Continuity relation

Continuity relation The mass flow rate in unit time is the product of the density multiplied by the volume flow in unit time. 

Dividing both sides of the equation by A Ax At and taking the limit yields the continuity relation... 

How does the equation of continuity relate flow rate of a fluid to the size of the tube through which it flows ... 

But with MCS you simply can t continue relations with people when they show such a lack of understanding, empathy and will to make the necessary changes. With this condition it s simply impossible to pretend it doesn t exist, no matter how much we all wish it were so ... 

The density of water at 20°C is 1000 kg/m3, and so we may calculate the velocities from the mass-continuity relation... 

Clearing terms, making use of the continuity relation (5-12) and neglecting second-order differentials, gives... 

Chapter 1 serves to remind readers of the basic continuity relations for mass, momentum, and energy. Mass transfer fluxes and reference velocity frames are discussed here. Chapter 2 introduces the Maxwell-Stefan relations and, in many ways, is the cornerstone of the theoretical developments in this book. Chapter 2 includes (in Section 2.4) an introductory treatment of diffusion in electrolyte systems. The reader is referred to a dedicated text (e.g., Newman, 1991) for further reading. Chapter 3 introduces the familiar Fick s law for binary mixtures and generalizes it for multicomponent systems. The short section on transformations between fluxes in Section 1.2.1 is needed only to accompany the material in Section 3.2.2. Chapter 2 (The Maxwell-Stefan relations) and Chapter 3 (Fick s laws) can be presented in reverse order if this suits the tastes of the instructor. The material on irreversible thermodynamics in Section 2.3 could be omitted from a short introductory course or postponed until it is required for the treatment of diffusion in electrolyte systems (Section 2.4) and for the development of constitutive relations for simultaneous heat and mass transfer (Section 11.2). The section on irreversible thermodynamics in Chapter 3 should be studied in conjunction with the application of multicomponent diffusion theory in Section 5.6. 

The SPR can be simply formalized, in a first approach, by solving Laplace s equation in tlie case of a single conducting sphere surrounded by a homogeneous transparent medium, with tlie appropriate continuity relations at the metal-dielectric interface and assuming tliat the sphere radius is much lower than the wavelength (quasistatic approximation). The homogeneous local electric field inside the particle, E, then writes... 

The principal assumption required to link the angular momentum equation (7.19) and the continuity relation (7.20) is that the flow exiting the impeller is tangential to the blade attachment. Although this is not absolutely correct, it does make a reasonable first approximation [65] ... 

Using the continuity relation (7.20), the radial component of the velocity can be expressed as a function of the impeller flow number ... 

The velocity field in these flows is governed by the incompressible Navier-Stokes equation (1.385) and the corresponding continuity relation (1.382). For incompressible fluids a generic transport equation for scalar species mass concentration fields can be deduced from (1.454) and expressed as ... 

TABLE 10.12 Continued Relations among Species Concentrations in EQOUT — ... 

If the continuity relation (4.2) is integrated with respect to z across the gap between the disks, making use of the boundary conditions on U , the result is... 

For most real (viscous) flow.s, U f (ai + 1)" in the region near the stagnation point because of the no-slip boundary condition and the continuity relation. In this case, (4.29) does not apply, the equation of particle motion cannot be put into the form of (4,30), and the analysis developed above is not valid. Instead, numerical calculations for the viscous flow regime ( / (x i + 1) ) indicate that the collection efficiency is finite for all nonzero values of Stk, vanishing for Stk -> 0 (Ingham et al., 1990). 

Transport-Limited Growth 285 Aerosol Phase, Reaction-Limited Growth 286 Dynamics Of Growth Continuity Relation in v Space 288... 

Systems not m equilibrium (continued)—Relation between the affinity and the heat of a reaction—Nernst s heat theorem and some of its applications... 

The mass flow continuity relation between the gas phase and solid is... 

The continuity relation (4.7) can be written, since the density is constant, as... 

To complete the analysis, one applies the continuity relation to the flux equation of the form given by Equation (134) or Equation (135), to obtain an equation where the factor time appears explicitly, i.e. the equivalent of Pick s second law of diffusion. For example, specifically for the case of water treated above (Zhang et al. 1991b) ... 

Equation (3-31) relates the interfacial concentrations to each other. So, it is valid only at that point on the equilibrium-distribution curve which represents the local interfacial compositions. For the purpose of locating that point, rewrite equation (3-31) as a continuous relation between the variables in the equilibrium-distribution diagram, namely xA and yA ... 

We can now use the continuity relation (Eq. 10.5.9) together with the above equation to obtain the variation in surface tension gradient with the gradient in free surface height ... 

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