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The closed surface enclosing the region is referred to as the control surface. [1] At steady state, a control volume can be thought of as an arbitrary volume in which the mass of the continuum remains constant. As a continuum moves through the control volume, the mass entering the control volume is equal to the mass leaving the control volume.
Control volume and control volume & boundary faces (Figure 2) Create control volumes near the edges in such a way that the physical boundaries coincide with control volume boundaries (Figure 1). Assume a general nodal point 'P' for a general control volume. Adjacent nodal points to the East and West are identified by E and W respectively.
1. Divide the domain into discrete control volume. 2. Place the nodal point between end points defining the physical boundaries. Boundaries/ faces of the control volume are created midway between adjacent nodes. 3. Set up the control volume near the edge of domain such that physical as well as control volume boundaries will coincide with each ...
As an effectively 1-D model, the flow into and out of the disk is axial, and all velocities are transversely uniform. This is a control-volume analysis; the control volume must contain all incoming and outgoing flow in order to use the conservation equations. The flow is non-compressible. Density is constant, and there is no heat transfer.
Specific volume is the volume occupied by a unit of mass of a material. [1] In many cases, the specific volume is a useful quantity to determine because, as an intensive property, it can be used to determine the complete state of a system in conjunction with another independent intensive variable. The specific volume also allows systems to be ...
In addition to the east (E) and west (W) neighbors, a general grid node P, now also has north (N) and south (S) neighbors. The same notation is used here for all faces and cell dimensions as in one dimensional analysis. When the above equation is formally integrated over the Control volume, we obtain
According to van der Waals, the theorem of corresponding states (or principle/law of corresponding states) indicates that all fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor and all deviate from ideal gas behavior to about the same degree.
Fig. 1. Manifold arrangement for flow distribution. Traditionally, most of theoretical models are based on Bernoulli equation after taking the frictional losses into account using a control volume (Fig. 2). The frictional loss is described using the Darcy–Weisbach equation. One obtains a governing equation of dividing flow as follows: Fig. 2.