Page 368 - Introduction to Continuum Mechanics

352 Equations Of Hydrostatics

Solution. Letpu and/?& be the pressure at the upper and the bottom surface of the cylinder.
Let Tbe the tension in the rope. Then the equilibrium of the cylindrical body requires that

That is,

Now, from Eq. (6.3.5)

Thus,

We note that the first term on the right hand side of the above equation is the buoyancy force
which is equal to the weight of the liquid displaced by the body.

Example 6.3.2
In Fig. 6.2, the weight W% is supported by the weight W^, via the liquids in the container.
The area under WR is twice that under W L. Find WR in terms of W^,pi,p2,A^h
<
(Pi Pi an( J assume no mixing).
Solution. Using Eq. (6.3.5), we have