Fluid Physics PDF

The Physics of Fluid 1 – INTRODUCTION Introduction and Concepts Mechanics The oldest physical science that deals with both stationery and moving boundaries under the influence of forces. Fluid Mechanics The science that deals with the behavior of fluids: at rest (fluid statics) ...

The Physics of Fluid 1 – INTRODUCTION Introduction and Concepts Mechanics The oldest physical science that deals with both stationery and moving boundaries under the influence of forces. Fluid Mechanics The science that deals with the behavior of fluids: at rest (fluid statics) in motion (fluid dynamics) interaction of fluids with solids or other fluids  Statics Fluid mechanics Dynamics FIGURE 1-1 Fluid deals with liquids and gases in motion or at rest. What Is a Fluid?  A substance either in gas (vapor) or liquid phase  Properties: ability to resist an applied shear (or tangential) stress deforms continuously under the influence of shear stress FIGURE1-5 The arrangement of atoms in different phases: (a)molecules are at relatively fixed positions in a solid, (b)groups of molecules move about each other in the liquid phase, and (c)individual molecules move about at random in the gas phase.  Liquid Gas  molecules can move  expands until it encounters relative to each other the walls of the container  volume remains relatively  fills the entire available constant (strong cohesive space forces)  cohesive forces between  take the shape of the molecules are very small container  cannot form a free surface  forms a free surface in a in an open container larger container in a  Intermolecular bonds are gravitational field weakest in gases Application Areas of Fluid Mechanics Automobile All components associated with the transportation of the fuel from the fuel tank to the cylinders – the fuel line, fuel pump, and fuel injectors or carburetors, mixing of fuel, air in the cylinder, and purging of combustion gases in exhaust pipes Heating and air-conditioning Aircraft, boats, submarines, rockets, wind turbines, etc. 2 – THE NO-SLIP CONDITION  No-Slip Condition Water in a river cannot flow through large rocks, and must go around them. That is, the water velocity normal to the rock surface must be zero, and water approaching the surface normally comes to a complete stop at the surface. A fluid in direct contact with a solid “sticks” to the surface, and there is no slip. This is known as the slip- condition. Figure 1–14 clearly shows the evolution of a velocity gradient as a result of the fluid sticking to the surface of a blunt nose. The layer that sticks to the surface slows the adjacent fluid layer because of viscous forces between the fluid layers, which slows the next layer, and so on. All velocity profiles must have zero values with respect to the surface at the points of contact between a fluid and a solid surface. The no-slip condition is responsible for the development of the velocity profile.  The flow region adjacent to the wall in which the viscous effect (and thus the velocity gradients) are significant is called the boundary layer.  Another consequence of the no-slip condition is the surface drag (or skin friction drag), which is the force a fluid exerts on a surface in the flow direction.  When a fluid is forced to flow over a curved surface, such as the back side of a cylinder, the boundary layer may no longer remain attached to the surface and separates from the surface.  This process called flow separation. 3 – CLASSIFICATION OF FLUID FLOWS Viscous versus Inviscid Regions of Flow Viscous flow is a flow where viscosity is important, while an inviscid flow is a flow where viscosity is not important. Inviscid flow: viscous forces are negligibly small compared to inertial or pressure forces. Gases and liquids alike are considered fluids and any fluid has a viscosity. Regions where frictional effects are significant are called viscous regions (i.e. boundary layer). They are usually close to solid surfaces. Regions where frictional forces are small compared to inertial or pressure forces are called inviscid flow regions.  Internal versus External Flow The flow of an unbounded fluid over a surface is treated as 'external flow' and if the fluid is completely bounded by the surface, then it is called as 'internal flow'. For example, flow over a flat plate is considered as external flow and flow in a pipe/duct is internal flow. Internal flows are dominated by the influence of viscosity throughout the flow field. For external flows, viscous effects are limited to boundary layers near solid surfaces and to wake regions downstream of bodies. Compressible versus Incompressible Flow A flow is classified as incompressible if the density remains nearly constant. Liquid flows are typically incompressible. Gas flows are often compressible, especially for high speeds. An important parameter in the study of compressible flow is the speed of sound (or the sonic speed), defined as the speed at which an infinitesimally small pressure wave travels through a medium. A second important parameter in the analysis of compressible fluid flow is the Mach number (Ma). V Ma = c V = local flow velocity c = speed of sound, 346 m/s Ma number Flow type 1 Sonic 1 Supersonic >> 1 hypersonic ≈1 Transonic Laminar versus Turbulent Flow Laminar: highly ordered fluid motion with smooth streamlines. Turbulent: highly disordered fluid motion characterized by velocity fluctuations and eddies. Transitional: a flow that contains both laminar and turbulent regions Reynolds numbers can be used to identify the flow type. Source: https://www.nuclear-power.net/nuclear-engineering/fluid-dynamics/flow-regime/internal-vs- external-flow/ Reynolds number (Re) 𝜌𝑢𝐿 𝑢𝐿 𝐷𝑢𝜌 𝑅𝑒 = = = 𝜇 𝜈 𝜇 where: ρ is the density of the fluid (SI units: kg/m3) u is the velocity of the fluid with respect to the object (m/s) L is a characteristic linear dimension (m) D is pipe diameter (m) μ is the dynamic viscosity of the fluid (Pa·s or N·s/m2 or kg/m·s) ν is the kinematic viscosity of the fluid (m2/s). Re < 2300: Laminar flow Re = 2300-4000: Transitional flow Re > 4000: Turbulent flow Natural (or Unforced) versus Forced Flow In forced flow, a fluid is forced to flow over a surface or in a pipe by external means such as a pump or a fan. In natural flows, any fluid motion is due to natural means such as the buoyancy effect, which manifests itself as the rise Rise of warmer (and thus of the warmer (and thus lighter) lighter) fluid and the fall of cooler (and thus fluid and the fall of cooler (and denser) fluid thus denser) fluid. Steady versus Unsteady Flow Steady implies no change of properties (velocity, temperature and etc.) at a point with time. Steady-flow conditions can be closely approximated by devices that are intended for continuous operation (turbines, pumps, boilers, condensers, and heat exchangers of power plants or refrigeration systems) Unsteady is the opposite of steady. Transient usually describes a starting, or developing flow. Periodic refers to a flow which oscillates about a mean. Unsteady flows may appear steady if “time-averaged” 4 – SYSTEM AND CONTROL VOLUME System, Surroundings, and Boundary A system is defined as a quantity of matter or a region in space chosen for study. The mass or region outside the system is called the surroundings. The real or imaginary surface that separates the system from its surroundings is called the boundary. The boundary of a system can be fixed or movable. The boundary is the contact surface shared by both the system and the surrounding. The boundary has zero thickness. A closed system, also known as a control mass, consists of a fixed amount of mass, and no mass can cross its boundary. But energy, in the form of heat or work, can cross the boundary, and the volume of a closed system does not have to be fixed. In a special case, even energy is not allowed to cross the boundary, that system is called as isolated system. An open system, or a control volume, as it is often called, is a selected region in space. It usually encloses a device that involves mass flow such as a compressor, turbine, or nozzle. Both mass and energy can cross the boundary (the control surface) of a control volume. 5 – DIMENSIONS AND UNITS  Any physical quantity can be characterized by dimensions.  The magnitudes assigned to dimensions are called units.  Primary dimensions (or fundamental dimensions) include: mass m, length L, time t, and temperature T, etc. Secondary dimensions (derived dimensions) can be expressed in terms of primary dimensions and include: velocity V, energy E, and volume V. Unit systems include English system and the metric SI (International System). Some SI and English Units In SI, the units of mass, length, and time are the kilogram (kg), meter (m), and second (s), respectively. The respective units in the English system are the pound-mass (lbm), foot (ft), and second (s). Force  Force = (Mass) x (Acceleration)  In SI, 1 Newton (N) is the force required to accelerate a mass of 1 kg at a rate of 1 m/s2.  In English system, 1 pound-force (lbf) is the force required to accelerate a mass of 32.174 lbm at a rate of 1 ft/s2.  32.174 lbm = 1 slug  Weight  Weight is a force.  It is the gravitational force applied to a body, and its magnitude is determined from an equation based on Newton’s second law: W = mg  The weight per volume of a substance is called the specific weight 𝛾 and it is determined from 𝛾 = 𝜌𝑔, where 𝜌 is density.  Work  Work is a form of energy, can simply be defined as force times distance, called a joule (J): 1 J = 1 Nm  In the English system, the energy unit is the Btu (British thermal unit), the energy required to raise the temperature of 1 lbm of water at 68℉ by 1℉.  Dimensional Homogeneity  Every term in an equation must have the same dimensions,  Unity Conversion Ratios  All nonprimary units (secondary units) can be formed by combinations of primary units. 6 – PROPERTIES OF FLUIDS Density  Density is defined as mass  Sometimes the density of per unit volume. a substance is given m relative to the density of = V a well-known substance.  The density of a  SG = substance, in general, H O 2 depends on temperature and pressure.  H O at 4oC = 1000kg / m3 2  The density of most gases If SG of crude oil is is proportional to pressure 0.98 at 4oC, what is and inversely proportional the density of crude to temperature. oil? Density of Ideal Gases  The simplest and best-known equation of state for substances in the gas phase is the ideal-gas equation of state, expressed as: P = RT or P =  RT or PV = nRT Values of R (Gas constant) Units P:pressure 8.31446261815324 J⋅K−1⋅mol−1 R:gas constant 8.314462618...×10−2 L⋅bar⋅K−1⋅mol−1 T:temperature 8.314462618... m3⋅Pa⋅K−1⋅mol−1 V:volume n:mol 8.314462618...×107 erg⋅K−1⋅mol−1 ρ:density 8.3144626211(25)×103 Da⋅m2⋅s−2⋅K−1 62.3635982215293... L⋅Torr⋅K−1⋅mol−1 1.98720425864083...×10−3 kcal⋅K−1⋅mol−1 8.20573660809596...×10−5 m3⋅atm⋅K−1⋅mol−1 0.0820573660809596... L⋅atm⋅K−1⋅mol−1 Ref: 2018 CODATA Value: molar gas constant. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20. Gas constant for some common substances Pressure  Pressure (symbol: p or P) is  Partial pressure is the force applied defined as the perpendicular to the pressure of a gas or surface of an object per vapor in a mixture unit area over which that with other gases. force is distributed. The ambient pressure  Gauge pressure (also on an object is the spelled gage pressure) is pressure of the surrounding medium, the pressure relative to the such as a gas or ambient pressure. liquid, in contact with the object Atmospheric pressure= 1  Various units are used to atm  At a given pressure, the temperature at which a pure substance changes phase is called the saturation temperature Tsat.  Likewise, at a given temperature, the pressure at which a pure substance changes phase is called the saturation pressure Psat also known as vapor pressure, Psat =PvP. v For pure substance only YouTube video about vapour pressure: source:  Cavitation possibility of the liquid pressure in liquid-flow systems dropping below the vapor pressure at some locations, and the resulting unplanned vaporization and form bubbles (called cavitation bubbles) This phenomenon, which is a common cause for drop in performance and even the erosion of impeller blades, is called cavitation. Cavitation must be avoided (or at least minimized) in most flow systems since it reduces performance, generates annoying vibrations and noise, and causes damage to equipment. FIGURE 2–8 Cavitation damage on a 16-mm by 23- mm aluminum sample tested at 60 m/s for 2.5 hours. Source:Photo by David Stinebring, ARL/Pennsylvania State University. Used by permission Viscosity  The state of being thick, sticky, and semi- fluid in consistency.  A quantity expressing the magnitude of internal friction in a fluid, as measured by Source: https://wiki.anton-paar.com/en/basic-of- the force per unit area viscometry/ resisting uniform flow.  Viscosity unit: kg/m·s, The viscosity of water at 20°C is 1.002 centipoise. N·s/m2,centipoise (cP),Pa.s  Dynamic (or absolute) viscosity, µ  Kinematic viscosity,  =   Unit is m2/s and stoke (1 stoke = 1 cm2/s = 0.0001 m2/s). Surface tension  Liquid droplets behave  The magnitude of this like small balloons filled force per unit length is with the liquid, and the surface of the liquid acts called surface tension or like a stretched elastic coefficient of surface membrane under tension 𝜎𝑠. tension.  Expressed in the unit N/m  The pulling force that causes this tension acts (or lbf/ft in English units). parallel to the surface and is due to the attractive forces between the molecules of the liquid. FIGURE 2–31 Some consequences of surface tension:(a) drops of water beading up on a leaf, (b) a water strider sitting on top of the surface of water Video about surface tension Source: https://www.youtube.com/watch?v=_RTF0 DAHBBM Friction Friction is the force that opposes the relative motion between the two surfaces of objects in contact. The force of friction always acts in the direction opposite to that of the applied force. Since friction is a type of force, it is measured in Newton (N). Fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other. Source: https://en.wikipedia.org/wiki/Friction  Skin friction is a  Internal friction is the component of drag, the force resisting motion force resisting the motion between the elements of a fluid across the making up a solid surface of a body. material while it undergoes deformation.  Drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid.