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LIFE IN A FLUID

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http://www.physics.usyd.edu.au/teach_res/jp/fluids09

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Ian Cooper

LecturesTutorialsLabsDuty TutorAssignmentsExamTextbookWorked examples

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Identify Setup Execute Evaluate

IDENTIFYIdentify what the question askingIdentify the known and unknown physical quantities (units) Identify the type of problem

SETUP need a good knowledge base (memory + understanding)Visualise the physical situation Diagrams - reference frames / coordination system / origin / directions Write down key concepts, principles, equations, assumptions that maybe needed to answer the question

EXECUTEAnswer to the question from what you know. Numerical questions - solve before calculations - manipulate equations then substitute numbers add comments.

EVALUATECHECK - answer reasonable, assumptions, units, signs, significantfigures, look at limiting cases

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mV

Definition ( Greek letter rho)

density of object

m mass of objectV volume of object

UnitsSI unit kg.m-3

Other units g.mL-1

1 mL = 1 cm3 = (10-2)3 m3 = 10-6 m3

1 g = 10-3 kg 1 g.mL-1 = 103 kg.m-3

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Density values (kg.m-3)

Interstellar space 10-20

Best laboratory vacuum 10-17

Air (20 °C and 1 atm) 1.21Styrofoam 100

Ice 917

Water (20 °C and 1 atm) 998

SaltWater 1024

Whole blood 1060

Earth (average) ~5500

Iron 7900

Mercury 13 600

Osmium (most dense found on earth)

22 500

Uranium nucleus 1017

Neutron star (core) 1018

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… and all the king's horses …

What force is required to separate the hemispheres? Is this force significant?

?What physical quantities do we need to consider?

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Pressure P

pressure !!!Is this pressure?

What pressure is applied to the ground if a person stood on one heel?

? What physical quantities do we need to consider?

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Pressure P

FpA

F force at right angles to surface A area of contact over which force acts

A

F

Units

pressure p Pa pascal 1 Pa = 1 N.m-2

force F N newton 1 N = 1 kg.m.s-2

area A m2

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How large is atmospheric pressure?

Rough calculation

p = F / A

p = m g / A

p = V g / A

p = A h g / A

p = h g

p = (1)(104)(10) Pa

p = 105 Pa

Pressure at Earth’s surface due to weight of atmosphere

air = 1.21 kg.m-3

g = 9.8 m.s-2

h ~ 10 km

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Atmospheric Pressure patm

1.013x105 Pa

101.3 kPa

1013 hPa (hecto)

1013 mb (millibar)

1.013 b (bar)

760 mmHg

14.7 lb.in2 (14.7 psi)

10.34 mH20

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? What does it mean when we are told to inflate a tyre to 100 kPa?

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What does it mean when we are told to inflate a tyre to 100 kPa?

Answer Pressure gauges measure the pressure above and below atmospheric (or barometric) pressure. Need to distinguish between a gauge pressure and absolute pressure.

patm = 101 kPa

pgauge = 100 kPa pabsolute = (101 + 100) kPa = 201 kPa pabsolute = pgauge + patm

0

100

200

300

4000

100

200

300

400

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? How does a gas or liquid exert a pressure on its container walls?

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?

How does a gas or liquid exert a pressure on its container walls?

Answer

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.

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patm = 1x105 Pa

R = m

A = 2 R2

p = F / A

F = p A

F = (1x105)()( )2 N

F = x10 N

70 kg person HOW MANY PEOPLE? N = F / Fperson ~

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pressure !!!

F = ? N

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m = 70 kg g = 10 m.s-2

FG = 700 N

A = 10 mm x 10 mm

A = (10x10-3)(10x10-3) m2

A = 10-4 m2

p = F / A

p = (9700 / 10-4) Pa

p = 700 x 104 Pa

p = 7 x 106 Pa

p / patm = 7x106 / 1x105 atm = 70 atm

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Why is it better is use a sharp knife?

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FLUID PRESSURE p

The oarfish may be the creature that gave rise to the legends about "sea serpents". This long, skinny fish, with its strange-looking head covered in protrusions and reaching lengths perhaps as long as 15 m,

Life Life in the deep sea must adapt to unique conditions of low or no light, high pressure, low energy- except at hot vents (superheated temperatures). One unexplained but fairly common feature of deep animals is gigantism (such as oarfish, the giant squid, etc.). Less than 1% of the deep-sea has been explored. What might be left undiscovered?

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Provided that an object im mersed in a fluid is not moving, the force on each small part of the contact surface is perpendicular to the surface so the interaction can be described completely in terms of pressure. Fluid pressure always acts perpendicular to any surface irrespective of how the surface is oriented. If there is relative motion between the fluid and solid object, the force has components parallel to the surface and the interaction is not simply described by the pressure. Pressure has no intrinsic direction of its own (pressure is a scalar).

t t

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How long can your snorkel be?

Why do your ears feel different when you dive into deep water?

Why does atmospheric pressure change as you go up a mountain?

How does a barometer work?

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Pressure increases with depth in a fluid

p0 pressure acting on surface

h

Liquid – uniform density

A

Weight of columnof liquid

F

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pressure at depth h = pressure acting on surface + pressure due to height of

liquid ph = p0 + F / A

F = weight of column liquid of cross sectional area A F = m g where m of liquid in column m = V = (A h) F / A = g h ph = p0 + g h (equation only applies for static fluids)

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Snorkelling

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200 mm

ph = patm + g h

p = ph – patm

p = g h

p = (1030)(9.8)(0.2) Pa

p = 2x103 Pa

if h > 200 mm p too large, lungs collapse

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A scuba diver's lungs can ruptureif he doesn't breathe while surfacing?

Why?

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You dive deep down into the water.

Does it matter whether it is in the ocean or a swimming pool?

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You dive deep down into the water. Does it matter whether it is in the ocean or a swimming pool?

! The pressure within a uniform stationary fluid is the same at all points in the same horizontal plane.

hh

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.