Develop an expression for buoyant force exerted by the fluid

Develop an expression for buoyant force exerted by the fluid on an immersed cube of side ‘a’ at a depth of ‘h’ from the free surface, where the side is parallel with the free surface.

Solution

Given, cube of side a

Volume of the cube V = a³

Let p_f denote the density of the fluid and g denote the acceleration due to gravity

By definition, buoyancy force = Weight of the fluid displaced by the cube

= p_f X (Volume of fluid displaced) X g

Volume of fluid displaced = Volume of the cube = a³ (since the fluid is incompressible)

Hence, buoyance force exerted by the fluid on the immersed cube of side a

F_B = p_f a³ g..............................(Answer)