Chapter 9
Fluids
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Fluids
•  Fluids: Have the ability to flow.
•  A fluid is a collection of molecules
that are randomly arranged & held
together by weak cohesive forces & by
forces exerted by the walls of a
container.
Both liquids & gases are fluids
Fluid Mechanics
•  Two basic categories of fluid mechanics:
•  Fluid Statics
–  Describes fluids at rest
•  Fluid Dynamics
–  Describes fluids in motion
•  The same physical principles (Newton’s
Laws) that have applied in our studies up to
now will also apply to fluids. But, first, we
need to introduce Fluid Language.
Density and Specific Gravity
The density ρ of an object is its mass per unit
volume:
The SI unit for density is kg/m3.
Density is also sometimes given in g/cm3
To convert g/cm3 to kg/m3, multiply by 1000.
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(here’s why)!
3
3
1g
100 cm
1kg
kg
×
= 1000 3
3 ×
3
3
1cm
1m
1000g
m
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Density and Specific Gravity
The density ρ of an object is its mass per unit
volume:
The SI unit for density is kg/m3.
Density is also sometimes given in g/cm3
To convert g/cm3 to kg/m3, multiply by 1000.
Water at 4°C has a density of 1 g/cm3 = 1000 kg/m3.
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Density and Specific Gravity
The density ρ of an object is its mass per unit
volume:
The SI unit for density is kg/m3. Density is also
sometimes given in g/cm3; to convert g/cm3 to kg/
m3, multiply by 1000.
Water at 4°C has a density of 1 g/cm3 = 1000 kg/m3.
The specific gravity of a substance is the ratio of
its density to that of water.
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Density & Specific Gravity
•  Density, ρ (lower case Greek rho, NOT p!) of object, mass M
& volume V:
ρ ≡ (M/V)
(kg/m3 = 10-3 g/cm3)
•  Specific Gravity (SG): Ratio of density of a substance
to density of water.
where ρwater = 1 g/cm3 = 1000 kg/m3
(the actual value is 998 kg/m3 )
NOTE:
1. The density for a substance varies slightly with temperature, since
volume is temperature dependent
2. The values of densities for various substances are an indication of
the average molecular spacing in the substance. They show that
this spacing is much greater than it is in a solid or liquid
ρ = (M/V)
SG = (ρ/ρwater) = 10-3ρ
(ρ water = 103 kg/m3)
Specific Gravity
Definition : A ratio of the density of a
liquid to the density of water at
standard temperature and pressure
Unit: dimensionless.
Example
A reservoir of oil has a mass of 825 kg.
The reservoir has a volume of 0.917 m3.
Compute the density and specific gravity
of the oil.
• Solution:
•  Note:
⇒
ρ = (M/V)
Mass of body, density ρ, volume V is
M = ρV
⇒ Weight of body, density ρ, volume V is
Mg = ρVg
You will use these relationships frequently!
Forces in Fluids
•  To study fluids using Newton’s Laws, we
obviously need to talk about forces in fluids.
•  The only force that can be exerted on an object
submerged in a Static Fluid is one that tends to
compress the object from all sides
•  The force exerted by a Static Fluid on an object is
always perpendicular to the surfaces of the object
Pressure
One of most important applications of a fluid is
it's pressure- defined as a Force per unit
Area
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Pressure
Plays the role for fluids that force plays for solid objects
•  Consider a cross sectional area A oriented horizontally
inside a fluid. The force on it due to fluid above it is F.
•  Definition: Pressure = Force/Area
F is perpendicular to A
SI units: N/m2
1 N/m2 = 1 Pa (Pascal)
Pressure in Fluids
Pressure is defined as the force per unit area.
Pressure is a scalar; the units of pressure in the
SI system are pascals:
1 Pa = 1 N/m2
Pressure is the same in every
direction in a fluid at a given
depth; if it were not, the fluid
would flow.
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•  Consider a solid object submerged in a
STATIC fluid as in the figure.
•  The pressure P of the fluid at the level
to which the object has been submerged
is the ratio of the force (due to the fluid
surrounding it in all directions) to the area
•  At a particular point, P has the following
properties:
1. It is same in all directions.
2. It is ⊥ to any surface of the object.
If 1. & 2. weren’t true, the fluid would be in motion,
violating the statement that it is static!
Pressure in Fluids
Also for a fluid at rest, there is no
component of force parallel to any
solid surface – once again, if there
were, the fluid would flow.
(doesn’t happen)
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•  P is ⊥ for any fluid on a solid surface:
•  P = (F⊥ /A)
Pressure Variation with Depth
P = F/A = mg/A =(ρV)g/A =ρAhg/A=ρgh
P = ρgh
Notice the area A doesn’t affect the
pressure at a given depth!
Therefore, the pressure at equal
depths within a uniform liquid is the
same.
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Pressure in Fluids
The pressure at a depth h below the surface of
the liquid is due to the weight of the liquid above
it. We can quickly calculate:
This relation is valid
for any liquid whose
density does not
change with depth.
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Conceptual Example 1
When blood pressure is measured,
why must the jacket be held at the
level of the heart?
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Answer
If the blood pressure is measured at a
location h lower than the heart, the blood
pressure will be higher than the pressure at
the heart, due to the effects of gravity, by an
amount
.
Likewise, if the blood pressure is measured
at a location h higher than the heart, the
blood pressure will be lower than the
pressure at the heart, again due to the
effects of gravity, by an amount ρgh.
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Conceptual Example 2
Explain how the tube in the figure, known as a
siphon, can transfer liquid from one container to
a lower one even though the liquid must flow
uphill for part of its journey. (Note that the tube
must be filled with liquid to start with.)
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The pressure at the
surface of both
containers of liquid
is atmospheric
pressure.
The pressure in each tube would thus
be atmospheric pressure at the level
of the surface of the liquid in each
container.
The pressure in each tube
will decrease with height
by an amount ρgh.
Since the portion of the tube going
into the lower container is longer
than the portion of the tube going
into the higher container, the
pressure at the highest point on the
right side is lower than the pressure
at the highest point on the left side.
The pressure at a
given depth is
independent of the
shape of the vessel.
(Read more about this in your
book, pg.292-293)
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Conceptual Example 3
Three containers are filled with water to
the same height and have the same
surface area at the base; hence the water
pressure, and the total force on the base
of each, is the same. Yet the total weight
of water is different for each. Explain this
“hydrostatic paradox.”
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It can be explained using force diagrams
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Notice how the net y force components are
all balanced.
More Pressure Units
At sea level the atmospheric pressure is about
this is called one atmosphere (atm).
A N/m2 is the same unit as the Pascal.
Other useful pressure conversions:
1 atm = 101.3 kPa
1 torr = 1 mmHg = 133 N/m2
760 torr = 1 atm
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