visual physics school of physics university of sydney australia
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VISUAL PHYSICS School of Physics University of Sydney Australia. gold m 1 V 1. gold m 2 V 2. r gold = m 1 / V 1 = m 2 / V 2. r V. r m. m = r V. V = m / r. pressure !!!. F. A. Gauge and absolute pressures. - PowerPoint PPT PresentationTRANSCRIPT
VISUAL PHYSICSSchool of PhysicsUniversity of SydneyAustralia
goldm1 V1
goldm2 V2
m V
gold = m1 / V1 = m2 / V2
m = V V = m /
pressure !!!
A
F
Gauge and absolute pressures
Pressure gauges measure the pressure above and below atmospheric (or barometric) pressure.
Patm = P0 = 1 atm = 101.3 kPa = 1013 hPa = 1013 millibars = 760 torr = 760 mmHg
Gauge pressure Pg
Absolute pressure P
P = Pg + Patm
0
100
200
300
400
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.
p0 pressure acting at on surface
h
Liquid – uniform density
A
Weight of column of liquid F
(0,0)h
ph
p0
(0,0)h
ph
p0
p0’
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
ph = p0 + 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.
Cloudy / rainsunshine
?
A
D
CB
h
hpatm
patm
B
A
C
h2
h1
F1F2
A1 A2
oil
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
Water displaced
Static equilibrium
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
Volume of water displaced. This volume is not necessarily the volume present.
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.
h
F
topbottom
Object partially submerged
A
o
h
F
topbottom
Object fully submerged
A
ow
FLOATING: weight of object = buoyant force
FB
FG
+
?water
oil
Flift + FB
FG
a = 0m
Flift + FB = FG
Cohesion: attractive forces between “like” molecules
F = 0F
Net force on molecule at surface is into bulk of the liquid
FT
Surface of any liquid behaves as though it is covered by a stretched membrane
pull up on surface push down on surface
restoring forces
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 NEEDLENot a buoyancy phenomena
FG
FT
Surface tension acts along length of needle on both sides
Length of needle, L
Equilibrium FT = FG
FT = 2 T L
Coefficient ofsurface tension T
k = 0.70 N.m-1
x = 3410-3 m
radius of ringR = 2010-3 m
mass of ring m = 7.0 10-4 kg
Fspring = Fe = k x
FT + FG
ring
FLOATING NEEDLENot a buoyancy phenomena
FG
FT
Surface tension acts along length of needle on both sides
Length of needle, L
Equilibrium FT = FG
FT = 2 T L
Coefficient ofsurface tension, T
Why can an insect walk on water?
FT = T L = 2 R TFG
FT
Surface tension force actsaround the surface of the leg
For one leg
FG = mg / 6
FT cos
stationary wall
L
Flow of a viscous fluid
low speed
high speed
plate moving with speed v
X
Z
linear velocity gradient
vz = (d / L) v
vz = (v / L) d
d
vz = 0
vz = v
Flow of a viscous newtonain fluid through a pipeVelocity Profile
Adhesive forces between fluid and surface fluid stationary at surface
Parabolic velocity profile
Cohesive forces between molecules layers of fluid slide past each other generating frictional forces energy dissipated (like rubbing hands together)
Poiseuille’s Law: laminar flow of a newtonian fluid through a pipe
volume flow rate Q = dV/dt
Q = dV/dt
R
L
p1 p2
p = p1 - p2
Q = dV = p R4
8 Ldt
parabolic velocity profile
p1 > p2 pressure drop along pipe energy
dissipated (thermal) by friction between
streamlines moving past each other
Velocity of particle - tangent to streamline
streamlines
Streamlines for fluid passing an obstacle
v
Velocity profile for the laminar flow of a non viscous liquid
A1
A2
v1
v2
A1
A2
v1
v2
A1
v1
Low speedLow KEHigh pressure
high speedhigh KElow pressure
Low speedLow KEHigh pressure
y1
y2
x1
x2 p2
A2
A1v1
v2
p1
X
Y
time 1
time 2
m
m
high speedlow pressure
force
force
velocity increasedpressure decreased
low pressurehigh
pressure(patm)
high velocity flow
1
5
Same speed and pressure across river
faster flow (streamlines closer together) low pressure
slow flow(streamlines further apart) high pressure
v small v smallv large
p large p large
p small
artery
External forces causes artery to collapse
Flow speeds up at constrictionPressure is lowerInternal force acting on artery wall is reduced
(1) Point on surface of liquid
(2) Point just outside hole
v2 = ? m.s-1
y1
y2
(1)
(2)
F
m
h
v1 = ?
C
B
A
D
yA
yB
yC
Ideal fluid
Real fluid
leg
lung
leg
lung
armhead
heart
arm
trunk
Floating ball
Lift FL
drag FD
Resultant FR
C
D
BA
low pressure region
high pressure region
rotational KE of eddies heating effect increase in internal energy temperature increases
Drag force dueto pressure difference
motion of air
motion of object
low pressure region
high pressure region
rotational KE of eddies heating effect increase in internal energy temperature increases
Drag force dueto pressure difference
NO CURVEDrag force is opposte to the direction of motion
Tear drop shape for streamlining
t t
vTvT
v v
Object falling from rest Object thrown down with initial speed v0 > vT
low pressure region
high pressure region
Drag force dueto pressure difference
v
v
flow speed (high) vair + v reduced pressure
flow speed (low) vair - v increased pressure
vair (vball)
Boundary layer – air sticks to ball (viscosity) – air dragged around with ball
MAGNUS EFFECT
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.
The trajectory of a golf ball is not parabolic
lift
Direction plane is moving w.r.t. the air
Direction air is moving w.r.t. plane
low pressure drag
attack angle
lift
downwashhuge vortices
momentum transfer
low pressure
high pressure