Fluids
I. Pascal’s Principle
A change in pressure applied to an enclosed fluid is
transmitted undiminished to every point of the fluid and to
the walls of the container.
A. Submarine Example
The first term in our previous work demonstrates Pascal’s
principle. The pressure applied by air on the surface of the
water, P0, is transferred to the submarine at any depth. The
second term is the increase in pressure due to the weight of
the water above the submarine pushing down upon the
submarine and the water surrounding the submarine.
For the submarine, we see that the pressure is applied at all
points around the submarine in order to ensure that the net
external force is zero (i.e. it is not accelerating). We
neglected this in our previous FBD work in order to simplify
the drawing. For the submarine, the pressure would need to
be greatest at the bottom since it must hold up the weight of
the submarine and the submarine has a finite size. Our
previous work suggests that this extra pressure must be the
second term in our equation which only depends on the
fluid!! This will lead us in the next section to Archimedes’s
principle which was known hundreds of years before Pascal’s
principle.
