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