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55 2FD V 2 ρ A CD C D Note: Intermediate divisions are 2, 4, 6, and 8. DRAG COEFFICIENTS FOR SPHERES, DISKS, AND CYLINDERS 24 = , Re < 10 Re DV FLUID MECHANICS (continued)
PROPERTIES OF SINGLE-COMPONENT SYSTEMS Nomenclature 1. Intensive properties are independent of mass. 2. Extensive properties are proportional to mass. 3. Specific properties are lower case (extensive/mass). State Functions (properties) Absolute Pressure, p (lbf/in 2 or Pa) Absolute Temperature, T (°R or K) Specific Volume, v (ft 3 /lbm or m 3 /kg) Internal Energy, u (usually in Btu/lbm or kJ/kg) Enthalpy, h = u + Pv (same units as u) Entropy, s [Btu/(lbm-°R) or kJ/(kg⋅K)] Gibbs Free Energy, g = h – Ts (same units as u) Helmholz Free Energy, a = u – Ts (same units as u) ⎛ ∂h ⎞ Heat Capacity at Constant Pressure, c p = ⎜ ⎟ ⎝ ∂T ⎠ ⎛ ∂u ⎞ Heat Capacity at Constant Volume, cv = ⎜ ⎟ ⎝ ∂T ⎠ Quality x (applies to liquid-vapor systems at saturation) is defined as the mass fraction of the vapor phase: x = mg/(mg + mf), where mg = mass of vapor, and mf = mass of liquid. Specific volume of a two-phase system can be written: v = xvg + (1 – x)vf or v = xvfg + vf, where vf = specific volume of saturated liquid, vg = specific volume of saturated vapor, and vfg = specific volume change upon vaporization. = vg – vf Similar expressions exist for u, h, and s: u = xug + (1 – x) uf h = xhg + (1 – x) hf s = xsg + (1 – x) sf For a simple substance, specification of any two intensive, independent properties is sufficient to fix all the rest. For an ideal gas, Pv = RT or PV = mRT, and P1v1/T1 = P2v2/T2, where p = pressure, v = specific volume, m = mass of gas, R = gas constant, and T = absolute temperature. v P THERMODYNAMICS 56 R is specific to each gas but can be found from R R = , where mol. wt. ( ) R = the universal gas constant = 1,545 ft-lbf/(lbmol-°R) = 8,314 J/(kmol⋅K). For Ideal Gases, cP – cv = R Also, for Ideal Gases: ⎛ ∂h ⎞ ⎜ ⎟ ⎝ ∂v ⎠ = 0 ⎛ ∂u ⎞ ⎜ ⎟ ⎝ ∂ν ⎠ = 0 T For cold air standard, heat capacities are assumed to be constant at their room temperature values. In that case, the following are true: ∆u = cv∆T; ∆h = cP ∆T ∆s = cP ln (T2/T1) – R ln (P2/P1); and ∆s = cv ln (T2/T1) + R ln (v2/v1). For heat capacities that are temperature dependent, the value to be used in the above equations for ∆h is known as the mean heat capacity ( c ) and is given by p T2 ∫T c dT 1 p c p = T − T 2 Also, for constant entropy processes: 1 P1v1 k = P2v2 k ; T1P1 (1–k)/k = T2P2 (1–k)/k T1v1 (k–1) = T2v2 (k–1) , where k = cp/cv FIRST LAW OF THERMODYNAMICS The First Law of Thermodynamics is a statement of conservation of energy in a thermodynamic system. The net energy crossing the system boundary is equal to the change in energy inside the system. Heat Q is energy transferred due to temperature difference and is considered positive if it is inward or added to the system. Closed Thermodynamic System No mass crosses system boundary Q – W = ∆U + ∆KE + ∆PE where ∆KE = change in kinetic energy, and ∆PE = change in potential energy. Energy can cross the boundary only in the form of heat or work. Work can be boundary work, wb, or other work forms (electrical work, etc.) ⎛ W ⎞ Work W⎜w= ⎟ is considered positive if it is outward or ⎝ m ⎠ work done by the system. Reversible boundary work is given by wb = ∫ P dv. T
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FUNDAMENTALS OF ENGINEERING SUPPLIE
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Published by the National Council o
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CONTENTS Units.....................
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CONVERSION FACTORS Multiply By To O
Page 9 and 10: Case 4. Circle e = 0: (x - h) 2 + (
Page 11 and 12: MATRICES A matrix is an ordered rec
Page 13 and 14: Taylor's Series f ( x) = f ( a) ( a
Page 15 and 16: MENSURATION OF AREAS AND VOLUMES No
Page 17 and 18: CENTROIDS AND MOMENTS OF INERTIA Th
Page 19 and 20: Numerical Integration Three of the
Page 21 and 22: PROBABILITY FUNCTIONS A random vari
Page 23 and 24: HYPOTHESIS TESTING Consider an unkn
Page 25 and 26: ENGINEERING PROBABILITY AND STATIST
Page 27 and 28: 22 CRITICAL VALUES OF THE F DISTRIB
Page 29 and 30: FORCE A force is a vector quantity.
Page 31 and 32: 26 y y y y y y C Figure Area & Cent
Page 33 and 34: 28 y y y Figure Area & Centroid Are
Page 35 and 36: Normal and Tangential Components y
Page 37 and 38: M is the moment applied to the part
Page 39 and 40: The figure shows a fourbar slider-c
Page 41 and 42: It may also be shown that the undam
Page 43 and 44: UNIAXIAL STRESS-STRAIN Stress-Strai
Page 45 and 46: STATIC LOADING FAILURE THEORIES Bri
Page 47 and 48: Using the stress-strain relationshi
Page 49 and 50: DENSITY, SPECIFIC VOLUME, SPECIFIC
Page 51 and 52: The Field Equation is derived when
Page 53 and 54: Specific fittings have characterist
Page 55 and 56: FLUID MEASUREMENTS The Pitot Tube -
Page 57 and 58: DIMENSIONAL HOMOGENEITY AND DIMENSI
Page 59: MOODY (STANTON) DIAGRAM e, (ft) e,
Page 63 and 64: Mixers, Separators, Open or Closed
Page 65 and 66: SECOND LAW OF THERMODYNAMICS Therma
Page 67 and 68: Temp. o C T 0.01 5 10 15 20 25 30 3
Page 69 and 70: P-h DIAGRAM FOR REFRIGERANT HFC-134
Page 71 and 72: Gases Substance Air Argon Butane Ca
Page 73 and 74: RADIATION The radiation emitted by
Page 75 and 76: Use the cylinder diameter in the ev
Page 77 and 78: Shape Factor Relations Reciprocity
Page 79 and 80: For more information on Biology see
Page 81 and 82: Stoichiometry of Selected Biologica
Page 83 and 84: Avogadro's Number: The number of el
Page 85 and 86: 80 Specific Example IUPAC Name Comm
Page 87 and 88: MATERIALS SCIENCE/STRUCTURE OF MATT
Page 89 and 90: HARDENABILITY Hardenability is the
Page 91 and 92: POLYMERS Classification of Polymers
Page 93 and 94: Signal Conditioning Signal conditio
Page 95 and 96: An alternative form commonly employ
Page 97 and 98: ENGINEERING ECONOMICS Factor Name C
Page 99 and 100: ENGINEERING ECONOMICS (continued) 9
Page 105 and 106: B. LICENSEE’S OBLIGATION TO EMPLO
Page 107 and 108: Common Names and Molecular Formulas
Page 109 and 110: For mixtures of ideal gases: fi o =
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Distillation Definitions: α = rela
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Cost Segments of Fixed-Capital Inve
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Concentrations of Vaporized Liquids
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COARSE- GRAINED SOILS More than 50%
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STRUCTURAL ANALYSIS Influence Lines
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Pu A's As Mu A's As UNIFIED DESIGN
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SHORT COLUMNS Limits for main reinf
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GRAPH A.15 Column strength interact
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BEAMS: homogeneous beams, flexure a
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124 CIVIL ENGINEERING (continued) B
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126 CIVIL ENGINEERING (continued) A
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Fy = 50 ksi φb = 0.9 φv = 0.9 Sha
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♦ 50.0 1.0 10.0 5.0 3.0 0.9 2.0 1
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ALLOWABLE STRESS DESIGN SELECTION T
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Kl r ASD Table C-50. Allowable Stre
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Open-Channel Flow Specific Energy 2
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Transportation Models See INDUSTRIA
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VERTICAL CURVE FORMULAS L = Length
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EARTHWORK FORMULAS Average End Area
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, METERS , METERS 144 ENVIRONMENTAL
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Cyclone Cyclone Collection (Particl
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FATE AND TRANSPORT Microbial Kineti
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LANDFILL Break-Through Time for Lea
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152 ENVIRONMENTAL ENGINEERING (cont
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No. 1 2 3 4 5 6 7 8 9 10 11 12 13 1
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Exposure Residential Exposure Equat
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TOXICOLOGY Dose-Response Curves The
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♦ Aerobic Digestion Design criter
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where R Cin = stripping factor H′
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Bed Expansion Monosized Multisized
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Stokes' Law V t 2 ( ρp − ρf ) g
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Resistors in Series and Parallel Fo
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RC AND RL TRANSIENTS v R + V 1 −
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AC Machines The synchronous speed n
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LAPLACE TRANSFORMS The unilateral L
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Fourier Transform Pairs x(t) X(f) 1
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FM (Frequency Modulation) The phase
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180 ELECTRICAL AND COMPUTER ENGINEE
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OPERATIONAL AMPLIFIERS Ideal v2 vo
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FLIP-FLOPS A flip-flop is a device
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Standard Deviation Charts n A3 B3 B
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LINEAR REGRESSION Least Squares bx
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ERGONOMICS NIOSH Formula Recommende
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PERT (aij, bij, cij) = (optimistic,
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HYPOTHESIS TESTING Table A. Tests o
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ERGONOMICS U.S. Civilian Body Dimen
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202 INDUSTRIAL ENGINEERING (continu
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The deflection θ and moment Fr are
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Failure by crushing of rivet or mem
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Only the tangential component Wt tr
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Cooling and Dehumidification ω Q
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Cycles and Processes Internal Combu
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Steam Trap Junction Pump See also T
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Compressor Isentropic Efficiency: w
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Infiltration Air change method ρ c
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compressible fluid, 50 compression
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jet propulsion, 48 JFETs, 182, 184
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esultant, 24 retardation factor R,
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State Code School Alabama Universit
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State Code School Minnesota Univers
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State Code School Virginia (Cont'd)
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