ME 3131 Fluid Mechanics and Machinery Oishi Kanta Lecturer Department of Mechanical Engineering, KUET. Reference Books • Fundamentals of Fluid Mechanics Bruce Munson, Donald Young, Theodore Okiishi & Wade Huebsch • Introduction to Fluid Mechanics Robert Fox, Alan McDonald & Philip Pritchard • Fluid Mechanics: Fundamentals and Applications Yunus Çengel & John Cimbala Outline of the Course • Introduction • Fluid Statics • Fluid Dynamics • Flow through Pipes • Measurement of Fluid Flow • Hydraulic Pumps • Hydraulic Turbines Introduction Definition of fluid & fluid mechanics Main difference between fluid and solid Applications of fluid mechanics What is Fluid & Fluid Mechanics ? • Fluid mechanics is the subject that deals with fluids either in motion or at rest and how it impacts on other objects that are in contact with it. • A fluid is defined as a substance that deforms (i.e., flows) continuously when acted on by a shearing stress of any magnitude. • A shearing stress (shearing force per unit area) is created whenever a tangential force acts on a surface. Main difference between solids, liquids & gases • Fluid vs Solid • Difference in behaviour of a solid and a fluid due to a shear force Applications of Fluid Mechanics • All means of transportation such as cars, trucks, aeroplanes, ships, submarines, … • Design all of fluid machinery such as pumps, turbines, compressors, … • Piping systems for transporting water, natural gas, … • Environmental and energy issues (large-scale wind turbines, energy generation from ocean waves, aerodynamics of large buildings) • Biomechanics (Artificial hearts & liver, Synovial fluid in joints, respiratory system, circulatory system, urinary system) • Sports (bicycles and bicycle helmets, skis, and sprinting and swimming clothing; aerodynamics of golf, tennis, soccer ball) Basic Equations of Fluid Mechanics • Dimensions and Units • SI units will be used • Basic dimensions and their SI units • Length L (m) • Mass M (kg) • Time t (s) • Temperature T (ºC & K) • Derived dimensions and their SI units • Speed (m/s) • Force (N or kg.m/s2) • Pressure (Pa or N/m2) Fundamental Concepts Measurement of fluid mass and weight Fluid as a continuum assumption Newton’s law of viscosity Classification of fluids Measures of Fluid Mass and Weight • Fluid as a Continuum • Definition of density at a point Fluid as a Continuum • Viscosity • Behaviour of a fluid placed between two parallel plates Viscosity • Viscosity • Viscosity • Variation of viscosities of common fluids with temperature Types of Fluids • Types of Fluids • For shear thinning fluids (pseudoplastic), apparent viscosity decreases with increasing shear rate-harder the fluid is sheared, less viscous it becomes. Latex paint, some greases, blood, water suspension of clay, polymer solutions are pseudoplastic fluids • For shear thickening fluids (dilatant), apparent viscosity increases with increasing shear rate-harder the fluid is sheared, more viscous it becomes. Shear thickening like water-corn starch, quicksand • Bingham plastic like toothpaste, mayonnaise, asphalt, paper pulp are neither a fluid nor a solid. Such material can withstand a finite shear stress without motion, but once the yield stress is exceeded it flows like a fluid Types of Fluids • Properties of Fluid Compressibility of fluids Surface tension & capillary effect Vapour pressure & cavitation Compressibility of Fluids • Compressibility of Fluids • Compressibility of Fluids • Surface Tension • Some consequences of surface tension Surface Tension o These surface phenomena are due to the unbalanced cohesive forces acting on the liquid molecules at the free surface of fluid. o To visualize how surface tension arises, consider two liquid molecules. o Attractive forces applied on the interior molecule by the surrounding molecules balance each other because of symmetry. • However, molecules along the surface are subjected to a net force that tends to pull them toward the interior of the liquid. The physical consequence of this unbalanced force along the surface is to create the hypothetical membrane or skin that compresses the interior liquid. • Resulting compression effect causes the liquid to minimize its surface area which is the reason for the tendency of the liquid droplets to attain a spherical shape, making minimum surface area for a given volume. • “a droplet that keeps growing by the addition of more mass will break down when the surface tension can no longer hold it together” Surface Tension • Free-body diagram of half a droplet and half a bubble Capillary Effect of Surface Tension • Capillary Effect of Surface Tension • Vapor Pressure & Cavitation • Liquids such as water and gasoline will evaporate if they are simply placed in a container open to the atmosphere. • Evaporation of liquid in open air takes place because some liquid molecules at the surface have sufficient momentum to overcome the intermolecular cohesive forces and escape into the atmosphere • If the container is closed with a small air space left above the surface, a pressure will develop in the space as a result of the vapor that is formed by the escaping molecules. • When an equilibrium condition is reached so that the number of molecules leaving the surface is equal to the number entering, the vapor is said to be saturated and the pressure the vapor exerts on the liquid surface is termed as vapor pressure, py. • Since the development of a vapor pressure is closely associated with molecular activity, the value of vapor pressure for a particular liquid depends on temperature. Vapor Pressure & Cavitation • Boiling, which is the formation of vapor bubbles within a fluid is initiated when absolute pressure of fluid reaches the vapor pressure. • When fluid flows, it is possible to develop very low pressure due to the fluid motion, and if the pressure is lowered to the vapor pressure, vapor bubble forms which are swept into high pressure regions causing sudden collapse with sufficient intensity to actually cause structural damage. • Formation and subsequent collapse of vapor bubbles in a flowing liquid, called cavitation. Types of Fluid Flow Viscous vs. inviscid flow Compressible vs. incompressible flow Laminar vs. turbulent flow Internal vs. external flow Description and classification of fluid motion • Two most difficult aspect to deal fluid mechanics problems are fluids viscous nature and its compressibility. Basically fluid mechanics is broadly classified based on this two properties: viscosity and density 1) Viscous versus inviscid flow 2) Compressible versus incompressible flow 3) Laminar versus turbulent flow 4) Internal versus external flow Possible classification of continuum fluid mechanics Description and Classification of Fluid Motion • Development of viscous and inviscid regions of flow as a result of inserting a flat plate parallel into a fluid stream of uniform velocity Description and Classification of Fluid Motion • Laminar versus turbulent flow: Some flows are smooth and orderly while others are rather chaotic • Highly ordered fluid motion characterized by smooth layers of fluid is called laminar flow. Fluid particles move in smooth layers • Turbulent flow is one in which the fluid particles rapidly mix as they move along due to random three-dimensional velocity fluctuations • Newton’s law of viscosity is not valid for turbulent flows Particle pathlines in one-dimensional laminar & turbulent flows Description and Classification of Fluid Motion • Compressible versus incompressible flow • Flows in which variations in density are negligible is incompressible flows • Flows in which variations in density are not negligible is compressible flows • Liquid flows are incompressible to a high level of accuracy, but the level of variation in density in gas flows depends on velocity of flow (govern by the Mach number, M) • Gas flows can often be approximated as incompressible if the density changes are under about 5%, which is usually the case when M < 0.3 • Mach number, M is the ratio of flow speed (V) to the local speed of sound (c). A flow is called sonic when M = 1, subsonic when M < 1, supersonic when M > 1, and hypersonic when M > 5 Description and Classification of Fluid Motion •
