Dr. Nidal Hussein What is a Fluid? A fluid is defined as a substance that deforms continuously whilst acted upon by any force (shear force) tangential to the area on which it acts The ratio of the shear force to the area on which it acts is known as the shear stress A Fluid owes its shape at any time to that of the vessel containing it Fluids flow Types of Fluids Fluids are divided into liquids and gases depending on their molecular structure A fixed amount of a liquid has a definite volume which varies only slightly with temperature and pressure A Fixed amount of a gas, by itself in a closed container, will always expand until its volume equals that of the container 1
When a shear stress is applied: Fluids continuously deform Solids deform or bend Types of Fluids Liquids have much greater densities than gases A given volume of a liquid contains larger number of molecules than an equal volume of a gas Weight of a liquid has an important role to play unlike gases Molecular structure The different characteristics of solids, liquids and gases result from differences in their molecular structure In solids and liquids the molecules are much closer together than in a gas Molecules are in continual movement Molecules have an attraction for one another When two molecules come close to one another (of the order of the diameter of a molecule), repulsion force pushes them apart (like two billiard balls) 2
In a solid, the movement of molecules is slight (vibration) and do not move relative to one another In a liquid the movement of is greater, but they attract and repel one another, they move in curves rather than in straight lines) The force of attraction between liquid molecules is sufficient to keep them together in a definite volume In gases, molecular movement is very much greater; the number of molecules in a given space is much less. Any molecule travels a much greater distance before meeting another. The forces of attraction between molecules (inversely proportional to the square of the distance) are negligible (molecules are free to travel away from one another until they are stopped by a solid or liquid boundary The continuum To understand fluids behavior, we need to model the action of each individual molecule and focus on the average conditions of velocity, pressure, temperature, density Reasonable and valid assumption when the number of molecules involved in the situation is huge 1 m 3 volume of air at STP (P = 101.3 kpa, T=15 C ) contains 2.5 x 10 25 molecules. NOT valid with small number of molecules (very very low pressure gases) In fluid mechanics, usually we do not deal with single molecules (scientists), we consider a continuous distribution of matter with no empty space = continuum (engineers) Quantities such as velocity, acceleration and the properties of the fluid are assumed to vary continuously (or remain constant) from one point to another in the fluid 3
Fluid Mechanics Principles of mechanics are those of the conservation of matter, the conservation of energy and Newton s laws of motion The field of study in which the fundamental principles of general mechanics are applied to liquids and gases to explain observed phenomena, and to predict the behavior of fluid under specified conditions Fluid mechanics Fluid statics for fluid at rest Fluid dynamics for fluid in motion Some History ARCHIMEDES (287 212 B.C.): Established elementary principles of buoyancy and flotation LEONARDO da VINCI (1452 1519) Expressed elementary principle of continuity; observed and sketched many basic flow phenomena; suggested designs for hydraulic machinery. EVANGELISTA TORRICELLI (1608 1647) Related barometric height to weight of atmosphere, and form of liquid jet to trajectory of free fall DANIEL BERNOULLI (1700 1782) Experimented fluid motion, coining name hydrodynamics ; devised manometry technique and adapted primitive energy principle to explain velocity-head indication 4
Some History GOTTHILF HEINRICH LUDWIG HAGEN (1797 1842) Conducted original studies of resistance in and transition between laminar and turbulent flow JEAN LOUIS POISEUILLE (1799 1869) Performed tests on resistance of flow through capillary tubes HENRI PHILIBERT GASPARD DARCY (1803 1858) Performed extensive tests on filtration and pipe resistance; initiated open-channel studies GEORGE GABRIEL STOKES (1819 1903) Derived analytically various flow relationships ranging from wave mechanics to viscous resistance particularly that for the settling of spheres. Fluid Mechanics The Basic laws governing the flow motion include: The conservation of mass Newton s second law of motion (Net force acting on a system is proportional to the system mass times its acceleration) The principle of angular momentum (The net torque acting on a system is equal to the rate of change of angular momentum of the system) The first law of theromdynamics - compressible fluids (Conservation of energy) The second law of theromdynamics - compressible fluids Basic Equation The ideal gas equation of state p RT 5
Fluid mechanics is applied in such areas as: Canal Design Dam systems The design of pumps, compressors, piping and ducting used in the water and air conditioning systems Piping systems needed in chemical, water and wastewater treatment plants Aerodynamics of automobiles and sub- and supersonic airplanes development of many different flow measurement devices such as gas pump meters Large-scale wind turbines, energy generation from ocean waves, artificial hearts and valves and liver, aerodynamics of the golf, tennis, and soccer ball, smart fluids and microfluids are just a small sampling of the newer areas of fluid mechanics A system is defined as a fixed, identifiable quantity of mass The system boundaries separate the system from the surroundings(fixed or movable), no mass crosses the system boundaries. A control volume is an arbitrary volume in space through which fluid flows The geometric boundary of the control volume is called the control surface real or imaginary 6
Control Volume (or Open System ) System (or Closed System ) A reducing water pipe section has an inlet diameter of 50 mm and exit diameter of 30 mm. If the steady inlet speed (averaged across the inlet area) is 2.7 m/s, find the exit speed. 7
Assumption: Water is incompressible (density ρ=constant) Use conservation of mass No reaction (mass in = mass out) ρv i A i = ρv e A e Qualitative understanding not enough Fast of slow Must express in quantitative terms Velocity is numerical value and units Quantity is used to identify any physical attribute capable of representation by measurement (e.g. mass, weight, volume, distance, time and velocity) The value of a quantity is defined as the magnitude of the quantity expressed as the product of a number (numeric) and a unit 8
Each quantity has A name (represented by a quantity symbol) A unit (represented by a unit symbol) A unit is a particular way of attaching a numerical value to the quantity System of units Units of the Système International d Unités (SI units ) international version of the metric system (Sanctioned in the US since 1866) Imperial system of measure Metric System (based on based on mètre des Archive (CGS-MKS-MTS) Units within a system of units are: Base units (primary units) independent-, taken together, the base units define the system of units Derived units (secondary units) which can be determined from the definition of the base units Velocity is reported as 30 m/s 30 is described as the numeric m/s are the units of measurement Equivalent to 108 km/h Find it in ft/week??? 9
Dimension Vs Units The dimension of a variable is a fundamental statement of the physical nature of that variable Physical quantities such as length, time, mass, and temperature are referred to as dimensions Distance, depth, height, width, thickness have different meanings, but all have the dimensions of length and can all be measured in the same units(e.g. meters) Flow rate: rate at which substance of mixture entering or leaving the system (Volume/time) 10
From these base or primary units, all other units, known as derived or secondary units m/s: a unit of velocity Two abbreviated forms of notation were in common use: metre/second =m/s or m s 1 Recently, The half-high dot (also known as the middle dot)was the most abbreviation used metre/second is expressed as m s 1 11
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Small Quantities: Deci(10^-1), centi(10^-2), milli(10^-3), micro(10^-6), nano(10^-9), pico(10^-12), femto(10^-15) Larg Quantities: deka(10^1), hecto(10^2), kilo(10^3), mega(10^6), giga(10^9), tera(10^12), peta(10^15) Equations must be dimensionally homogeneous Units must be consistent Absolute Metric system The unit of mass is the gram, of length is centimeter, of time is the second. Force units is 1 dyne 1 g cm/sec 2 British Gravitational (BG)system, the unit of force is the pound (lb f ), of length is the foot (ft) 1 slug 1 lb f sec 2 /ft English Engineering (EE)system A force of one pound (1 lb f ) gives a pound mass (1 lb m ) an acceleration equal to standard acceleration of gravity on Earth, 32.17 ft/sec 2. 13
Since a force of 1 lbf accelerates 1 lbm at 32.2 ft/sec2, it would accelerate 32.2 lbm at 1 ft/sec2. A slug also is accelerated at 1 ft/sec2 by a force of 1 lbf. Therefore, 1 slug = 32.2 lb m 28 14