Learning Goal
• To define a fluid.
• To distinguish a gas from a liquid

States of Matter
• Solids – definite volume, definite shape
• Liquids – definite volume, indefinite shape
• Gases – indefinite volume, indefinite shape
• (Also plasma and Bose-Einstein condensates but we don’t need to worry about those.)

What state of matter is glass?
1. Solid
2. Liquid
3. Gas
So lid
0% 0%
Li qu id
0%
G as

What state of matter is honey?
1. Solid
2. Liquid
3. Gas
So lid
0% 0%
Li qu id
0%
G as

The Nature of Fluids
Fluids:
• Liquids and Gases comprise the category of what we call fluids.
• Fluids exhibit certain characteristics that solids do not – they flow when subjected to shear stress

PROPERTIES OF STATIC FLUIDS

Learning Goal
• To use density to describe a fluid.
• To apply buoyant force to explain why some objects float or sink in a fluid.

Static Fluid Properties
• Density ( 
) = mass / volume
• Viscosity = internal resistance to flow
Note: Atmospheric pressure and temperature influence a fluid’s density and viscosity

Density
The density of an object is represented by:
Density = mass / volume
While this formula is familiar to us, we will use it in subsequent derivations.

Specific Gravity
• In order to have a constant comparison, we use specific gravity instead of density sometimes.
• Since water has a density of 1 g/mL or 1 x
10 3 kg/m 3 , we eliminate the units and call the number specific gravity.
• Ex. For iron which has a density of 7.86 g/mL, the specific gravity is 7.86 (or 7.86 as dense as water).

Which is more dense, a pound of feathers or a pound of bricks?
1. A pound of bricks
2. A pound of feathers
3. They are the same
0% 0% 0%
A
p ou nd
o f b ric ks
A
p ou nd
o f f ea th er s
T he y a re
th e s ame

Common Density
Misconceptions
• Let’s expel some common misconceptions about density.
• Refer to your worksheet for the following
Turning Point questions about whether the object will float or sink.

1. Sink
2. Float
A. (Refer to worksheet)
S in k
0% 0%
F lo at

1. Sink
2. Float
B. (Refer to worksheet)
S in k
0% 0%
F lo at

1. Sink
2. Float
C. (Refer to worksheet)
S in k
0% 0%
F lo at

1. Sink
2. Float
D. (Refer to worksheet)
S in k
0% 0%
F lo at

1. Sink
2. Float
E. (Refer to worksheet)
S in k
0% 0%
F lo at

1. Sink
2. Float
F. (Refer to worksheet)
S in k
0% 0%
F lo at

1. Sink
2. Float
G. (Refer to worksheet)
S in k
0% 0%
F lo at

1. Sink
2. Float
H. (Refer to worksheet)
S in k
0% 0%
F lo at

1. Sink
2. Float
I. (Refer to worksheet)
S in k
0% 0%
F lo at

1. Sink
2. Float
J. (Refer to worksheet)
S in k
0% 0%
F lo at

Buoyancy
• The upward force present when an object floats in a fluid, or feels lighter, is the buoyant force on the object.
• The weight of an object immersed in a fluid is the apparent weight of the object (versus the actual weight).
• Apparent weight = F
G
- F
B
(when sinking)

Floating Objects
• If, and only if, an object is floating on the surface:
– The buoyant force exerted by the fluid that is displaced is equal in magnitude to the weight of the floating object
• This is because when an object is floating, it is not moving up or down
– therefore the net force is zero and the buoyant force must equal the weight
F
B
 
F g , object

Archimedes’ Principle
F
Any object completely or partially submerged in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object
B

F g , fluid
 m fluid g
The hot air balloon rises because of the large volume of air that it displaces

Apparent Weight
• The apparent weight of an object is the net weight between the force of gravity and the buoyant force.
Apparent Weight= F net
= F
G
– F
B

The Red line

A boat has a mass of 8450kg. What is the minimum volume of water it will need to displace in order to float on the surface of pure water without sinking?
This is something you will have to think about with your cardboard boats!
Volume Displaced

If an object is sinking to the bottom of a glass of water, the buoyant force must be?
1. Equal to the Net
Force
2. Less than Fg
3. More than Fg
4. Equal to Fg
0% 0% 0% 0%
Eq ua l t o th e
N.
..
Le ss
th an
Fg
Mo re
th an
Fg
Eq ua l t o
Fg

What must be true for the buoyant force to be greater than gravitational force?
1. Object is floating continuously upward
2. Object is floating at the top of the fluid
3. Object is sinking
0% 0% 0%
O bj ec t i s f lo a.
..
O bj ec t i s f lo a.
..
O bj ec t i s s in k.
..

If a rock is completely submerged in a fluid, what must be true?
1. The volume of the displaced fluid = the volume of the rock
2. The weight of the rock = weight of the fluid that was displaced.
3. Both 1 and 2
4. None of the above
0% 0% 0% 0%
T he
vo lu me
o f .
..
T he
w ei gh t o f .
..
Bo th
1
a nd
2
N on e of
th e a b.
..

The apparent weight of an object in a fluid, F
B
– F g
, could also be called what?
1. Net Force
2. Tensional Force
3. Buoyant Force
4. Actual Weight
0% 0% 0% 0%
N et
Fo rc e
T en sio na l F or c..
.
Bu oy an t F or ce
A ct ua l W ei gh t

If a raft is floating and is partially submerged in a fluid, what must be true?
1. The volume of the displaced fluid = the volume of the raft
2. The weight of the raft = weight of the fluid that was displaced.
3. Both 1 and 2
4. None of the above
0% 0% 0% 0%
T he
vo lu me
o f .
..
T he
w ei gh t o f .
..
Bo th
1
a nd
2
N on e of
th e a b.
..

Archimedes Principle example
• A bargain hunter purchases a “gold” crown at a garage sale. After she gets home, she hangs the crown from a scale and finds its weight to be 7.84 N. She then weighs the crown while it is immersed in water, and the scale reads 6.86N. Is the crown made of pure gold?

Pressure in Fluids
• In solids, pressure is defined as the amount of force per unit area.
P = F/A
• Pressure occurs within fluids due to the constant motion of their molecules but it is more difficult to determine the area.

Common Pressure Units
• For example, standard atmospheric pressure is:
• 14.7 psi (pounds per square inch)
• 1.01 x 10 5 Pa (Pascal) = N/m 2
• 760 mmHg (millimeters mercury)
• 1 atm (atmosphere)

Pressure as a function of depth water dam

Which hole will have the water shoot out the furthest?
1. Top hole
2. Middle Hole
3. Bottom Hole
4. All will be equal 0% 0% 0% 0%
T op
h ol e
Mi dd le
H ol e
Bo tto m
Ho le
A ll w ill
b e e q.
..

Absolute and Gauge Pressure
• Absolute pressure = Atmospheric + Gauge
Pressure Pressure
• Atmospheric pressure is the pressure due to the gases in the atmosphere (always present)
• Gauge pressure is the pressure due to a fluid
(not counting atmospheric pressure)
• Absolute pressure is the total pressure

Ex. 3
• Calculate the absolute pressure at an ocean depth of 1,000m. Assume that the density of water is 1,025 kg/m 3 and that
P o
= 1.01 x 10 5 Pa.
What is the gauge pressure as well?

Pascal’s Principle

Pascal’s Principle
• Because force is directly proportional to area, one can vary the cross-sectional area to provide more force.
• Eg. Hydraulic brakes, car jacks, clogging of arteries

In order to use a lesser force to accomplish a difficult task, you should apply the force on the hydraulic cylinder with
1. Smaller radius
2. Larger radius
3.
Doesn’t matter
Sma lle r r ad iu s
0% 0% 0%
La rg er
ra di us
D oe sn
’t ma tte r

Ex. 2
• A car weighing 12000 N sits on a hydraulic press piston with an area of 0.90 m 2 .
Compressed air exerts a force on a second piston, which has an area of 0.20m
2 . How large must this force be to support the car?

Laminar versus Turbulent Flow
Laminar flow:
– Low velocity relative to fluid medium
– Streamline path
Turbulent flow:
– High velocity relative to fluid medium
– Irregular Flow (Eddy currents)

15-6

Ideal Fluids
• Laminar flow
• Nonviscous
• Incompressible
• Constant density and pressure
• All these characteristics must be true for these equations to hold true. (Hence, the name for the ideal gas laws.)

Fluids in Motion
• Steady, Laminar Flow (Ideal Fluid) :
-Every fluid particle passing trough the same point in the stream has the same velocity.

Flow Rate
• Flow rate stays constant (at constant pressure in a closed system)
Flow Rate = Av = V/t
A
1 v
1
= A
2 v
2
A = cross-sectional area (m 2 ) v = speed (m/s)
V = volume (m 3 /s) t = time (s)

How are cross-sectional area and velocity of fluids
1. Inversely proportional?
2. Directly
3. No relationship
In ve rs el y
0% 0% 0%
D ire ct ly
N o re la tio ns hi
...

Continuity Equation
• Based on Law of Conservation of Mass – what comes in has gotta come out

What will happen to the yellow foam ball?
1. It will stay in the funnel
2. It will shoot out
3. It will explode into yellow chunks
0% 0% 0%
It
w ill
st ay
i.
..
It
w ill
sh oo t .
..
It
w ill
e xp lo d.
..

What will happen to the pop cans when air is blown between them?
1. They will come together and collide.
2. They will move apart from each other
0%
3. It will remain motionless.
0% 0% 0%
4. Pop will fly out from the openings.
T he y w ill
co me
...
T he y w ill
mo ve
...
It
w ill
re ma in
...
P op
w ill
fl y o.
..

How are pressure and velocity of fluids proportional?
1. Inversely
2. Directly
3. No relationship
In ve rs el y
0% 0% 0%
D ire ct ly
N o re la tio ns hi
...

Bernoulli’s Equation
P
1
+ ρgh
1
+ ½ ρv
1
2 = P
2
+ ρgh
2
+ ½ ρv
2
2
Helpful notes:
• P = P atm if either side is open.
• Set bottom height (h
2
) = 0
• If there is a large volume up top, (v
1
) = 0

Bernoulli’s Equation
P + ρgh + ½ ρv 2 = constant
-Results from conservation of energy.
P = Pressure energy resulting from internal forces within the fluid
ρgh = similar to gravitational potential energy
½ ρv 2 = similar to kinetic energy

Bernoulli’s Principle
• Bernoulli’s Principle states that the flow speed (Av) in a constriction must be greater than the flow speed before or after it.
• Also, swiftly moving fluids exert less pressure than do slowly moving fluids.
• Eg. Tornadoes and blown off roofs

Bernoulli’s principle
• Pressure in a fluid varies inversely with the velocity