A B C
ACHE CAD, PLASTICATING SCREWS CAF, COMPRESSED ASBESTOS FIBRE JOINTING CALANDRIA CALCIUM CALCULATING TIME CHARACTERISTICS OF IGNITION OF HYBRID GAS SUSPENSIONS CALDER HALL CALORIE CALORIFIC VALUE OF FUEL CALORIMETRY CANDU NUCLEAR POWER REACTORS CANONICAL PARTITION FUNCTION CAP BUBBLES CAPACATIVE HEAT EXCHANGERS CAPILLARITY Capillary action CAPILLARY CONVECTION CARBOLIC ACID CARBON CARBON ARC CARBON DIOXIDE CARBON DIOXIDE POLLUTION CARBON DIOXIDE, AS A POLLUTANT CARBON DISULFIDE COMBUSTION CARBON MONOXIDE CARBON STEELS CARBON SUBNITRIDE COMBUSTION CARBON THERMOMETERS CARBONACEOUS FUELS CARBONTETRACHLORIDE CARNOT CYCLE CARNOT, NLS CARRYUNDER CARTESIAN COORDINATES CASTING OF METALS CATALYSIS CATALYSTS CATALYTIC ACTIVITY CATALYTIC CONVERSION CATALYTIC CONVERTERS CATALYTIC CRACKING OF PALM OIL CATALYTIC RICH GAS PROCESS, CRG CATHODE CAUCHY SURFACE CAUCHY'S CONVEYENCE PRINCIPLE CAUCHY'S THEOREM CAUSTIC SODA CAVITATING FLOWS CAVITATION CAVITIES, FOR NUCLEATION CAVITY, SQUARE CEA CEC CELL GROWTH CELL POTENTIAL CELLULOSIC FIRES CELSIUS TEMPERATURE SCALE CENTIGRADE TEMPERATURE SCALE CENTRIFUGAL FILTERS CENTRIFUGAL FLOWMETERS CENTRIFUGAL FLUIDIZED BED CENTRIFUGAL SCRUBBER CENTRIFUGAL SEPARATORS CENTRIFUGES CENTRIPETAL BUOYANCY CENTRIPETAL FORCE CERAMIC CRUCIBLE PLASMA FURNACE CERAMICS CERENKOV RADIATION CERMETS CFCS, CHLOROFLUOROCARBON CFD CFD MODELS CHAIN REACTION CHANG-LIN TIEN CHANNEL CONTROL Channel Flow CHANNEL INSTABILITY CHANNEL IRREGULARLY HEATED CHANNELING EFFECT CHAOS CHAR CHARACTERISTIC DRYING CURVE CHARACTERISTIC EQUATIONS, FOR SUPERSONIC FLOW CHARACTERISTICS, METHOD OF CHARACTERISTICS, OF DIFFERENTIAL EQUATIONS CHARCOAL CHARGE CARRIERS CHARGE COUPLED DEVICES, CCD CHARLES LAW CHEBYSHEV EQUATION CHEBYSHEV POLYNOMIAL EXPANSION CHEBYSHEV POLYNOMIALS CHELATION CHEMICAL COMPLEXITY CHEMICAL EQUILIBRIUM CHEMICAL KINETICS CHEMICAL LASERS CHEMICAL POTENTIAL CHEMICAL REACTION CHEMICAL REACTION FOULING CHEMICAL THEORIES, FOR CATALYSIS CHEMICAL THERMODYNAMICS CHEMISORPTION CHEN CORRELATION CHEVRON SEPARATORS Chezy Formula CHF CORRELATIONS CHF, CRITICAL HEAT FLUX CHILTON-COLBURN ANALOGY CHIMNEY PLUMES CHIMNEYS CHLOR-ALKALI ELECTROLYSIS CHLORINE CHLOROFLUOROCARBON, CFC CHLOROFORM CHOKED FLOW CHROMATIC DISPERSION CHROMATOGRAPHY CHUGGING INSTABILITIES Churn Flow CIRCUIT BREAKER CIRCULATION RATIO CISE CORRELATIONS CLADDING CLAPEYRON EQUATION CLAPEYRON-CLAUSIUS EQUATION CLARIFICATION CLARIFIERS Classification of foam structures CLASSIFICATION OF HEAT EXCHANGERS CLASSIFIERS CLAUSIUS CLAUSIUS NUMBER CLAUSIUS-CLAPEYRON EQUATION CLAUSIUS-MOSOTTI EQUATION CLEANING TECHNIQUES, HEAT EXCHANGERS Climate study CLIMATIZATION CLIMBING FILM EVAPORATOR Closed cell foam CLOSED CYCLE GAS TURBINE CLOSED CYCLE MHD GENERATORS CLOSED SYSTEM CLOSURE LAWS CLOUD POINT SPECIFICATION CNEN CO-GENERATION SYSTEMS CO-ORDINATE TRANSFORMATION METHODS COAGULATION COAGULATION, OF AEROSOLS COAGULATION, OF DROPS COAL COAL BURNERS COAL CARBONIZATION COAL COMBUSTION COAL GAS COAL GASIFICATION COAL RESEARCH ESTABLISHMENT, CRE COAL SLURRY COALESCENCE Coanda Effect COARSE VARIABLES FOR DYNAMICS COARSE-GRAINED APPROXIMATION COATINGS COAXIAL TWISTING FLOW COEFFICIENT OF PERFORMANCE, COP COHERENCE FUNCTION COHERENCE STRICTURES, IN TURBULENT FLOW COHERENCE, OF RADIATION COHERENT SYSTEM OF UNITS COIL IN TANK COILED TUBE BOILERS Coiled Tube, Flow and Pressure Drop in Coiled Tubes, Heat Transfer in COILED WIRE INSERTS COKE COKE OVENS COKE-OVEN GAS COLBURN CORRELATION COLBURN FACTOR COLBURN HEAT TRANSFER FACTOR COLBURN J-FACTOR COLBURN, ALLAN PHILIP (1904-1955) COLBURN-CHILTON ANALOGY COLD ROD EFFECTS COLEBROOK-WHITE EQUATION, FOR FRICTION FACTOR COLEBROOK-WHITE FORMULA COLLECTION EFFICIENCY COLLIGATIVE PROPERTIES COLLIGEND COLLOCATION COLLOIDAL DISPERSIONS COLOR SEGREGATION IN METAL-HALIDE LAMPS COLUMN CHROMATOGRAPHY COLUMNS COMBINATORIAL MODELING COMBINED BRINKMAN-ELECTRIC BOUNDARY LAYER COMBINED CYCLES COMBINED HEAT AND MASS TRANSFER Combined heat transfer by radiation, conduction, and convection COMBINED RADIATION AND COMBUSTION COMBUSTION COMBUSTION CHAMBER COMBUSTION PRODUCTS COMFORT CONDITIONS COMITATO NAZIONALE PER LA RICERCA E PER LO SVILUPPO DELL'ENERGIA NUCLEARE E DELLE ENERGIE ALTERNATIVE, ENEA COMMERCIAL PLASMATRON COMMISSARIAT A L'ENERGIE ATOMIQUE, CEA COMMISSION OF THE EUROPEAN COMMUNITY, CEC COMMON MODE FAILURE COMMONWEALTH SCIENTIFIC AND INDUSTRIAL RESEARCH ORGANISATION, CSIRO COMPACT HEAT EXCHANGERS COMPILER COMPLEX COMPOUND CATALYSIS COMPLEXIFICATION COMPLEXING IONS COMPLEXITY COMPOSITE FLOW COMPOSITE MATERIALS COMPOSITE MATERIALS, ABLATION OF COMPOSITE MATERIALS, COMPUTATION OF COMPOSITE POROUS LAYER COMPOSITES, THERMAL CONDUCTIVITY OF COMPOUND AUGMENTATION COMPRESSED ASBESTOS FIBER JOINTING, CAF COMPRESSIBILITY EFFECTS COMPRESSIBILITY FACTOR Compressible Flow COMPRESSION PLASMA FLOWS COMPRESSION POINT COMPRESSION ZONE COMPRESSION-IGNITION ENGINES COMPRESSORS COMPTON SCATTERING COMPUTATIONAL FLUID DYNAMIC MODELS Computational fluid dynamics Computational methods Computational methods for radiative transfer in disperse systems COMPUTER AIDED DESIGN, CAD COMPUTER PROGRAMMES COMPUTERS CONCAVE SURFACE, FLOW OVER CONCENTRATING COLLECTOR CONCENTRATION-DEPENDENT CHLORIDE DIFFUSIVITY Concept of regularization CONCRETE CONCURRENT MULTISCALE PROBLEMS CONDENSATE INUNDATION CONDENSATION COEFFICIENT CONDENSATION CURVE CONDENSATION IN ENCLOSURES CONDENSATION IN TUBE BANKS CONDENSATION IN TUBES CONDENSATION OF A PURE VAPOR CONDENSATION OF MOVING VAPOR INSIDE VERTICAL TUBES CONDENSATION OF MULTICOMPONENT VAPORS CONDENSATION ON OUTSIDE OF TUBES IN CROSSFLOW CONDENSATION RELAXATION OF SUPERSATURATED VAPOR CONDENSATION SHOCKS CONDENSATION, OF DROPS CONDENSATION, OVERVIEW CONDENSERS CONDUCTANCE PROBES, FOR LOCAL VOID FRACTION CONDUCTANCE, ELECTRICAL CONDUCTION CONDUCTION AND CONVECTION COMBINED CONDUCTION COMBINED WITH RADIATION CONDUCTION DRYING CONDUCTION EQUATION CONDUCTION IN HEAT EXCHANGER WALLS CONDUCTIVE HEAT FLUX CONDUCTIVITY CONDUCTIVITY RATIO CONDUCTIVITY, ELECTRICAL CONDUCTIVITY, OF PLASMA CONE CLASSIFIER Configuration factors for radiation transfer between diffuse surfaces CONFINED SPRAY FLAME CONFORMAL MAPPING CONFORMAL POTENTIALS CONICAL SHOCK WAVE CONJUGATE HEAT TRANSFER CONSERVATION EQUATIONS CONSERVATION EQUATIONS, SINGLE-PHASE Conservation equations, Two-phase Conservation Laws CONSERVATIVE SYSTEMS CONSTANT RATE PERIOD, DRYING CURVE CONSTITUTIVE EQUATIONS CONSTITUTIVE RELATION, THERMODYNAMICS Contact angle CONTACT CONDUCTANCE CONTACT DISCONTINUITIES CONTACT RESISTANCE CONTAINMENT CONTINUITY EQUATION CONTINUITY SHOCKS CONTINUITY WAVES CONTINUOUS CASTING CONTINUOUS CRYSTALLIZERS CONTINUOUS FILTERS CONTINUOUS WAVE LASERS Continuum Continuum Hypothesis CONTINUUM MECHANICS CONTINUUM MODELS Contraction, Flow and Pressure Loss in CONTRACTORS CONTROL THEORY CONVECTION CONDENSATION CONVECTION DRYING CONVECTION RADIATION CONVECTIVE BOILING CONVECTIVE HEAT FLUX CONVECTIVE HEAT TRANSFER CONVECTIVE HEAT TRANSFER ENHANCEMENT CONVECTIVE MASS TRANSFER CONVERGENCE FACTORS CONVERGENCE OF SERIES CONVERGING BOUNDARIES CONVERSION FACTORS COOL FLAME EVAPORATION COOLANTS, REACTOR COOPER CORRELATION, FOR NUCLEATE BOILING COORDINATE SYSTEM COPPER CORE, NUCLEAR REACTOR CORED BRICK HEAT EXCHANGERS CORIOLIS EFFECT CORIOLIS EFFECT, IN ATMOSPHERIC CIRCULATION CORIOLIS MASS FLOWMETER CORLISS VALVE CORONA DISCHARGE, ELECTROSTATIC PRECIPITATION CORONARY ARTERIES Correlated k-models CORRELATION CORRELATION ANALYSIS CORRELATION COEFFICIENT CORRELATION, FOR CONVECTIVE HEAT TRANSFER CORRELATIONS FOR NOx EMISSIONS FROM A SWIRL BURNER CONCEPT CORRESPONDING STATES, PRINCIPLE OF CORROSION FOULING CORROSION, PREDICTION METHODS FOR CORRUGATED CONDENSED TUBES CORRUGATIONS, PLAIN, PERFORATED, AND SERATED COUETTE VISCOMETER COULTER COUNTER COUNTER CURRENT FLOW LIMITATION, CCFL COUNTER CURRENT TWO-PHASE FLOW COUNTERIONIC ATTRACTION Coupled (combined) radiation and conduction COUPLED AUTOREGULATED OSCILLATING CELLS COUPLED CONDUCTION AND CONVECTION COUPLED HEAT AND MASS FLUXES Coupled radiation and convection Coupled radiation, convection and conduction COVALENT BONDING COWPER STOVES CRACKING CRAMER'S RULE CRE CREAGER-OFITSEROV PROFILE CREEPING FLOW CRITICAL CHOKING CRITICAL CONCENTRATION CRITICAL DEPOSITION VELOCITY Critical Flow CRITICAL FLOW RATE, IN ORIFICES CRITICAL HEAT FLUX IN BOILING LIQUID METALS CRITICAL HEAT FLUX IN COILS CRITICAL HEAT FLUX, CHF CRITICAL POINT, DRYING CURVE CRITICAL POINT, THERMODYNAMICS CRITICAL PRESSURE CRITICAL PRESSURE RATIO Critical Reynolds number CRITICAL SEDIMENTATION POINT CRITICAL STATE CRITICAL SURFACE TENSION CRITICAL TEMPERATURE CRITICAL TEMPERATURE, FOR SUPERCONDUCTIVITY CRITICAL TRANSITION VELOCITY CRITICAL ZONE CRITICALITY CROCCO TRANSFORMATION CROCCO'S THEOREM CROSS CORRELATION CROSS FLOW HEAT TRANSFER CROSS FLUXES CROSS SECTIONS CROSS SPECTRUM Crossflow CRUDE OIL CRYOGENIC FLUIDS CRYOGENIC PLANT CRYOGENIC PUMP CRYOGENIC USE OF STEEL CRYOSCOPIC CONSTANT CRYOSTATS CRYSTAL GROWTH CRYSTAL STRUCTURE ASYMMETRY CRYSTAL SUBLIMATION AND GROWTH CRYSTALLIZATION CRYSTALLIZATION FOULING CRYSTALLIZERS CRYSTALS CSIRO CUBIC LATTICES CUNNINGHAM COEFFICIENT CURRENT VOLTAGE CHARACTERISTICS CURRENTS, NEARSHORE CURVED FLOW CURVILINEAR CHANNELS CYANOGEN COMBUSTION CYCLIC HYDROCARBONS CYCLOHEXANOL CYCLONE FURNACES CYCLONE REYNOLDS NUMBER CYCLONE SEPARATOR CYCLONE STOKES NUMBER CYCLONES CYLINDER, INVISCID FLOW AROUND CYLINDERS, FLOW OVER CYLINDRICAL COORDINATES CYLINDRICAL FINS CYLINDRICAL POLAR COORDINATES
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Contraction, Flow and Pressure Loss in

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The flow of fluid through a contraction (decrease in pipe diameter) results in an increase in the velocity and consequently, a pressure drop greater than the value for the equivalent straight pipe. If the contraction is sharp or sudden, the behavior of single-phase flow is as shown in Figure 1 and involves two recirculation regions. The first starts about 1.5 inlet pipe diameters upstream whilst the second starts at the contraction and extends up to 15 outlet pipe diameters downstream. The dissipation of energy caused by these recirculation regions means that not all the pressure drop is converted to kinetic energy (and thence recoverable at a subsequent enlargement) and reversible, and irreversible components of pressure drop must be considered. If the contraction is being used to create kinetic energy from pressure, it is necessary to employ a more gradual change in diameter so as to eliminate or minimize recirculations and thus losses.

Flow structure and pressure profile for single-phase flow through a sudden contraction.

Figure 1. Flow structure and pressure profile for single-phase flow through a sudden contraction.

Lighthill (1986), in discussing the calculation of pressure drop through a generalized contraction, points out that it is not possible to use a momentum balance as there is an unknown reaction force from the walls to be accounted for. An energy balance gives a computable expression for the (reversible) pressure drop. To account for both the reversible and irreversible components of pressure drop, a balance is carried out from upstream to the minimum flow area point at the vena contracta (with no irreversibility) and a second balance downstream where most of the dissipation occurs. The combination of these results in

(1)

where is the mass flux; ρ, the density; S, the area ratio between upstream and downstream pipes; and Cc, the contraction coefficient (the ratio of areas of the vena contracta and the outlet pipe.) Equations for the contraction coefficient in terms of S are given by, for example, Benedict (1980) and Chisholm (1986).

In gas/liquid flow, the sudden contraction can act as a homogenizer mixing the phases and making their velocities more equal. For annular flows, the contraction can cause an increase in the proportion of liquid travelling as drops.

For two-phase pressure drop, Chisholm (1983) provides an equation equivalent to (1), derived using a separated flow approach. Comparison with experimental data shows that the homogeneous version of this equation gives the best results. However, there is recent evidence, Schmidt (1993), that the vena contracta does not always occur. The pressure profile shown in Figure 2 provides confirmation of this as it lacks the characteristic minimum seen in Figure 1, which is characteristic of the vena contracta.

Pressure profile for gas/liquid flow through a sudden contraction. Quality = 0.5.

Figure 2. Pressure profile for gas/liquid flow through a sudden contraction. Quality = 0.5.

REFERENCES

Benedict, R. P. (1980) Fundamentals of Pipeflow, Wiley-Interscience, New York.

Chisholm, D. (1983) Two-Phase Flow in Pipelines and Heat Exchangers, Pitman Press Ltd., Bath, England.

Lighthill, J. (1986) An Informal Introduction to Theoretical Fluid Mechanics, Oxford University Press, Oxford.

Schmidt, J. (1993) Berechnung und Messung des Druckabfalls uber plötzliche scharfkantige Rohrerweiterungen und -verengungen bei Gas/Dampf-Flüssigkeitsströmung, VDI-Forschungsheft.

References

  1. Benedict, R. P. (1980) Fundamentals of Pipeflow, Wiley-Interscience, New York.
  2. Chisholm, D. (1983) Two-Phase Flow in Pipelines and Heat Exchangers, Pitman Press Ltd., Bath, England. DOI: 10.1080/01457638508939624
  3. Lighthill, J. (1986) An Informal Introduction to Theoretical Fluid Mechanics, Oxford University Press, Oxford. DOI: 10.1063/1.2811466
  4. Schmidt, J. (1993) Berechnung und Messung des Druckabfalls uber plötzliche scharfkantige Rohrerweiterungen und -verengungen bei Gas/Dampf-Flüssigkeitsströmung, VDI-Forschungsheft.

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Pressure Drop, Two-Phase Flow
Pressure Drop, Single-Phase
Channel Flow

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