Lectures 1 & 2 Fluid and Their Properties

Lecture 1: Fluid and their propertiesLecture outcomes:Identify important fluid properties in a complex fluid phenomenonApply fluid properties to solve engineering problems

How do I swim?Activity 1: discuss in groups how jellyfish moves in the ocean2FluidsA fluid can be classified as liquid form and gas form.Fluid has no definite shape but conform the shape of containing vessel.A fluid is a substance which deforms continuously under the action of shearing forces, however small they may be.If a fluid is at rest, there can be no shearing forces acting and, therefore, all forces in the fluid must be perpendicular to the planes upon which they act.Shear stress in a moving fluidShear stresses are developed when the fluid move in such a way that the particles of the fluid move relative to each other so that they have different velocities. If the velocity of the fluid is the same at every point, no shear stresses will be produced, since the fluid particles are at rest relative to each other.For the fluid at rest, there are no shear stress.ReviewWhat is the difference between force and stress?Shear layersConsidering successive layers parallel to boundary, the velocity of the fluid will vary from layer to layer as y increases.Couette flow is fluid flow between two parallel platesFluid MechanicsFluid MechanicsFluid MechanicsTableWallLiquid in betweenthe platesNewtons law of viscosityLiquids dynamic viscosityRheometer = a device to measure viscosity7Shear and dynamic viscosity Review: What is shear?

Definition: The coefficient of dynamic viscosity (or simply dynamic viscosity) can be defined as the shear stress required to drag one layer of fluid with unit velocity past another layer a unit distance away from it in the fluid.Unit of : Ns/m2 Newtonian and Non-Newtonian FluidFluids obeying Newtons law of viscosity and has a constant value for are known as Newtonian FluidsMost common fluids fall into this category, for which shear stress is linearly related to velocity gradient.Fluids which do not obey Newtons law of viscosity are known as non-Newtonian Fluids. Shear stress, Rate of shear, du/dyIdeal fluid = 0PlasticBingham plasticPseudo-plasticDilatantNewtonian fluidDefinitions of densityMass Density is defined as the mass of the substance per unit volume, the unit is kg/m3.Specific Weight w is define as weight per unit volume, the unit is N/m3, such that w = gRelative Density is defined as the ratio of the mass density of a substance to some standard mass density, such that = substance / H2O at 4CSpecific Volume v is defined as the reciprocal of mass density 1/, the unit is m3/kg. Kinematic viscosityDefinition: The kinematic viscosity is defined as the ratio of dynamic viscosity to mass density.

= /, unit: m2/sQuiz 1A plate initially at rest on a flat surface covered with 0.05mm thin layer of oil requires a shear load of 2.2N/m2 to attain a relative speed of 1.2m/s . Find the dynamic viscosity and kinematic viscosity.Quiz 2A plate having an area of 0.6m2 is sliding down the inclined plane at 30o to the horizontal with a velocity of 0.36m/s. There is a cushion of fluid 1.8mm thick between the plane and the plate. Find the viscosity of fluid if the weight of the plate is 280N.

Activity 2: individually describe the behavior of a droplet hitting a fluid surface using fluid properties15Surface tensionWater drippings from a tap turn spherical

A water Strider uses surface tension to skim above the pond

Cause of surface tensionMolecule I in the interior of liquid is under attractive forces in all directions and the vector sum of these forces is zero.Molecule S at the surface of a liquid, the upward and downward attractions are unbalanced, the surface molecules being pulled inward towards the bulk of the liquid. This effect causes the liquid surface to behave as if it were an elastic membrane under tension, known as surface tension.

Droplet surface tensionThe surface tension is measured as the force acting across the unit length, the unit is N/m. Conventionally, we take spherical shape to represent the liquid droplet.For such a small droplet, surface tension will cause an increase of internal pressure p in order to balance the surface force.Quantifying surface tensionConsidering the forces acting on a diametrical plane through a spherical drop of radius r

Force balanceForce due to internal pressure = p r2Force due to surface tension around the perimeter = 2 r For equilibrium, p r2 = 2 r p = 2 / r

Quiz 3Air is introduced through a nozzle into a tank of water to form a stream of bubbles. If the bubbles are intended to have a diameter of 2mm, calculate by how much the pressure of the air at the nozzle must exceed that of the surrounding water. Assume that = 72.7 10-3N/mCapillary rise and depressionCapillarity is important (in fluid measurements) when using tubes smaller than about 10mm in diameter.

CapillarityRise or fall of a liquid in a capillary tube is caused by surface tension and depends on the relative magnitude of cohesion of the liquid and the adhesion of the liquid to the walls of the containing vessel.

Liquids rise in tubes if they wet (adhesion > cohesion) and fall in tubes that do not wet (adhesion < cohesion) Deriving the height of capillary riseCapillary rise (or depression) in a tube can be calculated by making a force balance.The force due to surface tension (liquid-solid pull), Fs = cos dThe force opposing the surface tension is the weight of the vertical-sided column of liquid of height, Fg =gh ( /4)d 2Since Fg = Fs , therefore

Quiz 4A clean tube of diameter 2.5mm is immersed in a liquid with a surface tension of 0.4N/m. The angle of contact of the liquid with the glass can be assumed to be 135o. The density of the liquid is 13600kg/m3. What would be the level of the liquid in the tube relative to the free surface of the liquid inside the tube?Quiz 5Two coaxial glass tubes forming an annulus with small gap are immersed in water in a trough. The inner and outer radii of the annulus are ri and ro respectively. What is the capillary rise if is the surface tension, is a mass density and is a contact angle of water with the glass tubes? Flaming cocktailCan fire burn in liquid?

Activity 3: Discuss in groups how liquid fuel interacts with fire27Exchange of molecules in constant equilibriumMolecules of liquid are in constant agitation.Some of the molecules in the surface layer have sufficient energy to escape from the attraction of the surrounding molecules into the space above the free surface. Other molecules will return, condense and turn to liquid. If the number of molecules condensing and evaporating are equal, the level of the free surface remains constant.Vapor pressureAt equilibrium, some molecules will stay in gas phase above the free surface, taking up a partial pressure of the space known as vapor pressure.The degree of molecular activity increases with increasing temperature and therefore, the vapor pressure will also increase.If the vapor pressure reaches the pressure at the surrounding, boiling occurs; for example if the pressure is reduced sufficiently boiling of water may occur at room temperature.CavitationUnder certain conditions, areas of low pressure can occur locally in a flowing fluid.If the pressure in such areas falls below the vapor pressure, there will be local boiling and cloud of vapor bubbles will form. This phenomenon is known as cavitation.Effects of cavitationCavitation can cause serious problems, since the flow of liquid can sweep the cloud bubbles on into an area of higher pressure where the bubbles will collapse suddenly.If this occurs in contact with solid surface, very serious damage can result due to the very large force with which the liquid hits the surface.Cavitation can affect the performance of hydraulic machinery such as pumps, turbines and propellers, and the impact of collapsing bubbles can cause local erosion of metal surfaces.

Bulk Modulus and CompressibilityAll fluids are compressible under the application of an external force and when the force is removed they expand back to their original volume exhibiting the property that stress is proportional to volumetric strain.

Pressure and volume in liquidWhen the liquid is compressed, the volume V of a given mass will be reduced to V V when a force is exerted uniformly all over its surface. If the force per unit area of surface increases from p to p + p, then

Negative sign for V indicates the volume decreases as pressure increase.

Deriving the bulk modulusTherefore,

Where K is bulk modulusWhen V 0,

Considering unit mass of substance,

Bulk modulus in liquidThe concept of bulk modulus is mainly applied to liquids, since for gases the compressibility is so great that the value of K is not a constant.For liquids, the changes in pressure occurring in many fluid mechanics problems are not sufficiently great to cause appreciable changes in density. It is therefore usual to ignore such changes and consider liquids as incompressible.

Compressibility in gasGases may also be treated as incompressible if the pressure changes are very small, but usually compressibility cannot be ignored.In general, compressibility becomes important when the velocity of the fluid exceeds about one-fifth of the velocity of a pressure wave (velocity of sound) in the fluid.Typical values of bulk modulusTypical values of Bulk Modulus for water and oil are 2.05 109 N/m2 and 1.62 109 N/m2 , respectively. Quiz 6When a pressure of liquid is increased from 3.5 MN/m2 to 6.5 MN/m2 its volume is found to decrease by 0.08%. What is the bulk modulus of elasticity of the liquid?