9 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.
11 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.
12 Liquid – uniform density r p pressure acting at on surfaceWeight of columnof liquid FhALiquid – uniform density r
13 phphp0’p0p0(0,0)(0,0)hhLinear 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.
15 hThe pressure exerted by a static fluid depends only upon the depth of the fluid, the density of the fluid, and the acceleration of gravityph = p0 + r g hStatic pressure does not depend upon mass or surface area of liquid and the shape of container due to pressure exerted by walls.
22 A sharp blow to the front of an eyeball will produce a higher pressure which is transmitted to the opposite side
23 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.tumorIncreased pressure transmitted down spinal cord
26 Floating: partially submerged Weight of object < weight of fluid that can be displaced by objectVolume of displaced water < volume of objectWeight of liquid displaced by partially submerged object = weight of objectWaterdisplaced
27 Floating: fully submerged Weight of object = weight of fluid displaced by objectVolume of displaced water = volume of objectWaterdisplacedStatic equilibriumSome 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
28 Sinks Weight of object > weight of fluid displaced by object Volume of displaced water = volume of objectWaterdisplaced
29 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 displacedWeight of ship = weight of water displaced
30 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
31 + FLOATING: weight of object = buoyant force FB FG Object partially submergedObject fully submergedtopbottomAbottomtoprohAhwrFrorF
35 at surface is into bulk of the liquid Cohesion: attractive forces between “like” moleculesSurface of any liquid behaves as though it is covered by a stretched membraneNet force on moleculeat surface is into bulk of the liquidFTSFSF = 0
36 pull up on surfacepush down on surfacerestoring forces
37 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
38 FT = 2 T L FLOATING NEEDLE FT Equilibrium FT = FG FG Not a buoyancy phenomenaFTFT = 2 T LEquilibriumFT = FGFGLength of needle, LCoefficient ofsurface tension TSurface tension acts along length of needle on both sides
39 k = 0.70 N.m-1 x = 3410-3 m Fspring = Fe = k x radius of ring FT + FG R = 2010-3 mmass of ringm = 7.0 10-4 kgring
40 FT = 2 T L FLOATING NEEDLE FT Equilibrium FT = FG FG Not a buoyancy phenomenaFTFT = 2 T LEquilibriumFT = FGFGLength of needle, LCoefficient ofsurface tension, TSurface tension acts along length of needle on both sides
41 q q Why can an insect walk on water? FT FT cosq FG FT = T L = 2 p R T Surface tension force actsaround the surface of the legFGqFT = T L = 2 p R TFor one legFG = mg / 6
43 Flow of a viscous fluid L stationary wall plate moving with speed v vz = vhigh speedZlinear velocity gradientLXvz = (d / L) vvz = (v / L) ddlow speedstationary wallvz = 0
44 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 velocityprofileAdhesive forces between fluid and surface fluid stationary at surface
45 Poiseuille’s Law: laminar flow of a newtonian fluid through a pipe Q = dV = Dp p R48 h Ldtp1 > p2 pressure drop along pipe energy dissipated (thermal) by friction between streamlines moving past each othervolume flow rate Q = dV/dtparabolic velocity profileDp = p1 - p2hp1p22RQ = dV/dtL
46 Streamlines for fluid passing an obstacle vVelocity of particle- tangent to streamline
47 Velocity profile for the laminar flow of a non viscous liquid
68 to pressure difference low pressure region Drag force dueto pressure differencelow pressure regionrotational KE of eddies heating effect increase in internal energy temperature increasesmotion of airhigh pressure regionmotion of object
69 NO CURVE Drag force due to pressure difference low pressure region rotational KE of eddies heating effect increase in internal energy temperature increasesNO CURVEDrag force is opposte to the direction of motionhigh pressure region
73 flow speed (high) vair + v reduced pressure Drag force dueto pressure differenceflow speed (high) vair + v reduced pressurevvair (vball)MAGNUS EFFECTflow speed (low) vair - v increased pressurevBoundary layer – air sticks to ball (viscosity) – air dragged around with ballhigh pressure regionlow pressure region
74 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.