Chapter 2 A BASIC THERMAL SCIENCES Fluid Flow

Chapter 2 A: BASIC THERMAL SCIENCES: Fluid Flow and Thermodynamics Agami Reddy (rev- Dec 2018) 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 HCB-3 Chap 2 A: Fluid Flow & Thermo 2. 6 Second law of thermodynamics 1

Disciplines A strong understanding of basic principles studied under thermal sciences is needed: • Fluid mechanics is the science dealing with (i) properties of fluids, (ii) governing laws and conditions of fluid statics and fluid motion, and (iii) with the resistance to flow outside and inside solid surfaces. • Thermodynamics is the science dealing with (i) energy and its transformations and (ii) 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 2 A: Fluid Flow & Thermo 2

Basic Concepts • Length- distance (m or ft) • Area (ft 2 or m 2 ) • Volume (ft 3 or m 3) • Velocity (m/s, ft/min, miles/h)- distance per unit time • Acceleration (m/s 2 ) - velocity per unit time Acceleration due to earth gravity = 9. 81 m/s 2 or 32. 17 ft/s 2 HCB-3 Chap 2 A: Fluid Flow & Thermo 3

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 = 32. 174 lbm-ft/s 2 - 1 Newton = Force reqd to accelerate 1 kg by 1 m/ s 2 • 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: m 3/s or cfm- cubic foot per min (air) gpm- gallons per min (water) HCB-3 Chap 2 A: Fluid Flow & Thermo 4

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 k. Wh 1 k. Wh = 1000 x 60=3. 6 x 106 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 k. Wh = 1000 x 60=3. 6 x 106 J General definition of energy of a system: capacity of a system to do work on its surroundings (this is the accepted definition even though work is just one form of energy) HCB-3 Chap 2 A: Fluid Flow & Thermo 5

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 2 A: Fluid Flow & Thermo 6

Properties Pressure: force per unit area p Unit: lbf/ft 2 (psf) or lbf/in 2 (psi) or Pascals (Pa) The pressures of air and water are very important pabs Absolute pressure: pressure exerted by fluid above zero pressure (vacuum) pg Gage pressure: pressure exerted by fluid above atmospheric pressure pvac Vacuum pressure: pressure exerted by fluid below atmospheric pressure patm Atmospheric pressure at sea level = 14. 7 psi = 101 k. Pa HCB-3 Chap 2 A: Fluid Flow & Thermo 7

pabs = patm + pg pabs = patm - pvac HCB-3 Chap 2 A: Fluid Flow & Thermo 8

Pressure Exerted by Column Area A • Caused by weight of the liquid Height H • Force (F) = density ( ) x accel due to gravity x volume (V) = x g x (H x A) Can be a large number • It takes denser liquid less height to generate the same pressure • Fluids used in monometer: commonly mercury (for high pressures) and water (for small pressures) • 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 = 62. 4 lbm/ft 3 p =( x g x H = 62. 4 lbf/ft 3 × 300 ft = 18720 lbf/ft 2 × 1 ft 2 / 144 in 2 = 130 lbf/ in 2 HCB-3 Chap 2 A: Fluid Flow & Thermo 9

Measuring Air Pressure in Ducts Fig. 2. 1 If H = 4” WG (typical in HVAC systems of buildings) Pressure difference = = 0. 144 psi which the fan has to overcome HCB-3 Chap 2 A: Fluid Flow & Thermo 10

Shear stress is force applied parallel to area Fig. 2. 2 Velocity profiles and gradient in shear flow Dynamic or absolute viscosity of water at 25 C = 6 x 10 -4 lbm/(ft. s) or 8. 9 x 10 -4 Pa. s HCB-3 Chap 2 A: Fluid Flow & Thermo 11

Temperature: A measure of 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 contract when their temperature is raised or lowered - Temperature scales: Fahrenheit(˚F) and Rankine (˚R) Celsius (˚C), and Kelvin (K) HCB-3 Chap 2 A: Fluid Flow & Thermo 12

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 + 273. 15 – Rankine • ˚ R = ˚ F + 459. 67 HCB-3 Chap 2 A: Fluid Flow & Thermo 13

Density and Specific Volume • Density – mass/volume (used for solids and liquids) Unit: lbm/ft 3 and kg/m 3 Density of water and air =1. 2 kg/m 3, water = 1000 kg/m 3 Ratio= 833 • Specific volume – volume/mass (used for liquids and gases) v=1/d Unit: ft 3 / lbm and m 3/kg Changes slightly with temperature, why? Because of volume change HCB-3 Chap 2 A: Fluid Flow & Thermo 14

Thermal Properties • Specific Heat (at constant pressure cp) – 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 (J/kg-°C) – Without phase change ! – Property of material which changes slightly with temperature Specific heat for water is 1. 0 Btu/lbm-°F at 60 °F or 4. 186 k. J/(kg-K) air is 0. 24 Btu/lbm-°F at 70 °F or 1. 00 k. J/(kg-K) HCB-3 Chap 2 A: Fluid Flow & Thermo 15

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+… (Important: a body does not contain heat; it contains thermal energy) HCB-3 Chap 2 A: Fluid Flow & Thermo 16

Enthalpy (h) – A property of a body that measures its heat content – Enthalpy includes: (i) Internal energy U and (ii) p. V 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 k. J or Btu (V is total volume) specific enthalpy h = u + p. v in k. J/kg or Btu/lbm (v is specific volume) HCB-3 Chap 2 A: Fluid Flow & Thermo 17

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 miscopic level within the system. Units of specific entropy are k. J/(kg. K) or Btu/(lbm. o. F) HCB-3 Chap 2 A: Fluid Flow & Thermo 18

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 2 A: Fluid Flow & Thermo 19

Change of State Molecular theory or Kinetic theory • Gas and liquid consists of large number of particles known as molecules • Molecules are in constant, random and rapid motion • Temperature is a measure of average molecule speed • Some liquid molecules have faster speed and are able to escape • Resisting pressure by gas molecules plays a role • During boiling process, average speed reaches a level at which the link between molecules break 20 HCB-3 Chap 2 A: Fluid Flow & Thermo

Gibbs Phase Rule An useful rule which specifies the number of independent intensive properties (or degrees of freedom F) needed to completely specify 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 = 2+2 -1 = 3, i. e. , three independent properties. HCB-3 Chap 2 A: Fluid Flow & Thermo 21

Types of Gases • Real gases: whose molecules occupy space and have inter-molecular attractions • Ideal gases: those that contain molecules which can be considered to be point masses and have no attractive forces – Semi-perfect: pv = f(T), u = f(T) Specific Heat c = f(T) (2. 9) – Perfect gases: Specific heat c = cte, follows ideal gas law HCB-3 Chap 2 A: Fluid Flow & Thermo 22

Ideal Gas Law – A gas is a perfect ideal gas when the following relation holds: p. V=m. RT or where p – pressure, lbf/ft 2 V – volume, ft 3 m – mass, lbm R – gas constant, (for air: 53. 35 ft-lbf/lbm-R) T – absolute temperature, °R (2. 12) = 287 (J/kg. K) – A more powerful relation (independent of substance) p V = (m/MW) R*T where 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 ) = 8. 314 J/(mol. K) HCB-3 Chap 2 A: Fluid Flow & Thermo 23

Ideal Gas Law contd… - Different forms under special conditions: • Same gas: m 1 = m 2 and R 1 = R 2 then Boyle’s Law • Same gas, same temperature, then • Same gas, same volume, then • Same gas, same pressure, then HCB-3 Chap 2 A: Fluid Flow & Thermo 24

Example 2. 1: Ideal Gas Law Determine the mass of air in a room of dimensions (10 m x 2. 5 m) at 100 k. Pa and 20 o C? 2. 12 HCB-3 Chap 2 A: Fluid Flow & Thermo 25

(2. 15) (2. 16) (2. 17) 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 2 A: Fluid Flow & Thermo 26

Table 2. 2 HCB-3 Chap 2 A: Fluid Flow & Thermo 27

Flow Regimes Laminar and turbulent Fig. 2. 3 Different types of flow regimes in a pipe HCB-3 Chap 2 A: Fluid Flow & Thermo 28

Fig. 2. 4 Fluid boundary layer and flow regimes over a flat plate flat If viscous force is strong, laminar flow Critical Re numberdepends on geometry HCB-3 Chap 2 A: Fluid Flow & Thermo 29

Conservation of Mass and Momentum (2. 22) HCB-3 Chap 2 A: Fluid Flow & Thermo 30

Continuity Equation- Conservation of Mass Assuming steady state flow: (2. 25) Fig. 2. 5 Steady flow through a duct or pipe with change in cross-section For incompressible fluids (such as water): HCB-3 Chap 2 A: Fluid Flow & Thermo 31

Continuity Equation Example 2. 2 Note: Density assumed constant HCB-3 Chap 2 A: Fluid Flow & Thermo 32

Stored Energy and Energy Transfer Body Forms of Stored Energy Internal energy Pressure energy Chemical energy Potential energy Kinetic energy Other forms Heat (Q) Work (W) Another Body Forms of Energy in Transfer Three forms of thermal energy transfer: Conduction, Convection, and Radiation HCB-3 Chap 2 A: Fluid Flow & Thermo 33

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/s 2 x 30 m = 294300 J = 294. 3 k. J • The above is accomplished in 10 seconds. What is the power of the crane? Power = Energy/time = 294. 3/10 = 29. 43 k. W HCB-3 Chap 2 A: Fluid Flow & Thermo 34

Forms of Mechanical Energy 2) Kinetic energy: energy possessed by a system due to the velocity of the molecules. KE = mass x half of velocity squared = m V 2/2 • 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 k. J • What is the corresponding power? Power = energy / time HCB-3 Chap 2 A: Fluid Flow & Thermo 35

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: (a) 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 2 A: Fluid Flow & Thermo 36

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 capturing facts that (i) certain forms of energy are of higher quality that others (ii) only certain directions of energy transfer are allowed 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 2 A: Fluid Flow & Thermo 37

First Law of Thermodynamics Energy Balance or energy conservation law – Different ways to express it A closed system is one where the fluid does not cross the system boundaries – 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 d. U = Qin – Qout d. U: change in internal or stored energy in the system Qin: heat added (entering ) to the system Qout: heat removed (leaving) from the system Qin Sign: +ve if thermal energy added to system –ve if thermal energy removed from system HCB-3 Chap 2 A: Fluid Flow & Thermo d. U Qout 38

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 internal energy 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 its internal energy • Solution: Qin = Ein-light + Ein-motor = 1000 W + 10 HP = … = 28, 860 Btu/hr Qout = 0 Btu/hr d. U = Q – Q in out = 28, 860 Btu/hr – 0 Btu/hr = 28, 860 Btu/hr HCB-3 Chap 2 A: Fluid Flow & Thermo 39

Closed system- for refrigerant inside piping Fig. 2. 7 Schematic diagram of an air-conditioning system using a vapor compression cycle HCB-3 Chap 2 A: Fluid Flow & Thermo 40

First Law of Thermodynamics contd. – For a OPEN system: Fig. 2. 8 (2. 32) HCB-3 Chap 2 A: Fluid Flow & Thermo 41

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 2 A: Fluid Flow & Thermo 42

Sensible Heat Sensible heat of a body is the energy associated with its temperature provided it does not change phase- it follows from the first law of thermodynamics when no work is involved. 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, (k. J or Btu) m is the mass (kg or lbm) c is the specific heat, (k. J/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 is the mass flow rate (kg/s) HCB-3 Chap 2 A: Fluid Flow & Thermo 43

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 capacity of the reheater? Solution: Use sensible heat equation: 55ºF From AHU Check to see whether we have all the necessary variables: – mass flow rate unknown - assume density = 0. 075 lbm/ft 3 HCB-3 Chap 2 A: Fluid Flow & Thermo 44

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 equation HCB-3 Chap 2 A: Fluid Flow & Thermo 45

Latent Heat During Boiling – How to calculatent heat at a given temperature • Inter-molecular changes occur although temperature does not change • Use latent heat equation: where Q is the stored energy (k. J or Btu) m is the mass flow rate (kg or lbm) hfg is the latent heat of vaporization ( k. J/kg or Btu/lbm) which depends on temperature or pressure of boiling (for water we can use steam tables) HCB-3 Chap 2 A: Fluid Flow & Thermo 46

Latent Heat Instead of sensible or latent heat equations, enthalpy equation is widely used since one does not have to worry about state of fluid: (we need lookup-up tables to find values of enthalpy for different fluids at different conditions either subcooled, saturated or superheated) HCB-3 Chap 2 A: Fluid Flow & Thermo 47

All forms of energy are not equal! Thermal energy (or heat) is a more “disordered” form of energy HCB-3 Chap 2 A: Fluid Flow & Thermo From Cengal and Boles 48

Entropy and Second Law 2 nd 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 thermal energy can be fully used to convert to work • 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) • Entropy balance is an important tool in designing and optimizing HX, heat engines and various othermodynamic systems Proper understanding important for energy resources sustainability 49 HCB-3 Chap 2 A: Fluid Flow & Thermo

Overall Efficiency: 1 st Law CEE 494: B 1 - Thermal Science_Reddy 50

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 2 A: Fluid Flow & Thermo 51