Control volumes for

Fig. 21. Control volumes for appHcation of the integral equations of motion where 1, 2, and 3 are the location of control surfaces and Sy (a) general,...

Figure 2.11 Control volume for compressible porous media...

Applying the conservation of momentum to the control volume for a onedimensional flow conduit, it is found that [62]... 

FIGURE 1.1 Control volume for total mass balance. 

Figure 34. Control volume for performing a number balance on granules. (From Litster and Ennis, 1994.)...

Figure 19.15 Control volume for continuity equation for axial dispersion model...

Figure 23.7 Schematic representation of control volume for material balance for bubbling-bed reactor model...

Figure 3.4 Illustration of a fixed control volume for pipe flow and a system...

It is necessary first to define the region or control volume for which the momentum equation is to be written. In this example, it is convenient to select the fluid within the nozzle as that control volume. The control volume is defined by drawing a control surface over the inner surface of the nozzle and across the flow section at the nozzle inlet and the outlet. In this way, the nozzle itself is excluded from the control volume and external forces acting on the body of the nozzle, such as atmospheric pressure, are not involved in the momentum equation. This interior control surface is shown in Figure 1.9(a). 

We will use the rectangular control volume for the development of our mass conservation (diffusion) equation. 

When considering the mass continuity of an individual species in a multicomponent mixture, there can be, and typically is, diffusive transport across the control surfaces and the production or destruction of an individual species by volumetric chemical reaction. Despite the fact that individual species may be transported diffusively across a surface, there can be no net mass that is transported across a surface by diffusion alone. Moreover homogeneous chemical reaction cannot alter the net mass in a control volume. For these reasons the overall mass continuity need not consider the individual species. At the conclusion of this section it is shown that that the overall mass continuity equation can be derived by a summation of all the individual species continuity equations. 

Fig. 4.3 A finite-volume control volume for the radial Couette-Poiseuille problem. Surface shear stresses, normal pressure, and heat fluxes are illustrated with arrows indicating in their positive directions.

Fig. 4.6 Force balance on a differential control volume for Hagen-Poiseuille flow in a circular tube.

Fig. 9.7 Thermodynamic analysis of an SOFC. CV represents the control volume for the analysis.

Figure 5.4. Determination of minimum radius of control volume for two different control volume centers (a) Effect of control volume on calculated particle volume fraction (b) Effect of control volume on relative deviation of calculated particle volume fraction.

FIGURE 7 Control volume for analysis of countercurrent differential contractor. 

When the fluid flows through a porous medium, the -.olid particles exert a force on the fluid equal and opposite to the drag force on the solid particles. This force must be balanced by the pressure gradient in the flow. i.e for flow through a control volume for any chosen direction ... 

Figure 22. Control volume for differential balance for component i in the recirculation zone of a circulating fluidized-bed reactor (adapted from Ref. 112).

The differential equations to describe the recirculation zone arc derived from mass balances. The control volume for identification of the different terms of these equations is depicted in Fig. 22. Simplifying assumptions for this approach are ... 

Fig. 5-4 Elemental control volume for force balance on laminar boundary layer.

Fig. 5-5 Elemental control volume for integral momentum analysis of laminar boundary layer.

Control volume for integral energy analysis of laminar boundary flow... 

Fig. 5-13 Control volume for energy analysis in tube flow.

Disregarding the kinetic and potential energy effects, the energy balance over the control volume for a steady-state operation is... 

This expression is derived by considering a control volume (for example, unit volume) in the material through which the sound is propagating. The total acoustic... 

FIGURE 1.1. Control volume for the derivation of interface conditions. 

The MHP is divided into several control volumes for which the conservation of mass, momentum and energy equations are written for the liquid and vapour phases. The numerical model was developed in [24-25] considering the counter current flows of vapour and liquid in microchannel. These conservation equations can be written as... 

FIGURE 1-3 a Examples of useful control volumes for three principal environmental media. Control volume (a) would be practical if we were studying the various processes that remove a contaminant from a river the difference between the input and output fluxes would represent internal sinks in the river or volatilization loss to the air (Figure continues). 

FIGURE 2-23 Definition of the control volume for which the DO mass balance is expressed in Eq. [2-62], The control volume is a slice of thickness Ax and cross-sectional area A and is stationary in the river. 

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