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Dimensionless

The Ft correction factor is usually correlated in terms of two dimensionless ratios, the ratio of the two heat capacity flow rates R and the thermal effectiveness P of the exchanger ... [Pg.223]

The above equation is valid at low pressures where the assumptions hold. However, at typical reservoir temperatures and pressures, the assumptions are no longer valid, and the behaviour of hydrocarbon reservoir gases deviate from the ideal gas law. In practice, it is convenient to represent the behaviour of these real gases by introducing a correction factor known as the gas deviation factor, (also called the dimensionless compressibility factor, or z-factor) into the ideal gas law ... [Pg.106]

Density is the most commonly measured property of a gas, and is obtained experimentally by measuring the specific gravity of the gas (density of the gas relative to air = 1). As pressure increases, so does gas density, but the relationship is non-linear since the dimensionless gas compressibility (z-factor) also varies with pressure. The gas density (pg) can be calculated at any pressure and temperature using the real gas law ... [Pg.107]

The flowrate of oil into the wellbore is also influenced by the reservoir properties of permeability (k) and reservoir thickness (h), by the oil properties viscosity (p) and formation volume factor (BJ and by any change in the resistance to flow near the wellbore which is represented by the dimensionless term called skin (S). For semisteady state f/owbehaviour (when the effect of the producing well is seen at all boundaries of the reservoir) the radial inflow for oil into a vertical wellbore is represented by the equation ... [Pg.216]

Fig.5 shows the relation of the echo height F/B to the thickness of the insert metal made dimensionless (/X. X is wave length of the material for an incidence of... [Pg.835]

Fig.5 Relation of echo height F/ to dimensionless thickness of insert metal H X... Fig.5 Relation of echo height F/ to dimensionless thickness of insert metal H X...
Harkins and Brown [21] concluded that / should be a function of the dimensionless ratio rja or, alternatively, of where V is the drop volume. (See... [Pg.20]

Harkins and Jordan [43] found, however, that Eq. 11-26 was generally in serious error and worked out an empirical correction factor in much the same way as was done for the drop weight method. Here, however, there is one additional variable so that the correction factor/ now depends on two dimensionless ratios. Thus... [Pg.21]

Molecular dynamics and density functional theory studies (see Section IX-2) of the Lennard-Jones 6-12 system determine the interfacial tension for the solid-liquid and solid-vapor interfaces [47-49]. The dimensionless interfacial tension ya /kT, where a is the Lennard-Jones molecular size, increases from about 0.83 for the solid-liquid interface to 2.38 for the solid-vapor at the triple point [49], reflecting the large energy associated with a solid-vapor interface. [Pg.267]

The potential has a spurious maximum at r where the r ° tenn again starts to dominate. The dimensionless parameter a is a measure of the steepness of the repulsion and is often assigned a value of 14 or 15. The ideas... [Pg.205]

A cautionary word about units equilibriuin constants are usually expressed in nnits, because pressures and concentrations have nnits. Yet the argument of a logaritlnn must be dimensionless, so the activities in eqnation (A2.1.66). defined in tenns of the absolute activities (which are dimensionless) are dimensionless. [Pg.365]

Figure A2.2.1. Heat capacity of a two-state system as a function of the dimensionless temperature, lc T/([iH). From the partition fimction, one also finds the Helmholtz free energy as... Figure A2.2.1. Heat capacity of a two-state system as a function of the dimensionless temperature, lc T/([iH). From the partition fimction, one also finds the Helmholtz free energy as...
Figure A2.2.3. Planck spectral density fimction as a fimction of the dimensionless frequency /)oi/(/rj 7). A2.2.4.7 APPLICATION TO IDEAL SYSTEMS ELASTIC WAVES IN A SOLID... Figure A2.2.3. Planck spectral density fimction as a fimction of the dimensionless frequency /)oi/(/rj 7). A2.2.4.7 APPLICATION TO IDEAL SYSTEMS ELASTIC WAVES IN A SOLID...
The upper limit of the dimensionless variable Vp, is typically written in tenns of the Debye temperature 9, as... [Pg.413]

Figure A2.5.2. Schematic representation of the behaviour of several thennodynamic fiinctions as a fiinction of temperature T at constant pressure for the one-component substance shown in figure A2.5.1. (The constant-pressure path is shown as a dotted line in figure A2.5.1.) (a) The molar Gibbs free energy Ci, (b) the molar enthalpy n, and (c) the molar heat capacity at constant pressure The fimctions shown are dimensionless... Figure A2.5.2. Schematic representation of the behaviour of several thennodynamic fiinctions as a fiinction of temperature T at constant pressure for the one-component substance shown in figure A2.5.1. (The constant-pressure path is shown as a dotted line in figure A2.5.1.) (a) The molar Gibbs free energy Ci, (b) the molar enthalpy n, and (c) the molar heat capacity at constant pressure The fimctions shown are dimensionless...
Figure A2.5.4. Themiodynamic fimctions (i, n, and C as a fimction of temperature T at eonstant pressure and eomposition x = 1/2) for the two-eomponent system shown in figure A2.5.3. Note the diflferenee between these and those shown for the one-eomponent system shown in figure A2.5.2. The fiinetions shown are dimensionless as in figure A2.5.2. The dashed lines represent metastable extensions (superheating or supereooling) of the one-phase systems. Figure A2.5.4. Themiodynamic fimctions (i, n, and C as a fimction of temperature T at eonstant pressure and eomposition x = 1/2) for the two-eomponent system shown in figure A2.5.3. Note the diflferenee between these and those shown for the one-eomponent system shown in figure A2.5.2. The fiinetions shown are dimensionless as in figure A2.5.2. The dashed lines represent metastable extensions (superheating or supereooling) of the one-phase systems.
For deep quenches, where the post-quench T is far below T, the equations are conveniently written in temis of scaled (dimensionless) variables t) = mid x... [Pg.738]

As is evident from the fomi of the square gradient temi in the free energy fiinctional, equation (A3.3.52). k is like the square of the effective range of interaction. Thus, the dimensionless crossover time depends only weakly on the range of interaction as In (k). For polymer chains of length A, k A. Thus for practical purposes, the dimensionless crossover time is not very different for polymeric systems as compared to the small molecule case. On the other hand, the scaling of to is tln-ough a characteristic time which itself increases linearly with k, and one has... [Pg.740]

Equation (A3.13.17) is a simple, usefiil fomuila relating the integrated cross section and the electric dipole transition moment as dimensionless quantities, in the electric dipole approximation [10, 100] ... [Pg.1048]

Flere, A and B are regarded as pool chemicals , with concentrations regarded as imposed constants. The concentrations of the intemiediate species X and Y are the variables, with D and E being product species whose concentrations do not influence the reaction rates. The reaction rate equations for [X] and [Y] can be written in the following dimensionless fomi ... [Pg.1113]

A related measure of the intensity often used for electronic spectroscopy is the oscillator strengdi,/ This is a dimensionless ratio of the transition intensity to tliat expected for an electron bound by Hooke s law forces so as to be an isotropic hanuonic oscillator. It can be related either to the experimental integrated intensity or to the theoretical transition moment integral ... [Pg.1126]

Note that ( ), ) p( )d E is dimensionless for all cases and yields unity for a single particle when... [Pg.2014]


See other pages where Dimensionless is mentioned: [Pg.14]    [Pg.835]    [Pg.13]    [Pg.14]    [Pg.14]    [Pg.16]    [Pg.27]    [Pg.171]    [Pg.362]    [Pg.41]    [Pg.194]    [Pg.205]    [Pg.365]    [Pg.593]    [Pg.653]    [Pg.738]    [Pg.738]    [Pg.739]    [Pg.740]    [Pg.746]    [Pg.783]    [Pg.851]    [Pg.1103]    [Pg.1114]    [Pg.1114]    [Pg.1415]    [Pg.1548]    [Pg.1932]    [Pg.2022]   
See also in sourсe #XX -- [ Pg.89 ]

See also in sourсe #XX -- [ Pg.153 , Pg.194 ]

See also in sourсe #XX -- [ Pg.89 ]

See also in sourсe #XX -- [ Pg.459 ]

See also in sourсe #XX -- [ Pg.93 ]

See also in sourсe #XX -- [ Pg.518 , Pg.521 ]

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A Dimensionless Number

Activation energy dimensionless

Activity coefficient, dimensionless

Activity dimensionless

Adiabatic temperature dimensionless

Adsorbent dimensionless temperature

Adsorption/desorption equilibrium constant dimensionless

Approach critical dimensionless parameters

BATCHD - Dimensionless Kinetics in a Batch Reactor

Balance in Dimensionless Variables

Batch reactor dimensionless

Boundary conditions dimensionless

Boundary layer thickness dimensionless

Butler-Volmer equation dimensionless

Capillary Rise and Dimensionless Numbers

Characteristic Dimensionless Numbers for Reactor Design

Characteristic dimensionless

Characteristic dimensionless parameters

Characteristics absolute dimensionless characteristic

Column dimensionless parameters

Conventions activity dimensionless

Correlation for Problems with More than Two Dimensionless Groups

Correlation for Problems with Two Dimensionless Groups

Crystallization dimensionless nucleation

Crystallizer dimensionless nucleation

Determining heat transfer coefficients. Dimensionless numbers

Diffusion dimensionless

Diffusion dimensionless form

Diffusion dimensionless groups

Diffusion dimensionless time

Diffusion equation dimensionless

Diffusivity Dimensionless numbers

Diffusivity Dimensionless time

Digital simulations dimensionless parameters

Dimensional Homogeneity and Dimensionless Quantities

Dimensional analysis and dimensionless

Dimensional analysis dimensionless numbers

Dimensional analysis relationships between dimensionless

Dimensionless (Nondimensional) Numbers and Their Importance in Process Engineering

Dimensionless Coordinates

Dimensionless Croups

Dimensionless Design Equations and Operating Curves

Dimensionless Equations for Heat Transfer

Dimensionless Extents

Dimensionless Fanning friction factor

Dimensionless Form of the Generalized Mass Transfer Equation with Unsteady-State Convection, Diffusion, and Chemical Reaction

Dimensionless Formulation of Kinetic Equations

Dimensionless Group Model

Dimensionless Groups Used to Plot Rheological Data

Dimensionless Groups and Their Relationships

Dimensionless Groups from the Conservation Equations

Dimensionless Groups in Chemical Engineering

Dimensionless Henry constant

Dimensionless Mathematical Model

Dimensionless Mechanical Energy Balance

Dimensionless Relative Variables

Dimensionless Reynolds

Dimensionless Scale-up of Equipment

Dimensionless Size Spectra Evolution

Dimensionless Variables and Numbers

Dimensionless absorption

Dimensionless absorption functions

Dimensionless absorption rotary elasticity

Dimensionless analysis

Dimensionless capacitance measurement

Dimensionless characterisation of viscoelastic flows

Dimensionless characteristic number

Dimensionless concentration

Dimensionless concentration gradient, Sherwood number

Dimensionless concentration variables

Dimensionless concentrations first-order kinetics

Dimensionless concentrations second-order kinetics

Dimensionless constants

Dimensionless correlations

Dimensionless coupling

Dimensionless coupling parameters

Dimensionless criterion

Dimensionless cumulative distributions

Dimensionless curvature

Dimensionless deformation time

Dimensionless diffusion flux

Dimensionless double layer thickness

Dimensionless duration

Dimensionless electron spin vector

Dimensionless equation

Dimensionless equation of motion

Dimensionless equation of state

Dimensionless equations, external mass transfer resistance

Dimensionless exchange

Dimensionless factors in a solution

Dimensionless figure of merit

Dimensionless flow rate

Dimensionless flux

Dimensionless form

Dimensionless form Navier-Stokes equations

Dimensionless form boundary conditions

Dimensionless form for

Dimensionless form heat transfer equation

Dimensionless form mass transfer equation

Dimensionless form, reduction

Dimensionless frequency

Dimensionless group

Dimensionless group 536 INDEX

Dimensionless group correlations

Dimensionless group model, hydrocyclones

Dimensionless groups Arrhenius group

Dimensionless groups Bond number

Dimensionless groups Deborah Number

Dimensionless groups Grashof number

Dimensionless groups Peclet Number

Dimensionless groups Prandtl numbers

Dimensionless groups Rayleigh number

Dimensionless groups Reynolds Number

Dimensionless groups Schmidt number

Dimensionless groups Weber number

Dimensionless groups capillary number

Dimensionless groups equations

Dimensionless groups for heat transfer

Dimensionless groups for mixing

Dimensionless groups heat transfer

Dimensionless groups interpretation

Dimensionless groups mixing

Dimensionless groups named

Dimensionless groups of quantities

Dimensionless groups relevant

Dimensionless groups rotary

Dimensionless groups table

Dimensionless groups tension

Dimensionless groups, relations

Dimensionless impinging distance

Dimensionless interaction energy

Dimensionless interface

Dimensionless internal coordinate

Dimensionless kinetic rate law

Dimensionless kinetics

Dimensionless limiting cases

Dimensionless limiting current

Dimensionless loss modulus

Dimensionless manifolds

Dimensionless mass transfer correlation

Dimensionless mass transfer equation

Dimensionless mean velocity, comparison

Dimensionless mechanical energy balanc

Dimensionless model

Dimensionless model equations

Dimensionless moderator

Dimensionless normal coordinates

Dimensionless number Archimedes

Dimensionless number Damkohler

Dimensionless number Eotvos

Dimensionless number Euler

Dimensionless number Knudsen

Dimensionless number Lewis

Dimensionless number Morton

Dimensionless number Schmidt

Dimensionless number Sherwood

Dimensionless number Stokes

Dimensionless number equation

Dimensionless numbers

Dimensionless numbers Bond number

Dimensionless numbers Brinkman

Dimensionless numbers Brinkman number

Dimensionless numbers Capillary number

Dimensionless numbers Froude

Dimensionless numbers Graetz

Dimensionless numbers Grashof

Dimensionless numbers Nusselt

Dimensionless numbers Peclet

Dimensionless numbers Prandtl

Dimensionless numbers Rayleigh

Dimensionless numbers Reynolds

Dimensionless numbers Reynolds number

Dimensionless numbers Schmidt number

Dimensionless numbers Stanton

Dimensionless numbers Weber

Dimensionless numbers method

Dimensionless numbers turbulent

Dimensionless numbers, definitions

Dimensionless numbers, from similarity

Dimensionless numbers, from similarity analysis

Dimensionless numbers, physical

Dimensionless numbers, physical interpretation

Dimensionless numbers, table listing

Dimensionless parameter, crossover

Dimensionless parameters

Dimensionless parameters for HPLC column characterization

Dimensionless parameters phase shifts

Dimensionless particle volume fraction

Dimensionless pressure

Dimensionless property

Dimensionless quantity

Dimensionless rate constant

Dimensionless rate constant, heterogeneous electron transfer

Dimensionless reaction time

Dimensionless real modulus

Dimensionless reduced

Dimensionless reduced energy

Dimensionless reduced surface parameter

Dimensionless relaxation rate

Dimensionless representation of material functions

Dimensionless scattering intensity

Dimensionless sensitivity

Dimensionless shape parameter

Dimensionless shear rate

Dimensionless solute concentration

Dimensionless spin

Dimensionless state

Dimensionless subsidence time

Dimensionless sweep rate

Dimensionless tension

Dimensionless terms

Dimensionless throughput

Dimensionless time, pressurization

Dimensionless transient response curves

Dimensionless units

Dimensionless variables

Dimensionless variables Subject

Dimensionless variables, definition

Dimensionless variables, renormalized

Dimensionless virial coefficients

Dimensionless viscosity

Dimensionless volumetric flow rate

Dimensionless wavenumber

Disperse systems dimensionless diameter

Energy balance expressions dimensionless

Energy dimensionless

Energy dimensionless unit

Equation dimensionless forms

Establishment of the Dimensionless Numbers

Evaporation dimensionless groups

Finding the Dimensionless Numbers

Flow resistance dimensionless

Fluid dynamics, dimensionless groups

Fluid mechanics dimensionless flows

Fluid mechanics, dimensionless numbers

Fractionation models dimensionless parameter

General design equations. Dimensionless groups

Heat dimensionless

Heat flux local dimensionless

Heat flux total dimensionless

Heat transfer dimensionless

Heat transfer dimensionless group correlation

Heat transfer parameter, dimensionless

Heterogeneous rate constant dimensionless

Hydrodynamics dimensionless analysis

Important Dimensionless Numbers

Liquid film thickness, dimensionless

Liquid load dimensionless

Mass dimensionless

Mass transfer boundary layer thickness dimensionless

Mass transfer dimensionless groups

Material function dimensionless representation

Mathematical Modeling Dimensionless Numbers Governing Electrochemical Promotion and Metal-Support Interactions

Mechanical dimensionless

Mixers dimensionless groups

Molar solubility dimensionless

Natural-convection dimensionless

Natural-convection dimensionless groups

Nernst equation dimensionless

Nondimensionalization dimensionless parameters

Normalization dimensionless

Nucleation dimensionless time

One Dimensionless Group Problem

Packed beds dimensionless variables

Particle-size distribution dimensionless

Pellets dimensionless form

Physical Interpretation of the Dimensionless Numbers

Population-balance equation dimensionless

Potential dimensionless

Pressure drop dimensionless

Process Evaluation by Dimensionless Numbers

Pumps dimensionless groups

Pumps performance, dimensionless

Radial velocity profile, dimensionless

Rates dimensionless

Reaction number, dimensionless

Reactor characteristic dimensionless number

Reactor design equation Dimensionless forms

Relating the Dimensionless Simulation Parameters to Physical Values

Residence time dimensionless

Reynolds number dimensionless parameters

Scale dimensionless groups

Scale-model experiments dimensionless numbers

Scaling analysis dimensionless groups

Scaling and Dimensionless Groups

Scaling and the Dimensionless Parameters for Convective Heat Transfer

Scaling number, dimensionless

Semi-dimensionless form

Set of governing dimensionless expressions for the reactive flash

Similarity Hypothesis, Dimensional Analysis, and Dimensionless Numbers

Solid conductivity, dimensionless

Some Dimensionless Parameters

Superficial velocity dimensionless

Surface potentials dimensionless

Temperature, dimensionless

Temperature, dimensionless INDEX

The Nernst diffusion layer and dimensionless variables

Three dimensionless parameters

Time dimensionless

Time, dimensionless, various stages

Transfer dimensionless

Transport dimensionless

Use of Dimensionless Groups in Scale-Up

Use of Dimensionless Variables

Using Dimensionless Criteria

Virial dimensionless

Weber number dimensionless measure

Weber number dimensionless parameters

Writing the Equation in Dimensionless Form

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