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♦ Submerged Orifice operating under steady-flow conditions: • Q = A2V2 = CcCv = CA 2g ( h − h ) 1 A 2 2g ( h − h ) 1 2 in which the product of Cc and Cv is defined as the coefficient of discharge of the orifice. Orifice Discharging Freely into Atmosphere • Q = CA 2gh in which h is measured from the liquid surface to the centroid of the orifice opening. ♦ Bober, W. & R.A. Kenyon, Fluid Mechanics, John Wiley & Sons, Inc., 1980. Diagrams reprinted by permission of William Bober & Richard A. Kenyon. • Vennard, J.K., Elementary Fluid Mechanics, J.K. Vennard, 1954. Diagrams reprinted by permission of John Wiley & Sons, Inc. 51 FLUID MECHANICS (continued)
DIMENSIONAL HOMOGENEITY AND DIMENSIONAL ANALYSIS Equations that are in a form that do not depend on the fundamental units of measurement are called dimensionally homogeneous equations. A special form of the dimensionally homogeneous equation is one that involves only dimensionless groups of terms. Buckingham's Theorem: The number of independent dimensionless groups that may be employed to describe a phenomenon known to involve n variables is equal to the number (n – r ), where r is the number of basic dimensions (i.e., M, L, T) needed to express the variables dimensionally. SIMILITUDE In order to use a model to simulate the conditions of the prototype, the model must be geometrically, kinematically, and dynamically similar to the prototype system. To obtain dynamic similarity between two flow pictures, all independent force ratios that can be written must be the same in both the model and the prototype. Thus, dynamic similarity between two flow pictures (when all possible forces are acting) is expressed in the five simultaneous equations below. ⎡ F ⎤ I ⎢ ⎥ ⎢⎣ Fp ⎥⎦ ⎡ F ⎤ I ⎢ ⎥ ⎣ FV ⎦ ⎡ F ⎤ I ⎢ ⎥ ⎣ FG ⎦ ⎡ F ⎤ I ⎢ ⎥ ⎣ FT ⎦ p p p p p ⎡ F ⎤ I = ⎢ ⎥ ⎢⎣ Fp ⎥⎦ ⎡ F ⎤ I = ⎢ ⎥ ⎣ FV ⎦ ⎡ F ⎤ I = ⎢ ⎥ ⎣ FT ⎦ m ⎡ F ⎤ I = ⎢ ⎥ ⎣ FG ⎦ m m m m ⎡ρV = ⎢ ⎣ p 2 ⎡Vlρ⎤ = ⎢ ⎥ ⎣ µ ⎦ 2 ⎡V ⎤ = ⎢ ⎥ ⎣ lg ⎦ ⎡ρlV = ⎢ ⎣ σ ⎤ ⎥ ⎦ 2 p p p ⎡Vlρ⎤ = ⎢ ⎥ ⎣ µ ⎦ 2 ⎡V ⎤ = ⎢ ⎥ ⎣ lg ⎦ p ⎤ ⎥ ⎦ p ⎡ρV = ⎢ ⎣ p 2 2 ⎡ F ⎤ ⎡ I F ⎤ ⎡ρ I V ⎤ ⎡ρV ⎤ ⎢ ⎥ = ⎢ ⎥ = ⎢ ⎥ = ⎢ ⎥ ⎣ FE ⎦ ⎣ FE ⎦ ⎣ Ev ⎦ ⎣ Ev ⎦ 2 m m ⎡ρlV = ⎢ ⎣ σ ⎤ ⎥ ⎦ = 2 m = [ Re] = [ Re] [ Fr] = [ Fr] m ⎤ ⎥ ⎦ m = p p [ Ca] = [ Ca] = p m m m [ We] p = [ We] m 52 FLUID MECHANICS (continued) where the subscripts p and m stand for prototype and model respectively, and FI = inertia force, FP = pressure force, FV = viscous force, FG = gravity force, FE = elastic force, FT = surface tension force, Re = Reynolds number, We = Weber number, Ca = Cauchy number, Fr = Froude number, l = characteristic length, V = velocity, ρ = density, σ = surface tension, Ev = bulk modulus, µ = dynamic viscosity, v = kinematic viscosity, p = pressure, and g = acceleration of gravity. Re = VD ρ = µ VD v
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FUNDAMENTALS OF ENGINEERING SUPPLIE
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Published by the National Council o
Page 5 and 6: CONTENTS Units.....................
Page 7 and 8: 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: FLUID MEASUREMENTS The Pitot Tube -
Page 59 and 60: MOODY (STANTON) DIAGRAM e, (ft) e,
Page 61 and 62: PROPERTIES OF SINGLE-COMPONENT SYST
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
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Common Names and Molecular Formulas
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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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