Will horizontal acceleration of container affect the bouyant force? I am asking this because bouyancy is all due to pressure and in horizontal acceleration of container pressure at the same horizontal level becomes different at every point
 A: Buoyancy is defined as,

Fb=phg

Here, p is the density of the fluid,  h is the height of the submerged part of the object, g obviously is the gravitational acceleration of earth.
If we take p and 'g' to be constants then,

Fb is proportional to h

So if the horizontal acceleration doesn't effect h (which it doesn't in most cases) then buoyancy will not be effected i.e. it won't change.
A: The bouyant force acts in the vertical direction. A force applied in the horizontal direction should not affect the buoyant force since the two forces are orthogonal.
On the the other hand, I suppose it may be possible for the horizontal force to create aerodynamic "lift" depending on the shape of the object, whether the object is floating fully submerged (density of object and fluid being equal), and whether or not there is a relative velocity between the fluid and surfaces of the object. But I don't know.
Hope this helps.
A: With many boats, a high speed can provide lift which greatly reduces the amount of water being displaced.  Boats with “foils” can be lifted clear out of the water.
A: Yes
If you accelerate a container of liquid, that acceleration will alter both the magnitude and direction of the buoyant force in that liquid.
For example, if gravity is a vertical acceleration of -9.8 m/s^2 and you add a +9.8 m/s^2 to the right, then the new buoyant force will be at 45° up and to the right and increased by a factor of $\sqrt{2}$. In general the buoyant force would be:
$$
\vec F = (\vec a + g \hat y ) \rho h
$$
Note that the height of the fluid, $h$, will no longer be measured from the vertical height but instead to the new surface level of the fluid, which is inclined by the same angle as the new acceleration makes to gravity.
