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Properties of Fluids-Basic Concepts Prof. Rohit Goyal Professor, Department of Civil Engineering Malaviya National Institute of Technology Jaipur E-Mail: rgoyal_jp@yahoo.com Topics Covered Applications of FM Definition of Fluid Properties of Fluids Density Viscosity Surface Tension Compressibility 2 Fluid Mechanics??? It is physical science dealing with the action of fluids at rest or in motion, and with applications and devices in engineering using fluids. Fluid mechanics can be subdivided into two major areas fluid statics, deals with fluids at rest fluid dynamics, deals with fluids in motion 3 Applications of Fluid Mechanics We experience fluid mechanics in every day life Blood circulation through body Water, sewerage, gas flow through pipes Pumps, turbines, hydraulic machines Aircraft, ship movements through air, water Spin and flight of cricket, golf ball etc. 4 Definition of Fluid Matter can have three physical form Solid, liquid and gaseous Liquid and gaseous phases are combined together to be represented as fluids – Why? Because these phases have some common characteristics 5 Definition of Fluid… A fluid is defined as a substance which deforms continuously under the action of shear stress, regardless of it’s magnitude 6 Definition of Fluid… So, in solids, deformation grows and with it the resistance to shear stress increases. It stops as soon as both shear stress and it’s internal resistance are equal For fluids, deformation continues till shear stress is applied and equilibrium is never reached 7 Liquid Vs Gases In liquids, molecules are packed closer Unlike solid, molecules can change relative position amongst themselves Still significant force of attraction between molecules Incompressible In Gases, molecules are further apart Very weak force of attraction, fills container Compressible 8 Continuum Concept Molecules of fluids are separated in space (more so in gases). Molecules may be in continuous motion Density, pressure, velocity for a point at any instant would not make sense if there is a void at that point at that instant In order to simplify things we do not go to molecular level for certain aspects and so assume fluid as “continuum” 9 Continuum Concept… This concept fails at extreme states of pressure and temperatures According to requirement of continuum, we must deal with dimensions much larger than mean free path of molecules Mean free path: Average path before colliding with another particle Air’s mean free path at earth surface is 6.25x10-6 cm. 10 Fluid Properties Fluid properties are measures of its characteristics Density, specific weight, specific gravity Viscosity Compressibility Surface Tension etc. 11 Density Density is defined as the mass in a unit volume, usually defined as (rho) = m/V (m is mass in kilograms and V is volume in m3) Density of water at 4oC is 1000 kg/m3. Density at a point is defined as m lim V 0 V 12 Measurement of Density-Solid Density = 103 g/27 ml = 3.81 g/ml or 3.81 g/cc. Volume=27 ml 13 Mass=103 g Measurement of Density-Liquid Density = 50 g/50 ml = 1.0 g/ml or 1.0 g/cc. Mass=93-43=50 g Volume=50 ml 14 Measurement of Density-Gases Density = 0.2 g/500 ml = 0.0004 g/ml or 0.0004 g/cc. Mass=110.2-110 =0.2 g Volume=500 ml 15 Specific Weight Specific weight of a fluid is the weight per unit volume, usually defined as (gamma) = g (where g is acceleration due to gravity) Specific weight of water = 9.81 kN/m3. Specific weight may vary with altitude, density usually remains constant 16 Specific Volume Specific Volume is volume occupied by unit mass of a fluid It is inverse of density (). It’s unit would be m3/kg It is commonly applied to gases Usually denoted by v. 17 Specific Gravity Specific gravity is the density of a substance divided by the density of another substance that is used as a standard. For solids and liquids, water at 4oC (39oF) is usually the standard. (In Engineering 20oC is used) Water has maximum density at 4oC 18 Viscosity The viscosity of a liquid is a measure of how much the liquid resists flow, usually denoted by . Viscosity tends to prevent fluids from flowing when subjected to an applied force. High-viscosity fluids resist flow; low-viscosity fluids flow easily. The tenacity with which a moving layer of fluid drags adjacent layers of fluid along with it determines its viscosity 19 Viscosity-Why?? Like solids in fluids also there is attraction between molecules known as cohesion Cohesion causes resistance to flow between two layers moving at different speeds Faster layer tries to increase velocity of slower layer and vice versa Also momentum transfer between the layer causes mix traffic and so cause resistance (mixing length theory) 20 Viscosity… The viscosity of water is lower than that of heavy oils because oils contain large, convoluted molecules that catch on one another. The polarity of the molecules in water, however, causes them to attract one another, making water more viscous than a nonpolar liquid, such as propane. Viscosity decreases as temperature increases because additional heat energy enables molecules to overcome attractions to one another and move more freely. Except for very high pressures viscosity usually does not vary with pressure 21 Definition of Viscosity Viscosity is defined by Newton's law of viscosity Newton formulated that shear stress is proportional to the rate of deformation in fluids (rate of shear strain) Shear stress () deformation rate (v/y) Constant of proportionality is defined as viscosity (). 22 Deformation of Fluid v is known as viscosity. Also known as 23 y dynamic viscosity or absolute viscosity Newtonian Fluids Not all fluids obey Newton’s law of viscosity Those fluids which follows it are known as Newtonian fluids Other are non-Newtonian fluids (like paints, printing ink, tar slurry etc.). Non-Newtonian fluids are studied under rheology, a science of deformation and flow. 24 Classification of Fluids 25 Unit of Viscosity Unit of Viscosity () is N.s/m2. In terms of mass it would be kg/m.s. Another unit is Poise (after French scientist Poiseuille) is also used to express viscosity 1 poise (P) = 1 g/(cm.s) 1 N.s/m2=10 P Viscosity of water at 20oC is 1 centipoise. 26 Kinematic viscosity We often encounter the term / So a term kinematic viscosity, referred as (nu) is defined as ratio of dynamic viscosity and density. = /. Unit of is m2/s. It is also expressed in terms of strokes (English mathematician) 1 stroke = 1 cm2/s. 27 Viscosity of some common fluids 28 Surface Tension A small drop of liquid becomes spherical, the smallest surface possible The molecules at the surface are pulled in by the cohesive force between themselves and molecules inside the droplet. The liquid keeps its droplet shape because there are no liquid molecules outside the surface to balance this inward pull. 29 Surface Tension in Water 30 Surface Tension Liquid behaves as if there free surface is stretched like membrane under tension This is because molecules on surface are pulled only from three sides by like molecules (cohesion) as compared to rest of them being pulled from all four directions Tensile strength computed per unit length is termed as surface tension, usually denoted by (Sigma). 31 Capillary action Like cohesion (attraction between like molecules) attraction between unlike molecules is called adhesion Cohesion and adhesion give rise to capillary rise when a small tube is inserted into a liquid. Degree of adhesion is represented by contact angle as shown next, water < 90o and mercury > 900 32 Capillary Rise/Depression 33 Capillary Rise/Depression Capillary rise in a small clean circular glass tube can be calculated by balancing the weight of liquid which has risen to height say h to the surface tension force, so h = 4 cos() / g d Or by observing h we can find value of surface tension () 34 Compressibility All fluid undergo changes in volume under pressure. Changes may be negligible for liquids up to certain pressures Compressibility is defined as C = -(V/V)/ p Negative sign because V is negative for positive p Bulk modulus of elasticity (K) is reciprocal of compressibility, so (K=1/C) Compressibility must usually be accounted for in phenomena such as water hammer/pressure waves 35 Vapor Pressure Vapor Pressure is pressure created by the vapor, or gas, of a substance that forms above a liquid or solid of the same substance. All liquids, and even some solids, vaporize continuously. The term vapor pressure usually refers to equilibrium vapor pressure, or the pressure at which the rate that particles (atoms or molecules) leave the substance to form vapor equals the rate that particles reenter the substance from the vapor. 36 Cavitations In some flow systems, liquid pressure at certain points may become less than vapor pressure of that liquid, causing vaporization. Vapor in form of bubble then travels of zone of higher pressure and collapses into liquid leading to cavitation. 37 Ideal Fluid Euler first recognized that dynamical laws for fluids can only be expressed in a relatively simple form if the fluid is assumed incompressible and ideal, that is, if the effects of friction or viscosity can be neglected. Because, however, this is never the case for real fluids in motion, the results of such an analysis can only serve as an estimate for those flows where viscous effects are small. 38 Flow Properties Apart from fluid properties, there are certain flow properties of interest in fluid mechanics Pressure Velocity Discharge Type and state of flow Pathline, streamline and streakline 39 Pressure Pressure is the force per unit area exerted by a liquid or gas on a body or surface, with the force acting at right angles to the surface uniformly in all directions. F Pressure at a point p A 0 lim A Unit of pressure is kN/m2 40 Velocity Velocity of a particle is the time rate of change of its distance. Velocity is vector quantity which has both magnitude and direction (Speed is scalar) Velocity may vary with space and time and so v= v(x, y, z, t) Velocity may be absolute or relative 41 Discharge Quantity of flow crossing a section per unit time is called the rate of flow or discharge. Section is usually physical section but may also be imaginary section as a concept (example discharge between two streamlines). Unit for discharge is m3/sec. 42 Discharge computation If we have velocity diagram for flow through a say, pipe Vav Velocity Diagram Q v dA A Average velocity is a useful concept which allows us to write simply Q = AV 43 Type of Flow Type of flow could be Steady or Unsteady Steady, when properties such as pressure and velocity does not change with time Uniform and Non-uniform When properties does not change with space 44 State of flow Fluid motion and resistance to motion may be governed by many different types of forces such as Inertia force Gravity force Viscous force Based on relative importance of forces state of flow may be defined as laminar or turbulent, sub or super critical etc. 45 Pathline, streamline & streakline In order to describe flow patterns we sometime make use of imaginary lines such as Pathline: This is a path traversed by a single particle over an interval of time. Streamline: It is a imaginary line joining points along the velocity vector at any instant. By definition there cannot be any flow perpendicular to direction of flow Streakline: It is a line joining particles which have passed a fixed point in flow field. 46