2 What do some liquids splash more? Why do we need to change brake fluid?Why do cars need different oils in hot and cold countries?Why do engines run more freely as it heats up?Have you noticed that skin lotions are easier to pour in summer than winter?Why is honey sticky?
3 “VISCOSITY IS DIFFERENT TO DENSITY” When real fluids flow they have a certain internal friction called viscosity. It exists in both liquids and gases and is essentially a frictional force between different layers of fluid as they move past one another.In liquids the viscosity is due to the cohesive forces between the molecules whilst in gases the viscosity is due to collisions between the molecules.“VISCOSITY IS DIFFERENT TO DENSITY”
4 L stationary wall plate moves with speed v vx = v high speed vx A useful model: Newtonian fluids water, most gasesplate moves with speed vvx = vhigh speedZvxlinear velocity gradientLXvx / d = v / Ldlow speedstationary wallvx = 0
5 (F/A) = (v / L) over area A velocity gradient shear A useful model: Newtonian fluids water, most gasesplate exerts force Fover area Avelocity gradientshearstressis proportional to(F/A) = (v / L)stationary wall
6 (F/A) = (v / L) = (F / A)(L / v) coefficient of viscosity (Greek letter eta).The greater the coefficient of viscosity , the greater the force required to move the plate at a velocity v.This relationship does not hold for all fluids. Viscous fluids that obey this equation are called Newtonian fluids and = constant independent of the speed of flow.
7 (F/A) = (v / L) toothpaste grease shear stress F / A wet sand corn flourshear stress F / ANewtonian fluidvelocity gradient Dv/DL(F/A) = (v / L)slope
8 Non-Newtonian or rheological fluids – viscosity is a function of the flow velocityExamples of non-Newtonian fluids* Blood - it contains corpuscles and other suspended particles. The corpuscles can deform and become preferentially oriented so that the viscosity decreases to maintain the flow rate.* Corn flour and water mixture.* Certain soils (more clay content) are non-Newtonian when moist to wet.
9 SI unit is (N.m-2)(m).(m-1.s) Pa.s ViscositySI unit is (N.m-2)(m).(m-1.s) Pa.sA common unit is the poise P (1 Pa.s = 10 P)Fluid (mPa.s)water (0 °C)water (20 °C)water (100 °C)white blood (37 °C) ~4blood plasma (37 °C) ~1.5engine oil (AE10) ~ 200airViscosity is very temperature dependent.Viscosity of a liquid decreases with increasing temp.Viscosity of a gas increases with increasing temp.1 mPa = 10-3 Pa
10 Why can't you get all the dust off your car by just squirting water from a hose onto it? Why can't you simply remove dust just be blowing across the surface?Why does dust cling to a fast rotating fan?How can a leaf stay on a car moving at high speed?
11 Boundary layerWhen a fluid moves over a surface, there is a thin layer of the fluid near the surface which is nearly at rest. This thin layer is called the boundary layer.
12 What happens to the velocity profile when a Newtonian fluid flows through a pipe?ParabolicvelocityprofileLinearvelocityprofileAdhesive forces between fluid and surface fluid stationary at surfaceCohesive forces between molecules layers of fluid slide past each other generating frictional forces energy dissipated (like rubbing hands together)
13 h What causes a fluid to flow through a pipe? A useful model: Poiseuille’s Law:laminar flow of a Newtonian fluid through a pipeparabolic velocity profilevolume flow rateQ = dV/dthp1p22RLDp = p1 - p2assumptions ?
14 p1 > p2 pressure drop along pipe A useful model: Poiseuille’s LawQ = dV = Dp p R 48 h LdthDp2RQ = dV/dtLp1 > p2 pressure drop along pipe energy dissipated (thermal) by friction between streamlines moving past each other
15 Pipes from Warragamba Dam Respiratory system Circulatory system APPLICATIONSIrrigation pipesPipes from Warragamba DamRespiratory system Circulatory systemAir conditioning, ducting, pipingSoils Water will rise quicker in large grain soils(Q R 4) but it will rise to greater height bycapillary attraction on fine grain soils (h 1/R)
16 The heart is so responsive to the changing needs of our body that cardiac output can vary from as little as 5 to a maximum of 35 litres of blood per minute, a sevenfold change, over a very short interval.Q = dV = Dp p R48 h LdtWhat happens to the flow as viscosity changes ?what happens to the flow as the radius changes ?
17 How do we apply conservation of energy in a flow system? FLUID FLOWSTREAMLINE – LAMINAR FLOWTURBULENT FLOWREYNOLDS NUMBERHow do we apply conservation of energy in a flow system?
18 LAMINAR FLOW Streamlines for fluid passing an obstacle streamlines v Velocity of particleVelocity profile for the laminar flow of a non viscous liquid-tangent to streamline
19 REYNOLDS NUMBER ReA British scientist Osborne Reynolds (1842 – 1912) established that the nature of the flow depends upon a dimensionless quantity, which is now called the Reynolds number Re.Re = v L / density of fluidv average flow velocity over the cross sectionof the pipeL characteristic dimension
20 Re = v L / [Re] [kg.m-3] [m.s-1][m] [Pa.s]-1 [kg] [m-1][s-1][kg.m.s-2.m-2.s]-1 = Re is a dimensionless numberAs a rule of thumb, for a fluid flowing through a tubeRe < ~ laminar flow~ < Re < ~ unstable laminarto turbulent flowRe > ~ turbulent flow
24 Re = v L / laminar flow Spermatozoa swimming r = 103 kg.m-3 v = m.s-1L = 10 mm = Pa.sRe = (103)(10-5)(10x10-6) / (10-3)Re = 10-4laminar flow
25 Household plumbing pipes Re = v L / Household plumbing pipesTypical pipes are about 30 mm in diameter and water flows at about 10 m.s-1Re ~ (10)(3010-3)(103) / (10-3) ~ 3105The circulatory systemSpeed of blood ~ 0.2 m.s-1Diameter of aorta L ~ 10 mmViscosity of blood say ~ 10-3 Pa.sRe ~ (0.2)(1010-3)(103) / 10-3) ~ 2103ImpactMethod of swimming/propulsionPump designFlow systems…