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VISUAL PHYSICS School of Physics University of SydneyAustralia

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**m = r V V = m / r gold m1 V1 gold m2 V2 rgold = m1 / V1 = m2 / V2 r V**

r m m = r V V = m / r

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pressure !!!

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F A

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**Gauge and absolute pressures**

Pressure gauges measure the pressure above and below atmospheric (or barometric) pressure. Patm = P0 = 1 atm = kPa = 1013 hPa = 1013 millibars = 760 torr = 760 mmHg Gauge pressure Pg Absolute pressure P P = Pg + Patm 200 100 300 400

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100 200 300 400

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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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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.

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**Liquid – uniform density r**

p pressure acting at on surface Weight of column of liquid F h A Liquid – uniform density r

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ph ph p0’ p0 p0 (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.

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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 + 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.

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Cloudy / rain sunshine

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?

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D h A B C

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A h patm patm B C r

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F2 F1 h1 oil h2 A1 A2

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A sharp blow to the front of an eyeball will produce a higher pressure which is transmitted to the opposite side

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**Increased pressure transmitted down spinal cord**

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

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**Partially submerged floating**

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**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

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**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

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**Sinks Weight of object > weight of fluid displaced by object**

Volume of displaced water = volume of object Water displaced

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**Volume of 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

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**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

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**+ FLOATING: weight of object = buoyant force FB FG**

Object partially submerged Object fully submerged top bottom A bottom top ro h A h w rF ro rF

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? oil water

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Flift + FB m a = 0 FG Flift + FB = FG

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**at surface is into bulk of the liquid**

Cohesion: attractive forces between “like” molecules Surface of any liquid behaves as though it is covered by a stretched membrane Net force on molecule at surface is into bulk of the liquid FT SF SF = 0

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pull up on surface push down on surface restoring forces

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**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

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**FT = 2 T L FLOATING NEEDLE FT Equilibrium FT = FG FG**

Not a buoyancy phenomena FT FT = 2 T L Equilibrium FT = FG FG Length of needle, L Coefficient of surface tension T Surface tension acts along length of needle on both sides

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**k = 0.70 N.m-1 x = 3410-3 m Fspring = Fe = k x radius of ring FT + FG**

R = 2010-3 m mass of ring m = 7.0 10-4 kg ring

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**FT = 2 T L FLOATING NEEDLE FT Equilibrium FT = FG FG**

Not a buoyancy phenomena FT FT = 2 T L Equilibrium FT = FG FG Length of needle, L Coefficient of surface tension, T Surface tension acts along length of needle on both sides

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**q q Why can an insect walk on water? FT FT cosq FG FT = T L = 2 p R T**

Surface tension force acts around the surface of the leg FG q FT = T L = 2 p R T For one leg FG = mg / 6

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**Flow of a viscous fluid L stationary wall plate moving with speed v**

vz = v high speed Z linear velocity gradient L X vz = (d / L) v vz = (v / L) d d low speed stationary wall vz = 0

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**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

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**Poiseuille’s Law: laminar flow of a newtonian fluid through a pipe**

Q = dV = Dp p R4 8 h L dt p1 > p2 pressure drop along pipe energy dissipated (thermal) by friction between streamlines moving past each other volume flow rate Q = dV/dt parabolic velocity profile Dp = p1 - p2 h p1 p2 2R Q = dV/dt L

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**Streamlines for fluid passing an obstacle**

v Velocity of particle - tangent to streamline

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**Velocity profile for the laminar flow of a non viscous liquid**

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A1 A2 r r v2 v1

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A1 A1 A2 v2 v1 v1 Low speed Low KE High pressure high speed high KE low pressure Low speed Low KE High pressure

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Y Dx2 p2 A2 m v2 X time 2 r p1 Dx1 y2 A1 m v1 y1 time 1

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force high speed low pressure force

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**high velocity flow high pressure (patm) velocity increased**

low pressure velocity increased pressure decreased

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5 slow flow (streamlines further apart) high pressure 1 Same speed and pressure across river faster flow (streamlines closer together) low pressure

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p large p large p small v small v large v small

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artery Flow speeds up at constriction Pressure is lower Internal force acting on artery wall is reduced External forces causes artery to collapse

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**(1) Point on surface of liquid**

y1 v2 = ? m.s-1 y2 (2) Point just outside hole

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(1) (2) v1 = ? rF h rm

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C yC A yA B yB D

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Ideal fluid Real fluid

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head arm arm lung lung heart trunk leg leg

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Floating ball

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Resultant FR Lift FL C A B drag FD D

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**to pressure difference low pressure region**

Drag force due to pressure difference low pressure region rotational KE of eddies heating effect increase in internal energy temperature increases motion of air high pressure region motion of object

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**NO CURVE Drag force due to pressure difference low pressure region**

rotational KE of eddies heating effect increase in internal energy temperature increases NO CURVE Drag force is opposte to the direction of motion high pressure region

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**Tear drop shape for streamlining**

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v v vT vT t t Object falling from rest Object thrown down with initial speed v0 > vT

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**flow speed (high) vair + v reduced pressure**

Drag force due to pressure difference flow speed (high) vair + v reduced pressure v vair (vball) MAGNUS EFFECT flow speed (low) vair - v increased pressure v Boundary layer – air sticks to ball (viscosity) – air dragged around with ball high pressure region low pressure region

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**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.

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lift

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**lift Direction plane is moving w.r.t. the air**

Direction air is moving w.r.t. plane low pressure lift q low pressure drag attack angle high pressure momentum transfer downwash huge vortices

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Fluid mechanics 3.1 – key points

Fluid mechanics 3.1 – key points

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