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INTRO TO FLUID MECHANICS • Define and explain fluid properties such as density, shear stress, velocity and etc. • Define, explain and derive viscosity, and explain its correlation with human blood. Viscosity measurement. • Define and explain the surface tension and capillary effect. • Explain the effect of surface tension in biomedical engineering. THERMAL-FLUID Science that deal with energy, and the transfer, transport, and conversion of energy. Fluid Mechanics + Thermodynamics + Heat Transfer CIRCULATION SYSTEM Heart, bloods, human body (Fluid Mechanics) Energy conversion, body cells, body heat rejected (Thermodynamics) Human comfort, rate of metabolic heat ejection. Control of heat transfer, clothes (Heat Transfer). THERMODYNAMICS Thermo (heat) & Dynamic (force) In earlier days, the capacities of hot bodies, work. Nowadays, broader scope, the science that studies energy and the transformation of energy into work, or moving things around. Energy Ability to cause changes. Thermal, mechanical, kinetic, potential, electric, magnetic, chemical, nuclear energy. THERMODYNAMICS The Zeroth law Temperature measurement. The First law Conservation of energy principle (energy change from on state to another). The Second law Energy has quality and quantity, actual processes occur in the direction of decreasing quality of energy. HEAT TRANSFER Heat A form of energy that can be transferred from one system to another as a result of temperature difference. Heat Transfer & Thermodynamics Thermodynamics – the amount of heat transfer from one equilibrium state to another. Heat Transfer – How long the heat transfer process will take, due to temperature difference, nonequilibrium. BETWEEN T’DYNAMICS AND HEAT TRANSFER Thermodynamics tells us: – how much heat is transferred (δQ) – how much work is done (δW) – final state of the system – equilibrium Heat transfer tells us: – how (with what modes) δQ is transferred – at what rate δQ is transferred – temperature distribution inside the body – Non equilibrium DIMENSIONAL HOMOGENEOUS What is the different between Weight and Mass? (Definition & Units.) - Quiz Every terms in an equation must have the same dimensions. Spotting Errors in unit E (kJ) = 25 kJ + 7 kJ/Kg Fundamental Dimension: M,L,T Obtain formulas from unit ρ = 850kg/m3; V = 2 m3 FLUID MECHANICS Fluid – A substance in the gas or liquid phase. – A liquid takes the shape of the container, free surface under gravity. – Gases cannot form a free surface SOLID AND FLUID Solid Resist an applied shear stress by deforming. Stress proportional to strain. Fluid Deforms continuously under the influence of shear stress. Stress proportional to strain rate. MECHANICS - QUIZ Statics? Dynamics? Kinetics? Kinematics? Normal Stress? Shear Stress? Weight? Mass? FLUID MECHANICS- CATEGORIES Fluid Statics & Dynamics The motion of fluids that are incompressible (density constant), HYDRODYNAMICS. GAS DYNAMICS, compressible (density change significantly) fluid flow, nozzles at high speed. AERODYNAMICS, flow of gases over bodies, aircraft, automobiles. FLUID PROPERTIES Any characteristic of a system is called a property. – Familiar: pressure P, temperature T, volume V, and mass m. – Less familiar: viscosity, thermal conductivity, modulus of elasticity, thermal expansion coefficient, vapor pressure, surface tension. FLUID PROPERTIES Density (mass/unit volume) Symbol: ρ --- rho Blood density, 1060kg/m3; water (1000kg/m3), Specific weight (Weight/Volume) Symbol: γ --- Gamma Water on earth is 9807Nm-3 at 5ºC FLUID PROPERTIES Specific volume is defined as, v = 1/r = V/m (m3/kg) Specific gravity, (Ratio of the density of a substance to the density of water at 4°C - relative density) Sg = ρ object / ρwater at 4°C = γobject/γwater at 4°C Unit: dimensionless or unitless, Blood???? EXAMPLE 1 Calculate the weight of a reservoir of oil if it has a mass of 825 kg. ANSWER 1 EXAMPLE 2 If the reservoir from Example 1 has a volume of 0.917m3, compute the density, the specific weight, and the specific gravity of the oil. ANSWER 2 EXAMPLE 3 Glycerine at 20°C has a specific gravity of 1.263. Compute its density and specific weight. ANSWER 3 VISCOSITY Density & specific weight, measures heaviness Additional properties to distinguish flow, fluidity (how easy it flows). Internal resistance of fluid to motion. A measure of the resistance of a fluid to deform under shear stress. FRICTIONAL FORCE Solid & Solid F = µ N, µ: Friction coefficient Analogous, Fluid & Solid, Fluid & Fluid. Move in air, walk in water, higher resistance. VISCOSITY y u=V Moveable Plate B F B’ h A Fluid at t=0 dγ (small deformation) Fixed Plate A u=0 Velocity gradient , dV/dy = V/h No slip condition VISCOSITY Based on the experimental analysis, F∝AV/h or F/A∝V/h Shear Stress acting on fluid layer is defined as, τ = F/A Finally, τ∝V/h ∝ du/dy----(1) VISCOSITY y u=V F h u=0 In STEADY operation, the fluid velocity between the plates varies linearly between 0 and V Thus create velocity profile, U(y)/y = V/h ; dU/dy=V/h ----------(2) VISCOSITY y da N N’ u=V F h dӨ M u=0 During differential time interval dt, fluid particles along vertical line MN rotate through a differential angle dӨ, while the upper plate moves a differential distance da = Vdt. VISCOSITY y da N’ N u=V F h dӨ M u=0 For small displacement, dƔ=da/h=tan(dӨ)=Vdt/h=du/dy * dt ----(3) Therefore, shear strain rate is, . Ɣ = du/dy ----(4) VISCOSITY From (1) , τ ∝V/h ∝ du/dy From (4), . du/dy = Ɣ Then, it is understand that shear stress is also proportional to the rate of shearing. Therefore, . τ ∝ du/dy ∝ Ɣ DYNAMIC VISCOSITY . τ =µdu/dy = µ Ɣ; µ: Dynamic Viscosity Fluid with constant µ is called Newtonian Fluid KINEMATIC VISCOSITY r – why do we need kinematic viscosity? – When shear stress and shear rate is influenced by fluid density. – An example of this is the measurement of viscosity using gravity techniques such as a cup with a small orifice in the bottom. With this type of measurement device, a specific volume of fluid passes through the orifice and the time it takes for the volume of fluid to pass through the orifice is proportional to the fluid viscosity. – However, it also depends on the density of the fluid since the more dense the fluid, the faster it will flow through the orifice. The property being measured in this example is then the kinematic viscosity and not the dynamic viscosity. – Unit m2/s and stoke (1 stoke = 1 cm2/s = 0.0001 m2/s) GAS AND LIQUID KINEMATIC VISCOSITY Resistance to deformation, internal friction force develop between fluid layers. Liquids, cohesive forces between the molecules. Collisions in gas molecules. Liquid, Temp increase, Viscosity Decrease. Gas, Temp increase, Viscosity Increase. GAS AND LIQUID KINEMATIC VISCOSITY • Liquid, molecules posses more energy at higher temperature, and oppose the large cohesive intermolecular force more strongly. • Gas, intermolecular forces are negligible, high temperature, gas move at higher velocities. More molecular collisions per unit volume per unit time and higher resistance to flow. FIG 2.4 SHOWS THE ROTATING-DRUM VISCOMETER VISCOMETRY • How is viscosity measured? A rotating viscometer. – Two concentric cylinders with a fluid in the small gap ℓ. – Inner cylinder is rotating, outer one is fixed. MEASUREMENT OF VISCOSITY T FR -----(1) du F A A dy V F A A 2RL l V R 2N 2 3 4 R NL T l VISCOSITY NEWTONIAN & NON NEWTONIAN τ Bingham Plastic – Toothpaste and Mayonnaise Shear thinning - Latex Newtonian - Oil, Water Shear thickening - quicksand dƔ/dt • Newtonian – constant viscosity • Non-Newtonian (apparent viscosity) Shear thinning – viscosity , shearing rate (velocity gradient) Shear thickening – viscosity , shearing rate (velocity gradient) • Bingham plastic – constant viscosity but at certain amount shear stress, fluid starts shearing BLOOD • Blood is a living tissue composed of blood cells suspended in plasma. It consists of aqueous and cellular phase. • The cellular phase is (95% red blood cells, 0.13% white blood cells and 4.9% platelets ) about 45% of the red blood cells. BLOOD • The Plasma (aqueous phase) is about 55% (Water 92%, miscellaneous elements and 7% protein – fibrinogen, globulin and albumin). BLOOD VISCOSITY • Plasma shows Newtonian, however, whole blood • exhibits non-Newtonian behaviour [A]. Blood behaves as: – Newtonian fluids in (> 100s-1), in large arteries where shear rate is above 100s-1 blood is assumed to have constant viscosity at 3.5 cP. – In the microcirculation (small arteries and capillaries) and in veins where the shear rates is low, blood is treated as non Newtonian fluid. – Bingham plastic – The yield stress for blood is very small, approximately 0.005 to 0.01N/m2 FACTORS AFFECTS BLOOD VISCOSITY • The percentage of red blood cell in blood • (Hematrocit). Higher Red Cell, Higher Viscosity . A normal Hematrocit in human males is 42 to 45%. A hematocrit of 40%, the relative viscosity is 4. At a hematocrit of 60%, the relative viscosity is about 8. Therefore, a 50% increase in hematocrit from a normal value increases blood viscosity by about 100%. Such changes in hematocrit and blood viscosity occur in a patients with polycythemia (more than 50%) FACTORS AFFECTS BLOOD VISCOSITY • The effect of temperature on the viscosity of bloods is still not clearly established. The normal practice is to measure the viscosity at body temperature [1]. Temperature decrease, viscosity increase. Viscosity increases approximate 2% for each °C decrease in temperature. Implications: When a person's hand is cooled by exposure to a cold environment, the increase in blood viscosity contributes to the decrease in blood flow (along with neuralmediated thermoregulatory mechanisms that constrict the vessels). FACTOR AFFECT BLOOD VOSCOSITY The apparent viscosity increases with the increase of tube diameter [3], Fahraeus-Lindqvist effect. Larger Arteries RBCs have great random motion: some move horizontally, others vertically, and others with an angle. Thus, internal friction is great, which increases viscosity. Smaller Arteries RBCs have no random motion: each RBC must move singly, one after the other. Thus, internal friction is minor, which decreases viscosity. FACTOR AFFECT BLOOD VOSCOSITY • Protein content in Plasma. • Globulin, Albumin has significant effects where fibrinogen effect is minimal [1]. BLOOD VISCOELASTICITY [4] Blood plasma shows viscosity only, while whole blood shows viscous and elastic. Viscosity - Energy dissipated during flow due to sliding and deformation of red blood cell and its aggregates. Elasticity - Energy stored during flow due to orientation and deformation of red blood cells. BLOOD VISCOELASTIC [4] The viscosity of the viscoelastics material gives the substance a strain rate dependent on time. Elastic Viscoelastics BLOOD VISCOELASTICITY [4] Blood Structure Vs Viscoelasticy Low shear rates - RBC’ cells, large aggregates, Viscoelasticity is dominated by the aggregation properties of RBC. Deformability play lesser role. Moderate shear rates - RBC’s cells disaggregate, cells orient in flow direction and moves. The influence of aggregation on viscoelasticity diminish, and deformability increase. Higher shear rates – Normal RBC’s cells stretch and deform and align with flow. RBC layers slide on plasma. Deformability dominates viscoelasticity. AGGREGATION,VISCOELASTICITY [4] The viscosity and elasticity of blood with low aggregation tendencies (RED) are below the values for normal blood (BLUE) at low shear rates. The viscosity and elasticity of blood with elevated aggregation tendencies (GREEN) are above those for normal blood at low shear rates. But, in the region of high shear rates, where aggregation effects no longer dominate, the viscosity and elasticity approach the same values in each case. DEFORMABILITY,VISCOELASTICITY [4] The idealized example shows how the viscoelasticity blood containing cells with low deformability (RED) can differ from the viscoelasticity of blood with normal cells (BLUE). VISCOELASTICITY, CLINICAL CONDITIONS [4] As an example, the viscoelasticity of an individual's blood with sickle cell disease is markedly different from the viscoelasticity of normal blood. This is clearly seen at high shear rates where the Patient's Elasticity (Red) is significantly higher than the Normal Elasticity (BLACK). SURFACE TENSION SURFACE TENSION The cohesive forces between molecules down into a liquid are shared with all neighboring atoms and balance each other because of symmetry. The attractive forces acting on the surface molecule are not symmetric, and the attractive forces applied by the gas molecules above are very small. It experiences forces only sideways and downward, which creates the surface tension effect. SURFACE TENSION? It can also be defined as the tendency of liquids to reduce their exposed surface to the smallest possible area [The Columbia Encyclopedia, Sixth Edition. Copyright 2008 Columbia University Press] It is denoted by σs, has units of force per unit length or energy per unit area. Since it is energy per area, it also represent the work perform to create a new surface. The unit of the surface tension is N/m or in energy terms as Nm/m2 SURFACE TENSION The external pressure is Po, and the pressure inside the drop is Pi. A force balance yields (Pi-Po) * Pi * R2 – Ɣ*2*Pi*R = 0 ΔP = Pi – Po, ΔP = 2Ɣ/R ---- Law of Laplace The smaller the R, the higher Delta P is required to inflate the surface. THE IMPORTANCE OF SURFACE TENSION IN ENGINEERING/SCIENCE APPLICATIONS Automobile Engineering Surface preparation before painting to ensure that the paint will stick to the surface. Food Engineering To dissolve powders such as milk or cocoa. Life Science Wetting of the eye. The cornea is by nature very hydrophobic, yet a normal eye is wet ! Proteins (called mucins), present in tears, turn the surface of the eye hydrophilic, stabilizing the lachrymal film. If one accidentally smears a fatty cream on the eye, it dries up, causing considerable discomfort. LUNG PHYSIOLOGY AND PATHOLOGY Respiration System Lung physiology and pathology Alveoli – – – – – Gas exchange from lung to the blood or vice versa Spherical in shape and are connected to terminal bronchi in lung Size vary widely Law of Laplace; ΔP = 2Ɣ/R Pressure to inflate smaller alveoli > larger alveoli Lung physiology and pathology SURFACE TENSION has tendency to collapsed the alveoli SURFACTANTS (lipoprotein-rich phospholipid) is secreted to prevent collapsed of alveoli (exhale) and avoid overdistension of alveoli (inhale) Lung physiology and pathology In developing fetuses, surfactant is not produced until last six weeks before normal delivery Danger to premature infant, respiratory distress syndrome (hard to breath) due to lack of surfactant. Labored breathing and incomplete expansion of the lungs. Death?? Synthetic surfactants. SURFACE TENSION • Table 1.5 shows the surface tension of water. CAPILLARY EFFECT • Capillary effect is the • W mg rVg rg (R h) Fsurface 2R s cos • 2 s h cos rgR 2 rise or fall of a liquid in a small-diameter tube. The curved free surface in the tube is call the meniscus. Force balance can describe magnitude of capillary rise. For water-glass in atmospheric air, Ø = 0 CAPILLARY EFFECT • When the attractive forces are between unlike molecules, they are said to be adhesive forces. The adhesive forces between water molecules and the walls of a glass tube are stronger than the cohesive forces (attraction between like molecules) lead to an upward turning meniscus at the walls of the vessel and contribute to capillary action. ASSIGNMENT Find 3 articles that related to the applications of the following fields in solving Biomedical Engineering related problems: 1. 2. 3. Fluid Mechanics. Thermodynamics. Heat Transfer. 2 of the articles must include the application of fluid mechanics concepts and the other article can be any one of the other listed field. Try to sort out the fundamental principles used in the article. Summarize and explain how the principles is used to solved related problems. ASSIGNMENT The report should not be less than 5 pages. The format are as follow: 1. Single spacing 2. Times New Roman - font size – 12 3. Should include: Introduction (Overall and related information on the problems) - 10 marks Problem Statement (What is the problem) - 15 marks Thermofluid Principles (What are the principles use?) – 15 marks How the problem were solved? – 5 marks References – 5 marks SUBMISSION – 11th of August 2008. LATE SUBMISSION – MINUS 25% MARKS PLAGIARISM – MINUS 75% MARKS ***PLAGIARISM IS NOT ALLOWED*** REFERENCE 1. 2. 3. 4. Biofluid Mechanics: The Human Circulation Thermal-Fluid Sciences, Yunus A. Cengel, Robert H. Turner, John M. Cimbala http://en.wikibooks.org/wiki/Biomechanics/Hemodynamics http://www.vilastic.com/FAQ_Blood.htm