Velocity flow profile

It should be emphasized that these results are applicable only to fully developed flow. However, if the fluid enters a pipe with a uniform ( plug ) velocity distribution, a minimum hydrodynamic entry length (Lc) is required for the parabolic velocity flow profile to develop and the pressure gradient to become uniform. It can be shown that this (dimensionless) hydrodynamic entry length is approximately Le/D = 7VRe/20. 

The "plug-like velocity flow profile for electrokinetically pumped capillary columns (see Figure 1) is important in minimizing resistance to mass transfer within the mobile phase (4). Hydrostatically-pumped capillaries, have parabolic flow profiles which tend to severely disperse solute bands unless extreme narrow-bore (i.d.s less than 10 pm) capillaries are employed (12). Fortunately, larger capillaries, with less stringent detector volume requirements, can be efficiently used in MECC. 

Figure S3. Velocity flow profile in a tube for a fluid with zero yield stress and assuming no slip at...

A broader study compared the effect of different surface chemistry and roughness on water flow (and thus wettability) in a CNT, a boron nitride nanotube (BNNT), a silicon nanotube, and a roughened nanotube. Figure 10.5 expresses the axial velocity profiles of each nanotube. The simulations found that there was a plug-like velocity flow profile with a "jump" in velocity at the solid-... 

Figure 20 Instantaneous particle velocity flow profile for basic case study.

When a sample is injected into the carrier stream it has the rectangular flow profile (of width w) shown in Figure 13.17a. As the sample is carried through the mixing and reaction zone, the width of the flow profile increases as the sample disperses into the carrier stream. Dispersion results from two processes convection due to the flow of the carrier stream and diffusion due to a concentration gradient between the sample and the carrier stream. Convection of the sample occurs by laminar flow, in which the linear velocity of the sample at the tube s walls is zero, while the sample at the center of the tube moves with a linear velocity twice that of the carrier stream. The result is the parabolic flow profile shown in Figure 13.7b. Convection is the primary means of dispersion in the first 100 ms following the sample s injection. 

Fig. 1. Flow profiles, where N is velocity (a) laminar, and (b) turbulent for fluids having Reynolds numbers of A, 2 x 10, and B, 2 x 10 .

Doppler Flow Meters. Doppler flow meters sense the shift in apparent frequency of an ultrasonic beam as it is reflected from air bubbles or other acoustically reflective particles that ate moving in a Hquid flow. It is essential for operation that at least some particles ate present, but the concentration can be low and the particles as small as ca 40 p.m. CaUbration tends to be influenced by particle concentration because higher concentrations result in mote reflections taking place neat the wall, in the low velocity portion of the flow profile. One method used to minimize this effect is to have separate transmitting and receiving transducers focused to receive reflections from an intercept zone neat the center of the pipe. 

The graphical integration method is based on graphical presentation of the average flow profile. For a circular duct, the cross-section is virtually divided into several concentric ring elements. The spatial mean velocity of such an element is determined as an arithmetical mean of local velocities along the circumference of the corresponding radius. For a circular cross-section the flow rate can be expressed as... 

The flow profiles of electrodriven and pressure driven separations are illustrated in Figure 9.2. Electroosmotic flow, since it originates near the capillary walls, is characterized by a flat flow profile. A laminar profile is observed in pressure-driven systems. In pressure-driven flow systems, the highest velocities are reached in the center of the flow channels, while the lowest velocities are attained near the column walls. Since a zone of analyte-distributing events across the flow conduit has different velocities across a laminar profile, band broadening results as the analyte zone is transferred through the conduit. The flat electroosmotic flow profile created in electrodriven separations is a principal advantage of capillary electrophoretic techniques and results in extremely efficient separations. 

For laminar flow in channels of rectangular cross-section, the velocity profile can be determined analytically. For this purpose, incompressible flow as described by Fq. (16) is assumed. The flow profile can be expressed in form of a series expansion (see [100] and references therein), which, however, is not always useful for practical applications where often only a fair approximation of the velocity field over the channel cross-section is needed. Purday [101] suggested an approximate solution of the form... 

Under chromatographic conditions, the flow profile Is usually laminar and therefore the mobile phase velocity can be described by Darcy s law... 

M. Nakagawa, S.A. Altobelli, A. Caprihan, E. Fukushima 1997, (NMR measurement and approximate derivation of the velocity depth-profile of granular flow in a rotating, partially filled, horizontal cylinder), in Powders and Grains 97, Proceedings of the Third International Conference on Powders el Grains, eds. 

Figure 5.3.5 displays dynamic NMR microscopy of xenon gas phase Poiseuille flow with an average velocity of 25 mm s-1 and self-diffusion coefficient of 4.5 mm2 s-1 at 130 kPa xenon gas pressure with numerical simulation (A) and experimental flow profiles (B-D) of xenon gas. 

FIGURE 11.32 Flow profiles in microchannels, (a) A pressure gradient, - AP, along a channel generates a parabolic or Poiseuille flow profile in the channel. The velocity of the flow varies across the entire cross-sectional area of the channel. On the right is an experimental measurement of the distortion of a volume of fluid in a Poiseuille flow. The frames show the state of the volume of fluid 0, 66, and 165 ms after the creation of a fluorescent molecule, (b) In electroosmotic flow in a channel, motion is induced by an applied electric field E. The flow speed only varies within the so-called Debye screening layer, of thickness D. On the right is an experimental measurement of the distortion of a volume of fluid in an electroosmotic flow. The frames show the state of the fluorescent volume of fluid 0, 66, and 165 ms after the creation of a fluorescent molecule [165], Source http //www.niherst.gov.tt/scipop/sci-bits/microfluidics.htm (see Plate 12 for color version). 

Thus the turbulent flow velocity profile is flatter than the corresponding laminar flow profile, as shown in Figure 1.24. 

The topic of concern here is the stability of laminar flames fixed to burner tubes. The flow profile of the premixed gases flowing up the tube in such a system must be parabolic that is, Poiseuille flow exists. The gas velocity along any streamline is given by... 

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