chapter 1 introduction1.pdf
- 1. Bahir Dar Institute of Technology(BiT) Faculty of Mechanical and Industrial Engineering Mechanical Engineering Department Fluid Mechanics I Chapter One Introduction By;Tereche Getnet
- 2. Contents of the Chapter Introduction to Fluids Definition of fluids Properties of fluids Unit conversion Factors Application Areas of Fluid Mechanics 2
- 3. Fluid mechanics is the study of fluids either in motion (fluid dynamics) or at rest (fluid statics). all matter consists of only two states, fluid and solid. Any shear stress applied to a fluid, no matter how small, will result in motion of that fluid. The fluid moves and deforms continuously as long as the shear stress is applied. we can say that a fluid at rest must be in a state of zero shear stress, a state often called the hydrostatic stress condition in structural analysis. A solid can resist a shear stress by a static deflection; a fluid cannot. There are two classes of fluids, liquids and gases. Introduction to Fluids
- 4. Solid Fluid can resist a shear stress by a static deflection, fluid moves and deforms continuously as long as shear stress is applied Liquid Gas strong cohesive forces Negligible cohesive force tends to retain its volume free to expand until it encounters confining walls will form a free surface in a gravitational field if unconfined from above. a gas forms an atmosphere that is essentially hydrostatic Concerned with buoyancy concerned with gravitational effects other than buoyancy water, oil, mercury, gasoline, and alcohol air, helium, hydrogen, and steam.
- 5. • A liquid, being composed of relatively close-packed molecules with strong cohesive forces, tends to retain its volume and will form a free surface in a gravitational field if unconfined from above. common liquids, such as water, oil, mercury, gasoline, and alcohol in there common temperature and pressure Ranges. • Since gas molecules are widely spaced with negligible cohesive forces, a gas is free to expand until it encounters confining walls. A gas has no definite volume, and when left to itself without confinement, a gas forms an atmosphere that is essentially hydrostatic. Gases cannot form a free surface, and thus gas flows are rarely concerned with gravitational effects other than buoyancy. common gases, such as air, helium, hydrogen, and steam.
- 6. Properties of Fluid 1. Properties of the Velocity Field; There are two different points of view in analyzing problems in mechanics. • Eulerian method of description; is concerned with the field of flow. In the eulerian method we compute the pressure field p(x, y, z, t) of the flow pattern, not the pressure changes p(t) that a particle experiences as it moves through the field. • lagrangian description; which follows an individual particle moving through the flow. which is more appropriate to solid mechanics, will not be treated in this book. Fluid dynamic measurements are also suited to the eulerian system. For example, when a pressure probe is introduced into a laboratory flow. a) The Velocity Field; Foremost among the properties of a flow is the velocity field V(x, y, z, t). In fact, determining the velocity is often tantamount to solving a flow problem, since other properties follow directly from the velocity field. velocity is a vector function of position and time and thus has three components u, v and w, each a scalar field in itself:
- 7. b) The Acceleration Field; The acceleration vector, a=dV/dt, occurs in Newton’s law for a fluid and thus is very important. the final result for acceleration is nonlinear.
- 8. Example1; Consider the steady, incompressible, two-dimensional velocity field. (a) Calculate the material acceleration at the point (x=2 m, y=3 m). Solution; Assumptions; 1.The flow is steady and incompressible. 2.The flow is two-dimensional, implying no z-component of velocity and no variation of u or v with z.
- 9. Properties of Fluid Thermodynamic properties(intensive) Intensive Transport Properties • Pressure p Internal energy û Coefficient of viscosity • Density ρ • Temperature T Enthalpy h Thermal conductivity k • Specific Gravity Entropy s Specific Weight Specific heats cp and cv Example2: Determine the density, specific gravity, specific volume and mass of the air in a room whose dimensions are 4 m*5 m*6 m at 100 kPa and 25°C .
- 10. Exercise1: Calculate the density, specific weight and weight of one liter of petrol of specific gravity = 0.7. Exercise2: Calculate the specific weight, density and specific gravity of one liter of a liquid which weighs 7 N. Exercise 3: Calculate the specific mass, specific weight, specific volume and specific Gravity of a liquid having a volume of 6 m3 and weight of 44 kN.
- 11. 3. Viscosity and Other Secondary Properties Viscosity; relates the local stresses in a moving fluid to the strain rate of the fluid element. Viscosity is a quantitative measure of a fluid’s resistance to flow. it determines the fluid strain rate that is generated by a given applied shear stress. Then, the applied shear is also proportional to the velocity gradient for the common linear fluids. The constant of proportionality is the viscosity coefficient µ.
- 12. µ has dimensions of stress–time (M/LT). • The linear fluids that follow the above are called Newtonian fluids. The shear stress is proportional to the slope of the velocity profile and is greatest at the wall. Further, at the wall, the velocity u is zero relative to the wall: This is called the no-slip condition and is characteristic of all viscous fluid flows. • The viscosity of a fluid increases only weakly with pressure. Temperature, however, has a strong effect, with µ increasing with T for gases and decreasing for liquids.
- 13. • Fluids for which the apparent viscosity increases with the rate of deformation (such as solutions with suspended starch or sand) are referred to as dilatant or shear thickening fluids, and those that exhibit the opposite behavior (the fluid becoming less viscous as it is sheared harder, such as some paints, polymer solutions, and fluids with suspended particles) are referred to as pseudoplastic or shear thinning fluids. • Some materials such as toothpaste can resist a finite shear stress and thus behave as a solid, but deform continuously when the shear stress exceeds the yield stress and thus behave as a fluid. Such materials are referred to as Bingham (ideal plastic). Example Sewage sludge, drilling muds.
- 14. The Reynolds Number; The primary parameter correlating the viscous behavior of all Newtonian fluids is The dimensionless Reynolds number. Very low Re indicates viscous creeping motion, where inertia effects are negligible. Moderate Re implies a smoothly varying laminar flow. High Re probably spells turbulent flow.
- 15. Flow between Plates With zero acceleration and assuming no pressure variation in the flow direction, you should show that a force balance on a small fluid element leads to the result that the shear stress is constant throughout the fluid. Hence a=0 and b=V/h. Then the velocity profile between the plates is given by
- 16. Example3: If the velocity distribution for flow over a plate is given by 𝑢 = 2𝑦 − 𝑦2 in which u is velocity in metre per second at a distance y metre above the plate, determine the velocity gradient and shear stress at y = 0 and y= 0.15 m. Take dynamic viscosity of fluid as 0.9 N.s/m2.
- 17. Mechanics of fluids is extremely important in many areas of engineering and science. Examples are: Biomechanics Blood flow through arteries and veins Airflow in the lungs Flow of cerebral fluid Households Piping systems for cold water, natural gas, and sewage Piping and ducting network of heating and air conditioning systems Meteorology and Ocean Engineering Movements of air currents and water currents Chemical Engineering Design of chemical processing equipment
- 18. Mechanical Engineering Design of pumps, turbines, air-conditioning equipment, pollution-control equipment, etc. Design and analysis of aircraft, boats, submarines, rockets, jet engines, wind turbines, biomedical devices, the cooling of electronic components, and the transportation of water, crude oil, and natural gas. Civil Engineering Transport of river sediments Pollution of air and water
- 19. Dimensions and Units A dimension is the measure by which a physical variable is expressed quantitatively. A unit is a particular way of attaching a number to the quantitative dimension. primary dimensions from which all other dimensions can be derived (secondary): mass, length, time, and temperature.
- 20. Thank you