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Mr. Borosky
Physics Section 13.3 Notes
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Section 13.3 Fluids at Rest and in Motion
Objectives
Relate Pascal’s principle to simple machines and occurrences.
Apply Archimedes’ principle to buoyancy.
Apply Bernoulli’s principle to airflow.
Read intro paragraph p. 352
FLUIDS AT REST
If you have ever dived deep into a swimming pool or lake, you know
that your body, especially your ears, is sensitive to changes in
pressure.
You may have noticed that the pressure you felt on your ears did not
depend on whether your head was upright or tilted, but that if you
swam deeper, the pressure increased.
Ideal Fluid – fluid with no internal friction among the particles.
Blaise Pascal – a French physician, that noted that the shape of a
container had no affect on the pressure at any given depth. He was
the first to discover that any change in pressure applied to a
confined fluid at any point is transmitted undiminished throughout the
fluid.
Pascal’s Principle – pressure applied to a fluid is transmitted
undiminished throughout it. Every time you squeeze a tube of
toothpaste you use Pascal’s Principle.
Pascal’s Principle is applied in the operation of machines that use
fluids to multiply forces, as in hydraulic lifts.
p1 = F1 / A1
and
p2 = F2 / A2
Since pressure is transmitted without change p2 is the same as p1.
So
F1 / A1 = F2 / A2
or
F2 = F1*A2 / A1
Do Practice Problem # 23 p. 353
F1 / A1 = F2 / A2
or
F2 = F1*A2 / A1
1600 / 1440 = F / 72
F = 1600(72) / 1440
80 N = F
F = 80 N
Physics Principals and Problems © 2005 Started 2006-2007 School Year
Mr. Borosky
Physics Section 13.3 Notes
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SWIMMING UNDER PRESSURE
When you are swimming, you feel the pressure of the water increase as
you dive deeper.
This pressure is actually a result of gravity; it is related to the
weight of the water above you.
The deeper you go, the more water there is above you, and the greater
the pressure.
Pressure Of Water on a Body – the pressure that a column of water
exerts on a body is equal to the density of water times the height of
the column times the acceleration due to gravity.
P = ρhg
(ρ is small Greek letter rho)
That formula works for all fluids.
The pressure of a fluid on a body depends on the density of the fluid,
its depth, and g.
Buoyant Force – is equal to the weight of the fluid displaced by the
object, which is equal to the Density of the fluid in which the object
is immersed multiplied by the object’s volume and the acceleration due
to gravity. It is the upward force on an object immersed in fluid.
Fbuoyant = ρVg ; Buoyant Force = Density times Volume times gravity
Archimedes – Greek scientist that found the relationship that the
buoyant force has a magnitude equal to the weight of the fluid
displaced by the immersed object.
Archimedes’ Principle – states that an object immersed in a fluid is
buoyed up by a force (or has an upward force) equal to the weight of
the fluid displaced by the object. It is important to note that the
buoyant force does not depend on the weight of the submerged object,
only the weight of the displaced fluid.
If you want to know whether an object sinks or floats, you have to
take into account all of the forces acting on the object.
The buoyant force pushes up, but the weight of the object pulls it
down.
The difference between the buoyant force and the object’s weight
determines whether an object sinks or floats.
Go over the Sink or Float? Example p. 354-355
Physics Principals and Problems © 2005 Started 2006-2007 School Year
Mr. Borosky
Physics Section 13.3 Notes
Page 3 of 3
An object will float if its density is less than the density of the
fluid in which it is immersed.
Ships can float because the hull is hollow and large enough so the
average density of the ship is less than the density of water. You
can notice that a ship filled with cargo will be submerged more than a
ship with no cargo.
Example 3 p.
a. Fbuoyant =
Fbuoyant =
Fbuoyant =
356
ρVg
1000(.001)(9.8)
9.8 N
b. Fg = mg = ρVg
Fg = 2700(.001)(9.8)
Fg = 26.46 N
Fapparent = Fg – Fb
Fa = 26.46 – 9.8
Fa = 16.66 N
Skip Practice Problems p. 356
FLUIDS IN MOTION: BERMOULLI’S PRINCIPLE
Bernoulli’s Principle – states that as the velocity of a fluid
increases, the pressure exerted by that fluid decreases. Or when a
fixed quantity of fluid flows, the pressure is decreased when the
velocity increases.
There are many common applications of Bernoulli’s principle, such as
paint sprayers and perfume bottles.
A gasoline engine’s carburetor, which is where air and gas are mixed,
is another common application of Bernoulli’s principle.
Part of the carburetor is a tube with a constriction, as shown in
figure 13-16b.
Streamlines – lines representing the flow of fluids around objects.
Skip 13.3 Section Review
Physics Principals and Problems © 2005 Started 2006-2007 School Year