Advanced Physics
Chapter 10
Fluids
Chapter 10 Fluids
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10.1 Density and Specific Gravity
10.2 Pressure in Fluids
10.3 Atmospheric and Gauge Pressure
10.4 Pascal's Principle
10.5 Measurement of Pressure
10.6 Buoyancy and Archimedes’ Principle
10.7 Fluids in Motion
10.8 Bernoulli’s Principle
10.9 Applications of Bernoulli’s Principle
10.10 Viscosity
10.11 Flow in Tubes
10.12 Surface Tension and Capillarity
10.13 Pumps; the Heart and Blood Pressure
10.1 Density and Specific Gravity
Four phases of matter
(each with different
properties)
 Solid
 Liquid
 Gas
 Plasma
Fluids are anything
that can flow so
they are ?
10.1 Density and Specific Gravity
Density- how compact an
object is
 Ratio of mass to volume

 = m/V
Many units for density
Specific Gravity- ratio of
the density of a
substance to the
density of a standard
substance (usually
water)
• No units (Why?)
•
10.2 Pressure in Fluids
Pressure—a force
applied per unit area

P = F/A

Units Pascal (N/m2)
10.2 Pressure in Fluids
Important properties of fluids at rest:
 Fluids exert a pressure in all directions
 The force always acts perpendicular to
the surface it is in contact with
 The pressure at equal depths within the
fluid is the same
10.2 Pressure in Fluids
Pressure variation with
depth

P = F/A = gh
Change in pressure
with change in
depth

P = gh
10.3 Atmospheric and Gauge
Pressure
Atmospheric
Pressure (PA)—the
pressure of the
Earth's atmosphere
at sea level
 1atm = 101.3kPa =
14.7 lbs/in2 = 760
mmHg
10.3 Atmospheric and Gauge
Pressure
Gauge Pressure (PG)—
the pressure measured
on a pressure gauge
 Measures the pressure
over and above
atmospheric pressure
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P = PA + PG
P = Absolute pressure
10.4 Pascal's Principle
Pascal's Principle
states that pressure
applied to a
confined fluid
increases the
pressure throughout
by the same amount
 Example: hydraulic
lift
10.4 Pascal's Principle
Pascal's Principle
Example: hydraulic lift
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Pin = Pout
Fout/Aout =
Fin/Ain
Fout/Fin =
Aout/Ain
Fout
Fin
10.5 Measurement of Pressure
Manometer—tubular
device used for
measuring pressure
To measure pressure
with a manometer
remember the Jenke
quote “Nothing
sucks in Science it
just blows”
10.5 Measurement of Pressure
Manometer—tubular
device used for
measuring pressure
Types:
 Open-tube
manometer
 Closed-tube
manometer
(barometer)
10.5 Measurement of Pressure
Open-tube
manometer
 both ends of tube
are open; one is
connected to the
container of gas and
the other is open to
the atmosphere
GAS
10.5 Measurement of Pressure
Open-tube
manometer
 P = Po + gh
Where:
 P = pressure of gas
 Po = atmospheric
pressure
 gh = pressure of
fluid displaced
GAS
10.5 Measurement of Pressure
Closed-tube
manometer
 one end of tube is
open; one is
connected to the
container of gas is
open and the other
is sealed
GAS
10.5 Measurement of Pressure
Closed-tube
manometer
 P = Po + gh
 But since it is closed
Po = 0 so…..
 P = gh
GAS
10.5 Measurement of Pressure
Barometer-closed-tube
manometer inverted in
a cup of mercury used
to measure atmospheric
pressure
 P = gh
 Where  is the density
of mercury (13.6 x 103
kg/m2)
10.6 Buoyancy and Archimedes’
Principle
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Objects submerged
in a fluid appear to
weigh less than they
do outside the fluid
Many objects will
float in a fluid
These are two
examples of
buoyancy
10.6 Buoyancy and Archimedes’
Principle
Buoyant force—the
upward force
exerted on an object
in a fluid.
 It occurs because
the pressure in a
fluid increases with
depth
10.6 Buoyancy and Archimedes’
Principle
Buoyant force (FB)
 The net force due to the
force of the fluid down
(F1) and up (F2)
 FB = F2 – F1
 Since F = PA =FghA
 FB = FgA(h2—h1)
 FB = FgAh = FgV
h2
h1
F1
h=h2-h1
F2
10.6 Buoyancy and Archimedes’
Principle
Archimedes’ Principle
 The buoyant force on a
body immersed in a
fluid is equal to the
weight of the fluid
displaced by that object
 FB = FgV = mFg
 To be in equilibrium the
weight of object must
be the same as the
weight of fluid displaced
so that it is equal and
opposite FB
FB
Wt = mg
10.6 Buoyancy and Archimedes’
Principle
Archimedes’ Principle
 So when an object is
weighed in water its
apparent weight (in
fluid, w’) is equal to its
actual weight (w) minus
its buoyant force (FB)
 w’ = w – FB
 w/(w—w’) = o/ F
FB
Wt = mg
10.6 Buoyancy and Archimedes’
Principle
Archimedes’ Principle
 Also relates to objects
floating in fluid
 Object floats in a fluid if
its density is less than
the density of the fluid
 The amount submerged
can be calculated by
 Vdispl/Vo = o/ F
FB = FVdisplg
W= mg=oVog
10.7 Fluids in Motion
Fluid Dynamics
(Hydrodynamics)
 The study of fluids in
motion
Two types of fluid flow:
 Streamline (laminar)
flow--particles follow a
smooth path
 Turbulent flow—small
eddies (whirlpool-like
circles) form
10.7 Fluids in Motion
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Turbulent flow
causes an effect
called viscosity due
to the internal
friction of the fluid
particles
10.7 Fluids in Motion
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Lets study the
laminar flow of a
liquid through an
enclosed tube or
pipe
Mass Flow rate is
the mass of fluid
(m) that passes a
given point per unit
time (t)
l1
l2
v1
v2
A1
A2
10.7 Fluids in Motion
Mass Flow rate
 The volume of fluid
passing through area A1
in time t is just A1 l1
l1
where l1 is the
distance the fluid moves v
1
in time t.
 Since the velocity of
fluid passing A1 is v =
l1/ t, the mass flow
rate m1/ t through
A1
area A1 is
 m1/ t = 1A1v1
l2
v2
A2
10.7 Fluids in Motion
Mass Flow rate
 m1/ t = 1A1v1
 Since what flow
through A1 must
also flow through A2
then
 m1/ t = m2/ t
 So
 1A1v1 = 2A2v2
l1
l2
v1
v2
A1
A2
10.7 Fluids in Motion
Mass Flow rate
 1A1v1 = 2A2v2
 Since for most fluids
density doesn’t change
(too much) with an
increase in depth so it
can be cancelled out.
 Equation of continuity
 A1v1 = A2v2
 [Av] represents the
volume rate of flow
V/t of the fluid
l1
l2
v1
v2
A1
A2
10.7 Fluids in Motion
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Since the volume
rate of flow V/t
of the fluid is the
same in all parts of
the pipe the velocity
through smaller
diameter sections
must be greater
than through larger
diameter sections
l1
l2
v1
v2
A1
A2
10.8 Bernoulli’s Principle
Bernoulli’s Principle—
where the velocity of a
fluid is high, the
pressure is low and
where the velocity is
low the pressure is
P1
high.
 This makes sense; if the
pressure was larger at
A2 then it would back
up fluid in A1 so its slow
down from A1to A2 but
it actually speeds up.
l1
l2
v1
v2
A1
A2
P2
10.8 Bernoulli’s Principle
Bernoulli’s Equation
(derivation in Book)
2
 P1 + 1/2v1 + gy1 =
P2 + 1/2v22 + gy2
 Or
 P + 1/2v2 + gy =
constant
 This is based on the
work needed to move
the fluid from Part 1 to
Part 2 of the tube.
l2
A2 P2
l1
V1
P1
A1
y2
y1
V2
10.9 Applications of Bernoulli’s
Principle
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Special cases of Bernoulli’s
Equation:
Liquid flowing out of an
open container with a
spigot at the bottom
Since both P’s are
atmospheric pressure and v1
v2 is almost zero
1/2v12 + gy1 = gy2
v1 = (2g(y2 – y1))1/2
V2 = 0
Y2 – y1
10.9 Applications of Bernoulli’s
Principle
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Special cases of
Bernoulli’s Equation:
Liquid flowing but there
is no appreciable change
in height
P1 + 1/2v12 = P2 +
1/2v22
Example: your Physics
toy
Read and Write Worksheet
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Read Sections 10.10
–10.13
Answer the
questions written on
½ sheet of paper