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• Definition: Strain is the definition of how much a material has been stretched (or compressed) when compared to its original length. The most common measure of strain in metals is called engineering strain, calculated as the change in length divided by the original length. For example, a 2.0&quot; titanium bar that has been stretched to 2.2&quot; is said to have experienced a tensile strain of 0.1, or 10%.
• ### 1. fs rho & mu class 1

1. 1. FLUID MECHANICS – 1 Semester 1 2011 - 2012 Week – 1 Class – 1 Properties of Fluid Compiled and modified by Sharma, Adam
2. 2. OBJECTIVES• Introduction to fluid mechanics• Applications of fluid mechanics• Dimensions and Units {CGS, FPS, MKS and SI system}• Fluid properties – Density and Viscosity
3. 3. INTRODUCTION - CONCEPTSMechanics: The oldest physical sciencethat deals with both stationary andmoving bodies under the influence offorces.Statics: The branch of mechanics thatdeals with bodies at rest.Dynamics: The branch that deals withbodies in motion.Fluid mechanics: The science that dealswith the behavior of fluids at rest (fluidstatics) or in motion (fluid dynamics),and the interaction of fluids with solidsor other fluids at the boundaries.Fluid dynamics: Fluid mechanics is alsoreferred to as fluid dynamics by Fluid mechanics dealsconsidering fluids at rest as a special with liquids and gases incase of motion with zero velocity. motion or at rest. 3
4. 4. INTRODUCTION – SOLIDS AND FLUIDSIntermolecular bonds are strongest in solids and weakest in gases.Solid: The molecules in a solid are arranged in a pattern that is repeatedthroughout.Liquid: In liquids, molecules can rotate and translate freely.Gas: In the gas phase, the molecules are far apart from each other, andmolecular ordering is nonexistent.The arrangement of atoms in different phases: (a) molecules are atrelatively fixed positions in a solid, (b) groups of molecules move abouteach other in the liquid phase, and (c) individual molecules move about atrandom in the gas phase. 4
5. 5. INTRODUCTION – LIQUID AND GASIn a liquid, groups of molecules can move relative to each other, but thevolume remains relatively constant because of the strong cohesiveforces between the molecules. As a result, a liquid takes the shape ofthe container it is in, and it forms a free surface in a larger container in agravitational field.A gas expands until it encounters the walls of the container and fills theentire available space. This is because the gas molecules are widelyspaced, and the cohesive forces between them are very small. Unlikeliquids, a gas in an open container cannot form a free surface.Unlike a liquid, a gas does not form a free surface, and it expands tofill the entire available space. 5
6. 6. INTRODUCTION – GAS AND VAPORGas and vapor are often used as synonymous words.Gas: The vapor phase of a substance is customarily called a gas whenit is above the critical temperature.Vapor: Usually implies that the current phase is not far from a state ofcondensation.On a microscopic scale, pressure isdetermined by the interaction ofindividual gas molecules.However, we can measure the pressureon a macroscopic scale with a pressuregage. 6
7. 7. INTRODUCTION - STRESSStress: Force per unit area.Normal stress: The normalcomponent of a force acting on asurface per unit area.Shear stress: The tangentialcomponent of a force acting on asurface per unit area.Pressure: The normal stress in afluid at rest.Zero shear stress: A fluid at restis at a state of zero shear stress.When the walls are removed or aliquid container is tilted, a sheardevelops as the liquid moves to The normal stress and shear stress atre-establish a horizontal free the surface of a fluid element. Forsurface. fluids at rest, the shear stress is zero and pressure is the only normal stress. 7
8. 8. DIFFERENCE BETWEEN SOLID & FLUIDFluid: A substance in the liquidor gas phase.A solid can resist an appliedshear stress by deforming.A fluid deforms continuouslyunder the influence of a shearstress, no matter how small.In solids, stress is proportionalto strain, but in fluids, stress is Deformation of a rubber block placedproportional to strain rate. between two parallel plates under theWhen a constant shear force is influence of a shear force. yapplied, a solid eventually stopsdeforming at some fixed strainangle, whereas a fluid never u=Ustops deforming and h u(y)approaches a constant rate ofstrain. x u=0 8
9. 9. AREAS OF APPLICATIONS Fluid dynamics is used extensively in the design of artificial hearts. Shown here is the Penn State Electric Total Artificial Heart. 9
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12. 12. DIMENSIONS AND UNITS 12
13. 13. DIMENSIONS AND UNITS• Any physical quantity can be characterized by dimensions.• The magnitudes assigned to the dimensions are called units.• Some basic dimensions such as mass m, length L, time t, and temperature T are selected as primary or fundamental dimensions, while others such as velocity V, energy E, and volume V are expressed in terms of the primary dimensions and are called secondary dimensions, or derived dimensions.• Metric SI system: A simple and logical system based on a decimal relationship between the various units.• English system: It has no apparent systematic numerical base, and various units in this system are related to each other rather 13 arbitrarily.
14. 14. Some SI and English UnitsWork = Force × Distance 1 J = 1 N∙m The SI unit prefixes are used in all branches of engineering. The definition of the force units. 14
15. 15. W weight m mass g gravitational acceleration A body weighing 60 kgf on earth will weigh only 10 kgf on the moon. The relative magnitudes of the force in newton (N) and kilogram-force (kgf)The weight of a unitmass at sea level. See page 21 15
16. 16. Unit conversion constants 16
17. 17. DENSITY 17
18. 18. DENSITY AND SPECIFIC GRAVITYDensity Relative density or Specific gravity: The ratio of the density of a substance to the density of some standard substance at a specifiedSpecific volume temperature (usually water at 4°C). Specific weight: The weight of a unit volume of a substance. Density is mass per unit volume; specific volume is volume per unit mass. 18
19. 19. VISCOSITY 19
20. 20. VISCOSITYViscosity: A property that represents the internal resistance of a fluid tomotion or the “fluidity”.Drag force: The force a flowing fluid exerts on a body in the flowdirection. The magnitude of this force depends, in part, on viscosity. The viscosity of a fluid is a measure of its “resistance to deformation.” Viscosity is due to the internal frictional force that develops between different layers of fluids as they are forced to move relative to each other. A fluid moving relative to a body exerts a drag force on the body, partly because of friction caused by viscosity. 20
21. 21. Newtonian fluids: Fluids for which the rate of deformation is proportional to the shear stress. Shear stress The behavior of a fluid in laminar flow Shear force between two parallel plates when the upper plate moves with a constant velocity. µ coefficient of viscosity Dynamic (absolute) viscosityAngular displacement or Shear strain kg/m ⋅ s or N ⋅ s/m2 or Pa ⋅ s 1 poise = 0.1 Pa ⋅ s 21
22. 22. Kinematic viscosity m2/s or stoke 1 stoke = 1 cm2/sFor liquids, both the dynamic andkinematic viscosities are practicallyindependent of pressure, and any smallvariation with pressure is usuallydisregarded, except at extremely highpressures.For gases, this is also the case fordynamic viscosity (at low to moderatepressures), but not for kinematic viscositysince the density of a gas is proportional toits pressure. Dynamic viscosity, in general, Viscosity for gases: does not depend on pressure, but kinematic viscosity does. Viscosity for liquids 22
23. 23. L length of the cylinder number of revolutions per unit timeThis equation can be used to calculate the viscosity of a fluid bymeasuring torque at a specified angular velocity.Therefore, two concentric cylinders can be used as a viscometer, adevice that measures viscosity. 23
24. 24. Summary Introduction to Fluid mechanics Concepts and definitions Applications of fluid mechanics Dimensions and Units Basic dimensions in FM Different units of measurement Properties of fluids Density and Relative density Absolute and kinematic viscosity 24