Chapter 2A: BASIC THERMAL SCIENCES: FLUID FLOW AND THERMO

Chapter 2A: BASIC THERMAL SCIENCES: FLUID FLOW AND THERMO
Agami Reddy (July 2016) Basic concepts 2.1 Fluid and thermodynamic properties - Physical properties - Thermal properties 2.2 Determining property values - Gibbs rule - Ideal gas law - Other properties 2.3 Types of flow regimes: laminar, turbulent flow- pipes and plates 2.4 Conservation of mass and momentum 2.5 First law of thermodynamics - Applied to closed-systems - Applied to open-systems 2.6 Second law of thermodynamics HCB-3 Chap 2A: Fluid Flow & Thermo

HCB-3 Chap 2A: Fluid Flow & Thermo
Disciplines A strong understanding of basic principles studied under thermal sciences is needed: Fluid mechanics is the science dealing with properties of fluids, governing laws and conditions of fluid statics and fluid motion, and with the resistance to flow outside and inside solid surfaces. Thermodynamics is the science dealing with energy and its transformations and the relationships of the various properties of a substance as it undergoes changes in pressure and temperature. Heat transfer is the science and art of determining the rate at which heat moves through substances under various externally imposed temperature and/or boundary conditions. HCB-3 Chap 2A: Fluid Flow & Thermo

Basic Concepts Length- distance (m or ft) Area (ft2 or m2 ) Volume (ft3 or m3) Velocity (m/s, ft/min, miles/h)- distance per unit time Acceleration (m/s2 ) velocity per unit time Acceleration due to gravity = 9.81 m/s2 or ft/s2 HCB-3 Chap 2A: Fluid Flow & Thermo

Mass, Force, Weight and Flow Rates
Mass of a body – quantity of matter the body contains Unit: pound mass (lbm) and kg Force - push or pull that one body may exert on another Unit: pound force (lbf) and Newton (N) - 1 lbf = lbm-ft/s2 - 1 Newton = Force reqd to accelerate 1 kg by 1 m/ s2 Weight of a body – force exerted by gravity on the body Unit: lbf or pound force and Newton - Flow rates (2 types): - Mass flow rate: kg/s or lbm/h - Volume flow rate: m3/s or cfm- cubic foot per min (air) gpm- gallons per min (water) HCB-3 Chap 2A: Fluid Flow & Thermo

Work and Energy L F Work: the effect created by a force when it moves a body Work = Force × Distance ( in the direction of the force) Unit: ft – lbf and Newton-m or Joule (J) and kWh 1 kWh = 1000 x 60 x 60=3.6 x 10^6 Joules In SI units, Joule (J) is used 1 J is the work done by a force of 1 N moving by 1 m Other energy units: 1 kWh = 1000 x 60 x 60=3.6 x 10^6 J General definition of Energy: the ability to do work This is the accepted definition even though work is just one form of energy Chemical energy: a form of stored energy in a body that is released from a body by combustion or other chemical process, it is energy possessed by the system caused by the arrangement of atoms composing the molecules Kinetic energy: due to motion, or velocity Potential energy due to its position or elevation Enthalpy is a property a body has that is a combination of its energy due to temperature, pressure, and volume Thermal (internal energy) is the energy possessed by a system caused by the motion of the molecular and/or intermolecular forces 5) Nuclear energy is energy possessed by the system from the cohesive forces holding protons and neutrons together as the atom’s nuclear HCB-3 Chap 2A: Fluid Flow & Thermo

Power Power: time rate of doing work or energy use per unit time More commonly used Unit: ft-lbf/min, horsepower (HP) and Watt (W) - 1 W = 1 Joule per second - 1 horse-power = 746 W or 550 ft-lb per second HCB-3 Chap 2A: Fluid Flow & Thermo

Properties Pressure: force per unit area p Unit: lbf/ft2 (psf) or lbf/in2 (psi) or Pascals (Pa) The pressures of air and water are very important Absolute pressure: pressure exerted by fluid above zero pressure (vacuum) pabs Gage pressure: pressure exerted by fluid above atmospheric pg pressure patm = 14.7 lbf/in2 (psia) at sea level (or 101 kPa) Vacuum pressure: pressure exerted by fluid below atmospheric pvac pressure patm Atmospheric pressure at sea level = 14.7 psi = 101 kPa HCB-3 Chap 2A: Fluid Flow & Thermo

Pressure: force per unit area Pabs = Patm + Pg Pabs = Patm - Pvac HCB-3 Chap 2A: Fluid Flow & Thermo

Pressure Exerted by Column
Height H Area A Caused by weight of the liquid Force (F) = density (d) x volume (V) = d x H x A  P = F / A = d x H Can be a large number It takes denser liquid less height to generate the same pressure Used in monometer, mercury (high P) and water (small P) are normal 760 mm Hg = 14.7 psia (atmospheric pressure at sea level) Also expressed as “HEAD” Height of liquid usually water Example: What is the pressure exerted by a 300 ft vertical pipe in a high rise building on a valve at the bottom of the pipe? Density of the water is 62.4 lbf/ft3 P = d H = 62.4 lbf/ft3 × 300 ft = lbf/ft2 × 1 ft2 / 144 in2 = 130 lbf/ in2 HCB-3 Chap 2A: Fluid Flow & Thermo

Measuring Air Pressure in Ducts
Pressure diff = 62.4 x (4/12)/144 = lbm/in^2 If H = 4” WG (typical in HVAC systems of buildings) Pressure difference = d x H = psi which the fan has to overcome HCB-3 Chap 2A: Fluid Flow & Thermo

Temperature Temperature: A measure of the thermal activity in a body Thermal activity depends on the velocity of the molecules and other particles of which a matter is composed. Thermometer is used to measure temperature rely on the fact that most liquids expand and contract when their temperature is raised or lowered Temperature scale: Fahrenheit(˚F) and Celsius (˚C), Rankine (˚R) and Kelvin (K) HCB-3 Chap 2A: Fluid Flow & Thermo

Temperature Scales Fahrenheit 0°F as the stabilized temperature when equal amount of ice, water, and salt are mixed Celsius 0°C as melting point of ice (water) and 100°C as boiling point of water ˚ F = 1.8 ˚ C + 32 Kelvin 0 K as absolute zero K = ˚ C Rankine ˚ R = ˚ F HCB-3 Chap 2A: Fluid Flow & Thermo

Density and Specific Volume
Density – mass/volume (used for solids and liquids) “d” Unit: lbm/ft3 and kg/m3 Density of water and air air =1.2 kg/m3, water = 1000 kg/m3  Ratio= 833 Specific volume – volume/mass (used for liquids and gases) n = 1 / d Unit: ft3 / lbm and m3/kg Changes slightly with temperature, why? Because of volume change Specific gravity – weight of the substance/weight of an equal volume of water at 39 °F HCB-3 Chap 2A: Fluid Flow & Thermo

Thermal Properties Specific Heat
Amount of heat that is required to change the temperature of 1 lbm (or 1 kg) of the substance by 1 °F ( or 1 °C ). Units of Btu/lbm-°F) or Without phase change !! Property of material which changes slightly with temperature Specific heat for water is Btu/lbm-°F at 60 °F or kJ/(kg-K) air is 0.24 Btu/lbm-°F at 70 °F or 1.00 kJ/(kg-K) (J/kg-°C) HCB-3 Chap 2A: Fluid Flow & Thermo

Thermal Energy Internal energy (U): microscopic energy possessed by a system caused by the motion/vibration of the molecules and/or intermolecular forces- - the motion/vibration increases with temperature Internal energy is thus often measured by the body’s temperature (this is not true when the body is a liquid or a solid (such as ice) which is changing phase!)- this leads to sensible and latent heat discussed later Total energy of a substance: E = U + KE + PE+… Enthalpy is a property a body has that is a combination of its energy due to temperature, pressure, and volume Thermal (internal energy) is the energy possessed by a system caused by the motion of the molecular and/or intermolecular forces (Important: a body does not contain heat; it contains thermal energy) HCB-3 Chap 2A: Fluid Flow & Thermo

Latent Heat How to calculate latent heat at a given temperature Inter-molecular changes although temperature does not change Use latent heat equation: where Q is the stored energy (kJ or Btu) m is the mass flow rate (kg or lbm) hfg is the latent heat of vaporization ( kJ/kg or Btu/lbm) (determined from steam tables- discussed later) HCB-3 Chap 2A: Fluid Flow & Thermo

Enthalpy (h) A property of a body that measures its heat content Enthalpy includes: (i) Internal energy U and (ii) pV or energy due to flow work Enthalpy is a combined property which is widely used in thermal analysis When T, p or V changes, H changes Enthalpy H = U + V.p in kJ or Btu (V is total volume) specific enthalpy h = u + p.v in kJ or Btu/lb (v is specific volume) Instead of sensible or latent heat equations, enthalpy equation is widely used since one does not have to worry about state of fluid: T P V P- pressure V- volume T- temperature HCB-3 Chap 2A: Fluid Flow & Thermo

Entropy Specific entropy s is another important property which cannot be directly measured (such as internal energy or enthalpy). - Defined from the second law of thermodynamics. Entropy is a measure of the energy that is not available for work during a thermodynamic process due to the fact that natural processes tend not to be reversible. For example, thermal energy always flows spontaneously as heat from regions of higher temperature to regions of lower temperature. Such processes reduces the state of order of the initial system by homogenization, and therefore entropy is an expression of the degree of disorder or chaos at the miscopscopic level within the system. Units of specific entropy are kJ/(kg.K) or Btu/(lbm.oF) HCB-3 Chap 2A: Fluid Flow & Thermo

Changes of State (Phase)
Substances can exist in three states: solid, liquid, and gas (vapor) Two factors that affect state: temperature and pressure Process of state change - Temperature change or phase change - Pressure dependent Molecular Theory of Liquids and Gases suggested to explain observed phenomena Concept of “saturated state” subcooled, saturated and superheated Saturated steam tables used to determine state HCB-3 Chap 2A: Fluid Flow & Thermo

Change of State Molecular theory or Kinetic theory Temperature is a measure of average molecule speed Some molecules have faster speed and escape Resisting pressure plays a role During boiling process, average speed reaches a level at which the link between molecules break HCB-3 Chap 2A: Fluid Flow & Thermo

Gibbs Phase Rule For pure substance An useful rule which specifies the number of independent intensive properties (or degrees of freedom F) needed to completely specify the thermodynamic state of a fluid (liquid or gaseous). It is expressed as F = 2+ N –P where P is the number of phases and N the number of components. The thermodynamic state of a single-substance system—e.g., air in a building, steam in a boiler, or refrigerant in an air conditioner—is defined by specifying F = 2+1-1=2 i.e., two independent, intensive thermodynamic coordinates or properties. For moist air which is a mixture of dry air and water vapor, F = = 3, i.e., three independent properties. HCB-3 Chap 2A: Fluid Flow & Thermo

Types of Gases Real gases Ideal gases Semi-perfect: pv=f(T), u=f(T), Specific Heat c=f(T) Perfect gases: Specific heat c=cte, follows ideal gas law HCB-3 Chap 2A: Fluid Flow & Thermo

Ideal Gas Law A gas is a perfect ideal gas when the following relation holds: P V = m R T where P – pressure, lbf/ft2 V – volume, ft3 m – mass, lbm R – gas constant, (for air: ft-lbf/lbm-R) T – absolute temperature, °R A more powerful relation (independent of substance) P V = (m/MW) R*T where (m/MW) is the atomic or molecular weight in moles, lbmol or mol R*is called universal gas constant= R x MW =1545 ft-lbf /( lbmol-°R )= J/(mol. K) MW is the molecular weight of the substance = 287 (J/kg.K) HCB-3 Chap 2A: Fluid Flow & Thermo

Ideal Gas Law contd… Different forms: Same gas: m1 = m2 and R1 = R2 then Same gas, same temperature, then Same gas, same volume, then Same gas, same pressure, then Boyle’s Law HCB-3 Chap 2A: Fluid Flow & Thermo

Example 2.1 Determine the mass of air in a room of dimensions (10 m x 10 m x 2.5 m) at 100 kPa and 20o C? HCB-3 Chap 2A: Fluid Flow & Thermo

The variation of the above properties with temperature is relatively small and can be approximated by constant average values for HVAC calculations HCB-3 Chap 2A: Fluid Flow & Thermo

Table 2.2 HCB-3 Chap 2A: Fluid Flow & Thermo

Flow Regimes Laminar and turbulent HCB-3 Chap 2A: Fluid Flow & Thermo

If viscous force is strong, laminar flow Critical Re number- depends on geometry HCB-3 Chap 2A: Fluid Flow & Thermo

Conservation of Mass and Momentum
HCB-3 Chap 2A: Fluid Flow & Thermo

Continuity equation Assuming steady state flow:

Continuity Equation Example 2.2 Note: Density assumed constant

Forms of Mechanical Energy
1) Potential energy: energy possessed by a system due to its elevation PE = force x distance = weight x height = (m.g). H Example- A crane lifts a block of concrete weighing 1 Ton to a height of 30 m. How much energy has been expended? 1 Ton = 1000 kg PE = 1000 kg x 9.81 m/s2 x 30 m = J = kJ The above is accomplished in 10 seconds. What is the power of the crane? Power = Energy/time = 294.3/10 = kW Chemical energy: a form of stored energy in a body that is released from a body by combustion or other chemical process, it is energy possessed by the system caused by the arrangement of atoms composing the molecules Kinetic energy: due to motion, or velocity Potential energy due to its position or elevation Enthalpy is a property a body has that is a combination of its energy due to temperature, pressure, and volume Thermal (internal energy) is the energy possessed by a system caused by the motion of the molecular and/or intermolecular forces 5) Nuclear energy is energy possessed by the system from the cohesive forces holding protons and neutrons together as the atom’s nuclear HCB-3 Chap 2A: Fluid Flow & Thermo

Forms of Mechanical Energy
2) Kinetic energy: energy possessed by a system caused by the velocity of the molecules. KE = mass x half of velocity squared = m V2/2 A truck of mass 1000 kg travels at 30 m/s. What is its kinetic energy? KE= 0.5 x 1000 kg x (30) 2 (m/s) 2 = 450,000 J = 450 kJ What is the corresponding power? Power = energy / time Kinetic energy: due to motion, or velocity Potential energy due to its position or elevation Enthalpy is a property a body has that is a combination of its energy due to temperature, pressure, and volume Thermal (internal energy) is the energy possessed by a system caused by the motion of the molecular and/or intermolecular forces 5) Nuclear energy is energy possessed by the system from the cohesive forces holding protons and neutrons together as the atom’s nuclear HCB-3 Chap 2A: Fluid Flow & Thermo

Conversion of Potential to Kinetic Energy
Consider a small spring near a mountain cabin. If 120 kg/min flows down a height of 15 m: What is the velocity of water at the bottom of the hill (b)How much power can be ideally delivered? (c) How much energy can be ideally delivered in a month? HCB-3 Chap 2A: Fluid Flow & Thermo

Stored Energy and Energy Transfer
Body Internal energy Pressure energy Chemical energy Potential energy Kinetic energy Other forms Forms of Stored Energy Heat (Q) Work (W) Another body Forms of Energy in Transfer Chemical energy: a form of stored energy in a body that is released from a body by combustion or other chemical process, it is energy possessed by the system caused by the arrangement of atoms composing the molecules Kinetic energy: due to motion, or velocity Potential energy due to its position or elevation Enthalpy is a property a body has that is a combination of its energy due to temperature, pressure, and volume Thermal (internal energy) is the energy possessed by a system caused by the motion of the molecular and/or intermolecular forces 5) Nuclear energy is energy possessed by the system from the cohesive forces holding protons and neutrons together as the atom’s nuclear Three forms of energy transfer: Conduction, Convection, and Radiation HCB-3 Chap 2A: Fluid Flow & Thermo

Laws of Thermodynamics
In simplest terms, the Laws of Thermodynamics dictate the specifics for the movement of heat and work. Basically, the First Law is a statement of the conservation of energy – the Second Law is a statement about the quality of energy or direction of that conservation – and the Third Law is a statement about reaching Absolute Zero (0 K). However, since their conception, these laws have become some of the most important laws of all science - and are often associated with concepts far beyond what is directly stated in the wording. Heat is the lowest form of energy Work (from which electricity is produced) is a higher form One unit of thermal energy at a high temperature is more VALUABLE than the same amount of energy at a lower temperature HCB-3 Chap 2A: Fluid Flow & Thermo

First Law of Thermodynamics
A closed system is one where the fluid does not cross the system boundaries Energy Balance or energy conservation law Different ways to express it Closed System: Change in the internal energy U is the difference in the heat Q added to the system minus work done by the system If no work involved: the change in total energy in a system equals the energy added to the system minus the energy removed from the system dU = Qin – Qout dU: change in internal or stored energy in the system Qin: heat added (entering ) to the system Qout: heat removed (leaving) from the system Sign: +ve if energy added to system –ve if energy removed from system Qin dU Qout HCB-3 Chap 2A: Fluid Flow & Thermo

Closed system- for refrigerant inside piping HCB-3 Chap 2A: Fluid Flow & Thermo

Example of Closed System
A business equipment room has 1000 watts of lighting and some small motors with a total output of 10 HP. All of the energy in the lighting and from the motors is converted into heat. What is the increase in enthalpy of the room air from these sources? Analysis: 1) system: room air 2) energy added to the system: from lighting and motor 3) added energy is in form of heat 4) effect of added energy is to increase the air temp., i.e. increase in enthalpy Solution: Ech = Ein – Eout Ein = Ein-light + Ein-motor = 1000 W + 10 HP = … = 28,860 Btu/hr Eout = 0 Btu/hr Ech = 28,860 Btu/hr – 0 Btu/hr = 28,860 Btu/hr Δh = Ech = 28,860 Btu/hr HCB-3 Chap 2A: Fluid Flow & Thermo

First Law of Thermodynamics contd.
For a OPEN system: HCB-3 Chap 2A: Fluid Flow & Thermo

First Law of Thermodynamics contd.
For a OPEN system where KE, PE and other energy sources are negligible - when W=0: Q = m (hout – hin) boiler - when Q=0: W = m (hin– hout) turbine where hin: enthalpy of fluid entering the system hout: enthalpy of fluid leaving the system Sign convention for Q: +ve when added to the system –ve when removed from the system Sign convention for W is opposite HCB-3 Chap 2A: Fluid Flow & Thermo

Sensible Heat Sensible heat of a body is the energy associated with its temperature. Example- heating water For liquids and solids, the change in stored energy when its mass undergoes a temperature change is given by: where Qs is the stored energy, (kJ or Btu) is the mass (kg or lb) c is the specific heat, (kJ/kg-C or Btu/lbm-°F) The same equation also applies when a fluid flow is involved. In that case, Q is the rate of heat transfer (Btu/hr) and m is the mass flow rate (kg/s) HCB-3 Chap 2A: Fluid Flow & Thermo

Sensible Heat Example A hot water re-heater heats duct air from 55 °F to 70 °F before it enters a room when the valve is 100 % open. The air flow rate is 500 cfm. What is the heating capability of the reheater? Solution: Use sensible heat equation: From AHU 55ºF - Check to see whether we have all the necessary variables. – mass flow rate unknown - Use density (d) to obtain mass flow rate from volumetric flow rate and then use equation HCB-3 Chap 2A: Fluid Flow & Thermo

Sensible Heat and Latent Heat
Why the need to distinguish between them? During a process with phase change, temperature is not the only variable that determines heat transfer rate. What is sensible heat? Energy (heat) that is added or removed during a process where the temperature of a substance changes but there is NO change in state (phase) of the substance. What is latent heat change? Energy (heat) absorbed or released during a process of state (phase) change. Both these can be treated together by using the enthalpy equations HCB-3 Chap 2A: Fluid Flow & Thermo

Example of Using Superheat Tables
Boiler example: A boiler heats up 130 lb/min of water from 80 F to 400 F at a pressure of 60 psia. What is the needed heat input? From the saturated table, the enthalpy of saturated liquid at 80 F 48.02 Btu/lb From the superheat table, corresponding to the sub- table of P=60 psia and temperature of 400 F, =1,233.5 Btu/lb Finally, heat input Q= (130 lb/min) ( ) Btu/lb x 60 min/h = 9.25 x 10^6 Btu/h HCB-3 Chap 2A: Fluid Flow & Thermo

All forms of energy are not equal! Thermal energy (or heat) is a more “disordered” form of energy- From Cengal and Boles HCB-3 Chap 2A: Fluid Flow & Thermo

Entropy and Second Law 2nd Law of Thermo places limit on energy conversion and direction of flow: Various statements: Heat will not flow spontaneously from cold object to hot object. Any system which is free of external influences becomes more disordered with time. This disorder can be expressed in terms of the quantity called entropy. All work can be converted in heat but all heat cannot be converted in to work (alternative statement: you cannot create a heat engine which extracts heat and converts it all to useful work). Understanding: Work is needed to move heat from low temp. to high temp. Not all the thermal energy can be fully used. Concept of entropy: a measure of the irreversibility of the process (due to friction, heat transfer across a temperature difference,…) a property (just like temperature, pressure, enthalpy) Proper understanding important for energy resources sustainability HCB-3 Chap 2A: Fluid Flow & Thermo

Outcomes Competence in basic physical properties: mass, volume, pressure, temperature, density, viscosity Competence in basic thermal properties: specific heat, heat of vaporization, internal energy, enthalpy, entropy Understand phase changes and kinetic theory. Familiarity with Gibbs phase rule and its usefulness Familiarity with real and ideal gases, and Ideal Gas Law Familiarity with different flow regimes, turbulent and laminar flows through pipes and flat surfaces Understand how to apply conservation of mass and momentum principles Familiarity with different forms of stored energy Understand the difference between stored energy and energy transfer Understand the application of the first law of thermodynamics to closed and open systems Familiarity with the second law of thermodynamic and its usefulness which limits energy conservation and the direction of flow HCB-3 Chap 2A: Fluid Flow & Thermo

Chapter 2A: BASIC THERMAL SCIENCES: FLUID FLOW AND THERMO

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Chapter 2A: BASIC THERMAL SCIENCES: FLUID FLOW AND THERMO

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