Cross section length

For axial capillary flow in the z direction the Reynolds number, Re = vzmaxI/v = inertial force/viscous force , characterizes the flow in terms of the kinematic viscosity v the average axial velocity, vzmax, and capillary cross sectional length scale l by indicating the magnitude of the inertial terms on the left-hand side of Eq. (5.1.5). In capillary systems for Re < 2000, flow is laminar, only the axial component of the velocity vector is present and the velocity is rectilinear, i.e., depends only on the cross sectional coordinates not the axial position, v= [0,0, vz(x,y). In turbulent flow with Re > 2000 or flows which exhibit hydrodynamic instabilities, the non-linear inertial term generates complexity in the flow such that in a steady state v= [vx(x,y,z), vy(x,y,z), vz(x,y,z). ... 

Figure 2. Effect of cross-section length on crystallinity index (------------) and on...

According to Cavalieri s law, the volume fraction of an object may be deduced analyzing cross-sections, lengths or points ... 

Computational constraints impose spatial and temporal limitations on simulated systems. The number of atoms considered is typically in the 10 -10 range. The corresponding cross-sectional length of the interface varies between 2 and 4 nm and each lamella is 2 to 5 nm wide. For the aqueous phase, this is equivalent to approximately 7-18 water diameters. The spatial extent of the system is primarily limited by the rapidly growing number of intermolecular interactions. In the pairwise additive approximation, this number is N x (N — l)/2, where N is the number of atoms in the system. In practice, pair interactions of an atom with other atoms are usually truncated spherically. The largest possible truncation distance is half the shortest box edge. 

In empty space a cylindrical sheet of current of any cross section and very longer than it s diameter, material by a long solenoid of length 1 with N single turn traversed by an current I. 

Now integrate the equation (5) taking into account the formulae for pi and pN. As a result we arrive to the specific volume flow rate in a film, referred to the unit of length for cross section ... 

Use now this equation to describe liquid film flow in conical capillary. Let us pass to spherical coordinate system with the origin coinciding with conical channel s top (fig. 3). It means that instead of longitudinal coordinate z we shall use radial one r. Using (6) we can derive the total flow rate Q, multiplying specific flow rate by the length of cross section ... 

Derive, from simple considerations, the capillary rise between two parallel plates of infinite length inclined at an angle of d to each other, and meeting at the liquid surface, as illustrated in Fig. 11-23. Assume zero contact angle and a circular cross section for the meniscus. Remember that the area of the liquid surface changes with its position. 

Let the rate of the event under study be R. It will be proportional to the cross section for the process under study, a, the incident electron current, Iq, the target density, n, the length of the target viewed by the detectors,, the solid angles subtended by the detectors, Aoi and A012 the efficiency of the detectors, and... 

Finally we require a case in which mechanism (lii) above dominates momentum transfer. In flow along a cylindrical tube, mechanism (i) is certainly insignificant compared with mechanism (iii) when the tube diameter is large compared with mean free path lengths, and mechanism (ii) can be eliminated completely by limiting attention to the flow of a pure substance. We then have the classical Poiseuille [13] problem, and for a tube of circular cross-section solution of the viscous flow equations gives 2... 

Electric current ampere A Magnitude of the current that, when flowing through each of two straight parallel conductors of infinite length, of negligible cross-section, separated by 1 meter in a vacuum, results in a force between the two wires of 2 X 10 newton per meter of length. 

We will consider first the case of rods of length I and of square cross-section, the square having ades of length d (Fig. 1.16(b)). Let the ratio l d be denoted by y i.e. 

Next we recognize that 6 and X always appear as a ratio in our theory. If we argue that the hole and the polymer chain have comparable cross-sectional areas, we can multiply both the numerator and denominator of the X/6 ratio by this cross section and convert it into the ratio V /V, where is the volume of the flow segment of length X. While we know neither of these volumes directly, there are indications that V /V may be on the order of 10-20 for many linear... 

A steady-state material balance can be carried out on a small section of length and volume (on the basis of unit cross-sectional area) ia the contactor ... 

It is difficult to determine the cross-sectional area of a fiber. Direct observation and measurement of a cross section under a microscope is the most accurate method (15). This is a destmctive test that does not allow subsequent study of fiber mechanical properties, and is slow and tedious. Also, it does not take into account any variations in the cross-sectional area along the fiber length. Measurement of fiber diameters from microscopic observations of longitudinal views is somewhat easier, but the eUipticity of the cross section in certain fibers can lead to serious errors. 

---