Clicker Question
Room Frequency BA
Cube A has edge length L and mass M. Cube B has edge
length 2L and mass 4M. Which has greater density?
A) A has larger density
B) B has larger density
C) A and B have the
same density.
Cube A has larger density. ρA = M/L3 , ρB = (4M)/(2L)3 = (1/2)M/L3 so
object A has twice the density of object B.
1
Announcements
• CAPA assignment #12 is due on Friday at 10 pm.
• Next week in Section: Assignment #6
• Finish reading Chapter 10 on Fluids
• Midterm 3 scores are uploaded on CU Learn. Solutions
are posted on CULearn. Rough grade scale is
Average = 62.2 out of 100
Stan. Dev. = 17.3
A range (80-100)
B range (60-80)
C range (45-60)
D range (30-45)
F range (0-30)
2
Fluid Density
We imagine that the volume V is completely filled with some
“continuous” substance. We measure the mass m and the
volume V then calculate the mass density ρmass as m/V.
Gases: Compressible (expand or compress)
Liquids: Often nearly incompressible
We’ll typically assume, for a given
substance, that the mass density is the
same everywhere in side the fluid! This is a
good assumption for statics.
SI Units are kg/m3 =1000 g/cm3
3
Specific Gravity
Another common and useful measure
of density is the specific gravity (SG).
X
Specific Gravity (SG) of substance X 
Water
SGWater = 1
SGIron = 7.9
SGPb = 11.9
SGIce = 0.92
SGAlcohol= 0.79
No “visible” units because it is a ratio!
4
Back to square 2: Fluid “Forces”
When we try to apply Newton’s Laws to Fluids what do we use
for the force?
Again we consider a “small” imaginary volume or box
inside the body of fluid.
To find the force on the imaginary
volume V, we use the concept of
pressure. We find the force F on
each side of the volume V and
divide the magnitude of that force
by the area A of that side. The
pressure P is then F/A
r
Fon side of V
Pat side of V 
Aof side V
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Units of Pressure
Pat side of V 
r
Fon side of V
Aof side V
SI Units of Pressure: N/m2 = 1 Pascal (Pa)
English Units of Pressure:
lb/in2 = 1 pound per square inch (psi)
How do these unit compare in size?
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Room Frequency BA
Clicker Question
Approximately(!) what is 1 psi in the SI unit Pa? (1 lb = 4.45 N)
A)
B)
C)
D)
E)
5
200
7000
4 x 104
1 x 105
Both force and area units have to be converted!
2
lb 5 N  40 in 
N
Guess estimate 1 2 
g
 8000 2

in
lb  1 m 
m
2
lb 4.45 N  39.4 in 
N
Accurate Calculation 1 2 
g
 6910 2

 1m 
in
lb
m
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Atomic View of Fluid Pressure from Air
Air consists mostly of oxygen and
nitrogen molecules. At room
temperature, the molecules have
thermal energy and are moving
around rapidly (speed ≈ 400 m/s),
colliding with each other and with
every exposed surface. The
pounding of the air molecules on a
surface, like the pitter-pat of rain
on the roof, adds up to a large
force per area: Patm = 14.7 psi.
In a later chapter we’ll calculate the force on the walls directly
from these atomic collisions!
8
Too Many Units of Pressure!
The most common pressure in everyday life is that
coming from the atmosphere (at sea level) !
1 atmosphere = 1 atm = 14.7 psi
= 1.013 x 105 Pa
= 1.013 bar
= 760 torr
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Clicker Question
Room Frequency BA
The air pressure inside the Space Station is P = 12 psi. There are
two square windows in the Space Station: a little one and a big
one. The big window is 30 cm on a side. The little window is 15
cm on a side. How does the pressure on the big window compare
to the pressure on the little window?
A) same pressure on both windows
B) 2 times more pressure on the big window
C) 4 times more pressure on the big window
D) 9 times more pressure on the big window
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Clicker Question
Room Frequency BA
The air pressure inside the Space Station is P = 12 psi. There are
two square windows in the Space Station: a little one and a big
one. The big window is 30 cm on a side. The little window is 15
cm on a side. How does the total force on the big window
compare to the total force on the little window?
A) same force on both windows
B) 2 times more force on the big window
C) 4 times more force on the big window
D) 9 times more force on the big window
F = P*A
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Direction of Fluid Forces
Newton’s law deals with forces which are vectors! What is the
direction of the force from fluid pressure?
For static fluids (no flow) the force is perpendicular to the
surface of the side.
In the figure you see arrows for
the force on each side of an
imaginary cube of volume V.
Critical point: Pressure does not have any
direction; the direction of the force from
pressure depends on the orientation of the
surface the pressure acts on.
12
Is 15 psi a big pressure?
Yes!!!
We are normally unaware of this because forces on us are balanced.
Here are two video examples and a demo!
13
Applying Outside Pressure to a Fluid
Pascal’s Principle: If an external pressure is applied to a
confined fluid, the pressure at every point within the fluid
increases by that amount.
POUT  PIN
FOUT
FIN

AOUT AIN
FOUT
 AOUT 

FIN

 A 
IN
Example: Hydraulic lift
14
Pressure in Fluids on a Planet I
For our first application of Newton’s 2nd Law on Fluids, let’s
consider the result of gravity on the pressure in a fluid.
Consider an imaginary cube with each side of area A, the
top at the surface and the bottom at depth h.
Patm
Each of the six faces contributes to
the net force!
Four side faces cancel each other;
what about top and bottom faces?
Fnet = Ftop + Fbottom = 0
Fnet = -PatmA + PhA - Mwaterg = 0
Ph
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Pressure in Fluids on a Planet II
Fnet = -PatmA + PhA - Mwaterg = 0
Ph A  Patm A  M Water g
Patm
M Water g
Ph  Patm 
A
Ph  Patm 
Water (Ah)g
A
 Patm  Water hg
Ph
Pressure increases linearly with depth, proportional to g and ρ!
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More on Gravity and Pascal’s Principle
Ph  Patm  Water hg
Pressure only depends on the depth; at
a given depth the pressure is the same.
Often people leave out the Patm, but if you want
the total, absolute pressure, you must include it.
Gauge Pressure is the amount of pressure after subtracting Patm
How do you know what kind of gauge you are reading?
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Example. At the surface of a swimming pool the
pressure on a swimmer is due to air: Patm = 1 atm. At
what depth in the pool will the pressure be 2 atm?
Ph  Patm   gh
Ph  Patm
h
g
1 atm ~ 105 Pa
2x10 1x10 Pa
h
 10 m
3
2
(1000kg/m )(10 m/s
5
5
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Clicker Question
Room Frequency BA
As shown, two containers are
connected by a hose and are filled
with water. Which picture correctly
depicts the water levels?
Different depths would give different
pressures! The net force on the fluid
at the connection tube would not be
zero and there would be flow!
P   gh
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