A B C D
DALL TUBE DALTON'S LAW DALTON'S LAW OF PARTIAL PRESSURES DAMAGE INTERFACE DAMPING, OF HEAT EXCHANGER TUBES DARCY EQUATION DARCY FREE CONVECTION DARCY NUMBER DARCY'S LAW DARCY-PRANDTL NUMBER Data for molecules of practical interest DATING OF ARCHAEOLOGICAL SAMPLES DDT, DEFLAGRATION TO DETONATION TRANSITION DE LAVAL NOZZLES DE-ICING DEBORAH NUMBER DEBYE TEMPERATURE DECANTATION DECANTERS DECELERATING DROPS DECONVOLUTION, OPTICS DEEP SHAFT DEFINITE INTEGRALS DEFLAGRATION DEFLAGRATION TO DETONATION TRANSITION, DDT DEGENERACY DEGREES OF FREEDOM DEHYDRATION DELIQUESCENCE DELTA FUNCTION DENDRITE LAYER DENDRITIC CRYSTALS DENSITY GAS MODEL DENSITY MAXIMUM OF WATER DENSITY MEASUREMENT DENSITY OF GASES DENSITY OF LIQUIDS DENSITY, HOMOGENEOUS DENSITY, OF THE ATMOSPHERE DENSITY-WAVE OSCILLATIONS DEPARTMENT OF THE ENVIRONMENT, DoE DEPARTURE FROM FILM BOILING DEPARTURE FROM NUCLEATE BOILING, DNB DEPHLEGMATOR DEPOSITION DEPOSITION OF HOMO- AND HETERO-EPITAXIAL SILICON THICK FILMS BY MESO-PLASMA CVD DEPOSITION OF PARTICLES DEPOSITION RATE OF DROPLETS IN ANNULAR FLOW DERIAZ TURBINES Derivative (derived) unit of measurement DESALINATION DESALINATION OF OIL DESALINATION, FLASH EVAPORATION FOR DESICCANTS DESICCATION DESIGN BASIS ACCIDENT DESTRUCTION OF SURFACES DETECTION OF CHEMICAL AND BIOLOGICAL AEROSOLIZED POLLUTANTS DETERGENTS DETERMINANTS Determination of material properties: optical tomography applications DETERMINISTIC CHAOS DETONATION DETONATION WAVE DEUTERIUM DEUTERIUM OXIDE DEUTSCH-ANDERSON EQUATION DEVIATORIC STRESS DEVOLATIZATION OF COAL PARTICLES DEW POINT DEWAR DEWATERING DIAMETER, HYDRAULIC DIAMOND-SHAPED CYLINDER BUNDLE DIAPHRAGM GAUGE DIE DIE-CASTING DIELECTRIC HEATING DIELECTROPHORETIC FORCES DIESEL CONDITIONS DIESEL ENGINES DIESEL FUEL DIESEL JET DESTRUCTION DIESEL SPRAY DIESEL-EMITTED PARTICLES Differential approximations DIFFERENTIAL CONDENSATION CURVE DIFFERENTIAL EQUATIONS DIFFERENTIAL PRESSURE FLOWMETERS DIFFERENTIAL PRESSURE TRANSDUCERS DIFFRACTION DIFFUSER DIFFUSION DIFFUSION APPROXIMATION IN MULTIDIMENSIONAL RADIATIVE TRANSFER PROBLEMS DIFFUSION COEFFICIENT DIFFUSION COEFFICIENT OF GASES DIFFUSION EQUATIONS DIFFUSION FLAMES DIFFUSION IN ELECTROLYTE SOLUTION DIFFUSION LAW DIFFUSION PUMP DIFFUSIVE CONVECTION DILATANCY DILATANT FLUIDS DILATION OF GRANULAR MATERIAL DILUTANT FLUIDS DILUTE SUSPENSION Dimension (of a secondary quantity with respect to a given primary quantity) Dimensional Analysis Dimensional Analysis and Similarity Dimensional equation DIMENSIONAL MATRIX Dimensional quantity (variable) DIMENSIONAL STABLE ANODES, DSAS DIMENSIONALLY HOMOGENEOUS EQUATIONS DIMENSIONLESS GROUPS Dimensionless Parameters Dimensionless quantity (Dimensionless variable) DIMERS DIOXINS DIPHENYL DIPOLE MOMENT DIRAC DELTA FUNCTION DIRECT CONTACT CONDENSERS DIRECT CONTACT EVAPORATORS DIRECT CONTACT HEAT EXCHANGERS DIRECT CONTACT HEAT TRANSFER DIRECT CONTACT MASS TRANSFER DIRECT INVERSION OPTICAL TECHNIQUE DIRECT NUMERICAL SIMULATIONS, DNS DIRICHLET CONDITIONS DIRICHLET'S PROBLEM DISCHARGE COEFFICIENT DISCRETE ENERGY DISCRETE ORDINATE APPROXIMATION Discrete ordinates and finite volume methods Discrete ordinates method Discrete ordinates method for one-dimensional problems DISK AND DOUGHNUT BAFFLES DISK TYPE CENTRIFUGE DISK TYPE STEAM TURBINE DISORDER Dispersed Flow DISPERSED FLOW, IN NOZZLES DISPERSED LIQUID FLOWS DISPERSION IN POROUS MEDIA DISPERSION OF PARTICLES DISPERSION RELATIONSHIPS, FOR WAVES IN FLUIDS DISPLACEMENT CHROMATOGRAPHY Displacement thickness DISPLACEMENT THICKNESS, OF BOUNDARY LAYER DISSIPATION OF HEAT FROM EARTH'S SURFACE DISSIPATIVE SYSTEMS DISSOLVED AIR FLOTATION, DAF DISSOLVED SOLIDS DISTILLATION DISTILLATION REBOILERS DISTRIBUTIONS DISTURBANCE WAVES, IN ANNULAR FLOW DISYMMETRY OF SCATTERED LIGHT DITTUS-BOELTER CORRELATION DITTUS-BOELTER EQUATION DNB, DEPARTURE FROM NUCLEATE BOILING DOE DOLINSKII, A.A. DOMESTIC WATER HEATER DONNEN EFFECT DOPING DOPPLER ANEMOMETRY DOPPLER BROADENING DOPPLER BURST DOPPLER EFFECT DOPPLER GLOBAL VELOCIMETRY DOPPLER SHIFT DOUBLE DIFFUSIVE CONVECTION IN A ROTATING POROUS LAYER DOUBLE EXPOSURE HOLOGRAPHY DOUBLE FLASH METHODS DOUBLE-DIFFUSIVE MAGNETOCONVECTION DOUBLE-PIPE EXCHANGERS DOUBLING TIME DOUBLY STRATIFIED DARCY POROUS MEDIUM DOWTHERM DRAFT TUBE MIXER DRAG Drag Coefficient DRAG FORCE DRAG FORCE ON PARTICLES DRAG INDUCED FLOW DRAG ON A PARTICLE DRAG ON PARTICLES AND SPHERES DRAG ON REACTOR DRAG ON SOLID SPHERES AND BUBBLES DRAG REDUCTION DRAINING INTENSELY EVAPORATED WAVE FILMS DREITSER, G.A. DRIFT FLUX Drift flux models DRIFT VELOCITY DROP FORMATION DROP SHAPES DROP SPLITTING DROP TOWERS DROPLET COLLISION DROPLET DEPOSITION AND ENTRAINMENT, IN ANNULAR FLOW DROPLET DETECTION DROPLET GENERATION DROPLET MEASUREMENTS DROPLET SIZE DISTRIBUTION DROPLET SPRAYS DROPLET STREAM DROPLET SURFACE TENSION DROPLET/LIQUID SEPARATION DROPLETS Drops DROPS, MASS TRANSFER TO AND FROM Dropsize measurement DROPWISE CONDENSATION DROPWISE PROMOTERS DROWNING OUT DRUM TYPE STEAM TURBINE DRY CONTAINMENTS, FOR NUCLEAR REACTORS DRY-BULB TEMPERATURE DRYERS DRYING DRYING CHAMBERS DRYOUT DUAL-PURPOSE HEAT PUMPS DUBOIS' BODY SURFACE DUCTILE FRACTURE DUCTS, NONCIRCULAR, FLOW IN DUFOUR EFFECT DUNE FLOW DUST, AS AN AIR POLLUTANT DUSTS DUSTY PLASMAS DWARF GALAXIES DYE LASERS DYNAMIC INSTABILITIES IN TWO-PHASE SYSTEMS Dynamic Pressure DYNAMIC WAVES DYNAMICAL SIMILARITY DYNAMICS
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Drag Coefficient

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Drag coefficient is a dimensionless factor of proportionality between overall hydrodynamic force vector on a body in a liquid or gas flow and the product of reference area S of the body (commonly at midship section) and velocity head q

where , and vs are the velocity vectors of the fluid and the body, is the relative velocity of the body, ρ the liquid (gas) density, S the midship section area of the body, and Cd the drag coefficient.

This relation follows from similarity theory and is extensively used in engineering for simplified calculation of the force acting on a body or a particle in liquid or gas in which it moves.

In practice, drag coefficient is calculated in most cases using empirical relations generalizing experimental data. The most widely studied case is the sphere. Figure 1 graphs the dependence of drag coefficient for a sphere and a cylinder in crossflow on the Reynolds Number Re = ρuD/η, where D is the sphere (cylinder) diameter, η the viscosity of liquid, and . The drag coefficient decreases drastically from extremely high values at small Re numbers, to unity and lower at Re > 103. For Re < 0.2, Stokes has derived a theoretical formula for drag coefficient for a sphere:

Here, a purely viscous nonseparating flow occurs. The drag is governed by a high molecular friction of the liquid, the effect of which extends far upstream. With increasing Re number, inertial forces begin to predominate over viscosity forces and a laminar boundary layer is originated. Now, viscous forces are manifested only in this fairly thin layer. Flow beyond the boundary layer is virtually not affected by viscosity. Flow separation in the stern (point S in Figure 1) also occurs. As Re grows, the area of separation increases and attains the highest values at Re ~ 103; the drag coefficient in this case no longer diminishes and even slightly increases, remaining close to 0.4 for the range 2 × 103 < Re < 2 × 105.

Drag coefficient for cylinders (1) and spheres (2) as a function of Reynolds number (Re).

Figure 1. Drag coefficient for cylinders (1) and spheres (2) as a function of Reynolds number (Re).

In the 0.2 < Re < 2 × 103 range, an approximation formula for calculating a drag coefficient for a sphere is:

(1)

If Re continues to increase, the situation arises (at Re ~ 2 × 105) when the laminar boundary layer becomes partially turbulent in the nonseparating flow region of the sphere. The velocity profile in the turbulent boundary layer is fuller and better resists a positive pressure gradient. The area of separation is sharply displaced toward the stern, thereby drastically decreasing the drag coefficient. A self-similarity regime sets in and with further enhancement of the Re number, drag coefficient remains unchanged.

At high gas velocitiy, the drag coefficient also depends on the Mach number Ma = u/a, where a is the velocity of acoustic waves in the gas. At Ma < 1, a formula approximating a vast body of experimental data is:

where Cd0 is calculated using Eq. (1), has gained acceptance.

Drag coefficient is strongly affected by a body's shape. It is taken into account via the sphericity coefficient, which is the ratio of the sphere surface area of the same volume as the body relative to the body's surface area. For a tetrahedron, this is 0.67; for a cube, 0.806; and for octahedron, 0.85. Introduction of the sphericity coefficient in reality means the changing from an irregular shape of the body to some equivalent spherical shape, with sphere diameter taken as a reference dimension for determining the Re number and the midship section area.

Bodies of irregular shape, e.g., those of great length or twisted ones, move by tortuous trajectories and rotate, substantially changing the drag coefficient.

Where there are two spheres in close proximity, the drag coefficient is increased as shown in Figure 2.

Figure 2. 

Following from:

Immersed Bodies, Flow Around and Drag

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Immeresed Bodies, Flow Around and Drag in Fundamentals
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