Pressure | AP Physics B
Molecular Forces on a Submerged
Object
• Suppose a cubic box is
submerged in a fluid
• The fluid molecules move in all
directions, colliding with all
sides of the box
o With the millions of
molecules, probability
suggests that each side of
the cube will experience
an equal number of
collisions
Hydrostatic Pressure
• We previously discussed the
pressure due to molecular
collisions
• But, a fluid also has pressure due
to gravity – hydrostatic pressure
Hydrostatic Pressure in a Well
The gravitational pull on water in a deep well
produces hydrostatic pressure, which varies with
depth.
•
Box Submerged in a Fluid-Filled Cup
The rules of probability suggest that each side of
the cube will experience an equal number of
collisions (blue arrows).
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•
•
Collectively, these collisions
impose a force on the box
o The average force of
these molecules divided
by the area over which
that force is exerted
yields the fluid pressure
Favg
o
=P
A
o Favg = average force
A = area
P = fluid pressure
Pressure is commonly measured
in pascals (Pa)
Fluid pressure is also exerted on
the container walls, as molecules
collide there, too
•
•
At greater depths, there is a
greater volume of water above
being “pulled down”
o Thus, hydrostatic
pressure increases at
greater depths
Calculating hydrostatic pressure:
o P = ρgy
P = hydrostatic pressure
g = gravitational constant
y = depth at which you
are finding the pressure
Calculating hydrostatic pressure
of several stacked fluids:
Hydrostatic Pressure of Stacked Fluids
Suppose you needed to find the hydrostatic
pressure at the point circled in the blue layer.
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© 2017 J Co Review, Inc., Accessed by Guest on 06-16-2017
Pressure | AP Physics B
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First, find the hydrostatic
pressure at the bottom of the
green and orange layers
o P = ρgy
Use correct ρ and
y for each fluid
For the blue layer, we don’t set y
equal to the blue column’s height
o We don’t want the
pressure at the bottom
Instead, we set y equal to the
depth of the circle where we are
measuring the pressure
o Notice in the diagram that
y3 isn’t the depth of the
whole blue layer
Once you’ve found the
hydrostatic pressure for each
individual layer, add them
o This produces the total
hydrostatic pressure at the
circled point
A good example of a stacked
fluid is a well
o The atmosphere is a
gaseous fluid, and it is
stacked on top of the fluid
column of the well
o We needn’t calculate the
hydrostatic pressure of
the atmosphere
Near ground level,
it’s constant at
101,000 Pa
o We’d add this 101,000 Pa
to the hydrostatic
pressure at a point in the
well to get the total
hydrostatic pressure at
that particular depth
(a)
(b)
(c)
Three Containers of Different Depths
Though the containers are shaped differently,
their liquids have the same density and depth.
Thus, the pressure at the bottom of each will be
the same, according to P = ρgy.
•
Though the above three
containers have the same
pressure at the bottom, their
forces will differ
Favg
o Recall that P =
A
o We already deduced that
P is the same for all three
containers
Since (a) has a
larger area at the
bottom, it will
experience a
larger force there
(c), with a smaller
area at the bottom,
experiences a
smaller force there
Container Shape
• Since hydrostatic pressure is
related only to ρ, g, and y,
container shape doesn’t affect P
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© 2017 J Co Review, Inc., Accessed by Guest on 06-16-2017