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VISUAL PHYSICS School of Physics University of Sydney Australia

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gold m 1 V 1 gold m 2 V 2 m V gold = m 1 / V 1 = m 2 / V 2 m = VV = m /

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pressure !!!

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A F

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Gauge and absolute pressures Pressure gauges measure the pressure above and below atmospheric (or barometric) pressure. P atm = P 0 = 1 atm = kPa = 1013 hPa = 1013 millibars = 760 torr = 760 mmHg Gauge pressure P g Absolute pressure P P = P g + P atm

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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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p 0 pressure acting at on surface h Liquid – uniform density A Weight of column of liquid F

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(0,0) h phph p0p0 h phph p0p0 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.

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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 p h = p 0 + 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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A D C B h

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h p atm B A C

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h2h2 h1h1 F1F1 F2F2 A1A1 A2A2 oil

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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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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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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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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.

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h FF top bottom Object partially submerged A oo h FF topbottom Object fully submerged A oo w FLOATING: weight of object = buoyant force FBFB FGFG +

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? water oil

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F lift + F B FGFG a = 0m F lift + F B = F G

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

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pull up on surfacepush 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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FLOATING NEEDLE Not a buoyancy phenomena FGFG FTFT Surface tension acts along length of needle on both sides Length of needle, L Equilibrium F T = F G F T = 2 T L Coefficient of surface tension T

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k = 0.70 N.m -1 x = 34 m radius of ring R = 20 m mass of ring m = 7.0 kg F spring = F e = k x F T + F G ring

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FLOATING NEEDLE Not a buoyancy phenomena FGFG FTFT Surface tension acts along length of needle on both sides Length of needle, L Equilibrium F T = F G F T = 2 T L Coefficient of surface tension, T

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Why can an insect walk on water? F T = T L = 2 R T FGFG FTFT Surface tension force acts around the surface of the leg For one leg F G = mg / 6 F T cos

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stationary wall L Flow of a viscous fluid low speed high speed plate moving with speed v X Z linear velocity gradient v z = (d / L) v v z = (v / L) d d v z = 0 v z = v

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Flow of a viscous newtonain fluid through a pipe Velocity 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)

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Poiseuille’s Law: laminar flow of a newtonian fluid through a pipe volume flow rate Q = dV/dt Q = dV/dt RR L p1p1 p2p2 p = p 1 - p 2 Q = dV = p R 4 8 L dtdt parabolic velocity profile p 1 > p 2 pressure drop along pipe energy dissipated (thermal) by friction between streamlines moving past each other

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Velocity of particle - tangent to streamline streamlines Streamlines for fluid passing an obstacle v

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Velocity profile for the laminar flow of a non viscous liquid

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A1A1 A2A2 v1v1 v2v2

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A1A1 A2A2 v1v1 v2v2 A1A1 v1v1 Low speed Low KE High pressure high speed high KE low pressure Low speed Low KE High pressure

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y1y1 y2y2 x1x1 x2x2 p2p2 A2A2 A1A1 v1v1 v2v2 p1p1 X Y time 1 time 2 m m

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high speed low pressure force

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velocity increased pressure decreased low pressure high pressure (p atm ) high velocity flow

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

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v small v large p large p small

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

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(1) Point on surface of liquid (2) Point just outside hole v 2 = ? m.s - 1 y1y1 y2y2

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(1) (2) FF mm h v 1 = ?

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C B A D yAyA yByB yCyC

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Ideal fluid Real fluid

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leg lung leg lung arm head heart arm trunk

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Floating ball

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Lift F L drag F D Resultant F R C D B A

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

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

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Tear drop shape for streamlining

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t t vTvT vTvT v v Object falling from restObject thrown down with initial speed v 0 > v T

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

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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

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lift

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

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