefore:

$$F = m (a_{gravity} + a_{inertial}) = V \rho (a_{gravity} + a_{inertial})$$

as you said in your question.

• Thanks! But now, if we take the time frame in consideration, archimedes was wrong in saying that wasn't he? Since at his time, Equivalence Principle was not given... – Saurabh Raje Jan 20 '14 at 16:33
• @Rohinb97, take that! – Saurabh Raje Jan 20 '14 at 16:34
• @John Rennie will this thing be true in an horizontally accelerated container also,?? I don't think it will be ...right??...or am I missing something....or putting it in another way..does force of buoyancy also depend on the horizontal acceleration of the container ??...as after reading this ..I now understand that it depends on vertical acceleration ...but I am not so sure about horizontal acceleration..? – Freelancer Feb 5 '16 at 3:56
• @Freelancer: this would apply to horizontal acceleration as well. See for example Why does a helium filled ballon move forward in a car when the car is accelerating?. – John Rennie Feb 5 '16 at 6:03

Consider a small amount of water at the surface of mass m , then when m is accelerating upward with acceleration a then from Newton second law upward resultant force acting on m is :

buoyant force - m g = ma So buoyant force = m(a+g)

Buoyant force is actually force acting on immersed part of body due to all fluids surrounding the body and this arises due to difference in maximum and minimum pressures acting on body due to fluids around it.So when a container is accelerating upward then maximum pressure is at it,s lower surface and minimum pressure is at its top surface. I am attaching a solution .If I am wrong then give suggestions 