Transcript Document
VISUAL PHYSICS School of Physics University of Sydney
Australia
gold
m
1
V
1
r gold
=
m
1
/
V
1
=
m
2
/
V
2
gold
m
2
V
2
r
V
m
=
r
V
r
m
V
=
m
/
r
pressure !!!
F A
Gauge and absolute pressures
Pressure gauges measure the pressure above and below atmospheric (or barometric) pressure.
P
atm =
P
0 = 1 atm = 101.3 kPa = 1013 hPa = 1013 millibars = 760 torr = 760 mmHg
Gauge pressure
P
g
Absolute pressure
P
100 200 300 0 400
P
=
P
g
+
P
atm
0 100 200 300 400
Impact of a molecule on the wall of the container exerts a force on the wall and the wall exerts a force on the molecule. Many impacts occur each second and the total average force per unit area is called the
pressure
.
The pressure in a fluid can be defined as the ratio of the force exerted by the fluid to the area over which it is exerted. To get the pressure at a point you need to take the limit as this area approaches zero. Because of the weak cohesive forces between the molecules of the fluid, the only force that can be applied by the fluid on a submerged object is one that tends to compress it. This means the force of the fluid acts perpendicular to the surface of the object at any point.
p
0 pressure acting at on surface
h
Weight of column of liquid
F
A
Liquid – uniform density r
p
h
p
0
p
h
p
0 ’
p
0
(0,0) (0,0)
h h
Linear relationship between pressure and depth.
If the pressure at the surface increases then the pressure at a depth
h
also increases by the same amount.
h
The pressure exerted by a static fluid depends only upon the depth of the fluid, the density of the fluid, and the acceleration of gravity
p
h =
p
0 +
r
g h
Static pressure does not depend upon mass or surface area of liquid and the shape of container due to pressure exerted by walls .
convergence divergence divergence convergence
HIGH
- more uniform conditions - inhibits cloud formation
LOW
- less uniform conditions - encourages cloud formation sunshine sunshine Cloudy / rain
?
A B D C
h
A
p
atm
B
h
C
p
atm r
A
1
oil
A
2
F
1
h
1
h
2
F
2
A sharp blow to the front of an eyeball will produce a higher pressure which is transmitted to the opposite side
Another example is the pressure exerted by a growing tumour. This increased pressure is transmitted down the spinal column via the cerebrospinal fluid, and may be detected lower in the spinal cavity which is less invasive than trying to detect it in the brain itself.
tumor Increased pressure transmitted down spinal cord
Partially submerged floating
Floating: partially submerged Weight of object < weight of fluid that can be displaced by object Volume of displaced water < volume of object Weight of liquid displaced by partially submerged object = weight of object Water displaced
Floating: fully submerged Weight of object = weight of fluid displaced by object Volume of displaced water = volume of object Static equilibrium Water displaced Some fish can remain at a fixed depth without moving by storing gas in their bladder. Submarines take on or discharge water into their ballast tanks to rise or dive
Sinks Weight of object > weight of fluid displaced by object Volume of displaced water = volume of object Water displaced
A steel ship can encompass a great deal of empty space and so have a large volume and a relatively small density.
Volume of water displaced Weight of ship = weight of water displaced
The buoyant force is equal to the weight of the water displaced, not the water actually present. The
missing water
that would have filled the volume of the ship below the waterline is the displaced fluid. Volume of water displaced.
This volume is not necessarily the volume present.
Weight of ship = weight of water displaced
FLOATING: weight of object = buoyant force Object partially submerged top bottom
A h
r o r F F B
+
F G Object fully submerged bottom top
A h w
r o r F
water oil
?
F
lift +
F
B =
F
G
m F
lift +
F
B
a
= 0
F
G
Cohesion: attractive forces between “like” molecules
Surface of any liquid behaves as though it is covered by a stretched membrane
F
T S
F
= 0 Net force on molecule at surface is into bulk of the liquid S
F
pull up on surface restoring forces push down on surface
Which shape corresponds to a soap bubble?
Surface of a liquid acts like an elastic skin minimum surface potential energy minimum surface area for given volume
FLOATING NEEDLE Not a buoyancy phenomena
F
T = 2
T L
Length of needle,
L
Coefficient of surface tension
T F
T Equilibrium
F
T =
F
G
F
G Surface tension acts along length of needle on both sides
k
= 0.70 N.m
-1
x
= 34 10 -3 m radius of ring
R
= 20
10
-3
m
mass of ring
m
= 7.0
10 -4 kg ring
F
spring =
F
e =
k x F
T +
F
G
FLOATING NEEDLE Not a buoyancy phenomena
F
T = 2
T L
Length of needle,
L
Coefficient of surface tension,
T F
T Equilibrium
F
T =
F
G
F
G Surface tension acts along length of needle on both sides
Why can an insect walk on water?
F
T q
F
T cos q
F
G q Surface tension force acts around the surface of the leg
F
T =
T L
= 2 p
R T
For one leg
F
G =
mg
/ 6
Z Flow of a viscous fluid plate moving with speed
v
high speed
v
z =
v
X
L
low speed
d
linear velocity gradient
v
z
=
(
d / L
)
v v
z
=
(
v / L
)
d
stationary wall
v
z = 0
Flow of a viscous newtonain fluid through a pipe Velocity Profile Cohesive forces between molecules layers of fluid slide past each other generating frictional forces energy dissipated (like rubbing hands together) Parabolic velocity profile Adhesive forces between fluid and surface fluid stationary at surface
Poiseuille’s Law: laminar flow of a newtonian fluid through a pipe
Q
= d
V
d
t
= D
p
p
R
4 8 h
L
volume flow rate
Q
= d
V
/d
t
parabolic velocity profile
p
1 >
p
2 pressure drop along pipe energy dissipated (thermal) by friction between streamlines moving past each other D
p
=
p
1 -
p
2 2
R p
1 h
p
2
Q
= d
V
/d
t L
Streamlines for fluid passing an obstacle streamlines
v
Velocity of particle - tangent to streamline
Velocity profile for the laminar flow of a non viscous liquid
A
1 r
v
1 r
A
2
v
2
A
1
A
2
A
1
v
1 Low speed Low KE High pressure
v
2 high speed high KE low pressure
v
1 Low speed Low KE High pressure
Y X
p
1 D
x
1
A
1
y
1
m v
1 time 1 r D
x
2
m p
2
v
2
A
2 time 2
y
2
force high speed low pressure force
high velocity flow high pressure (
p
atm ) low pressure velocity increased pressure decreased
5 1 Same speed and pressure across river faster flow (streamlines closer together) low pressure slow flow (streamlines further apart) high pressure
p
large
p
small
p
large
v
small
v
large
v
small
Flow speeds up at constriction Pressure is lower Internal force acting on artery wall is reduced artery External forces causes artery to collapse
y
1
y
2
(1)
Point on surface of liquid
v
2 1 = ? m.s
-
(2)
Point just outside hole
(1)
v
1 ?
=
h
r m (2) r F
A C B D
y
B
y
A
y
C
Ideal fluid Real fluid
arm head lung heart trunk leg arm lung leg
Floating ball
Lift
F
L Resultant
F
R drag
F
D C A D B
Drag force due to pressure difference low pressure region rotational KE of eddies heating effect internal energy increase in temperature increases motion of air high pressure region motion of object
Drag force due to pressure difference low pressure region high pressure region rotational KE of eddies heating effect internal energy increase in temperature increases
NO CURVE
Drag force is opposte to the direction of motion
Tear drop shape for streamlining
v v
T Object falling from rest
t v v
T Object thrown down with initial speed
v
0 >
v
T
t
Drag force due to pressure difference
v
air (
v
ball )
v v
high pressure region low pressure region flow speed (high)
v
air reduced pressure +
v
MAGNUS EFFECT
flow speed (low)
v
air increased pressure
v
Boundary layer – air sticks to ball (viscosity) – air dragged around with ball
The trajectory of a golf ball is not parabolic Golf ball with backspin (rotating CW) with air stream going from left to right. Note that the air stream is deflected downward with a downward force. The reaction force on the ball is upward. This gives the longer hang time and hence distance carried.
lift
Direction plane is moving w.r.t. the air Direction air is moving w.r.t. plane low pressure q attack angle momentum transfer lift high pressure low pressure drag
downwash huge vortices