Velocity maximum

The solution flow is nomially maintained under laminar conditions and the velocity profile across the chaimel is therefore parabolic with a maximum velocity occurring at the chaimel centre. Thanks to the well defined hydrodynamic flow regime and to the accurately detemiinable dimensions of the cell, the system lends itself well to theoretical modelling. The convective-diffiision equation for mass transport within the rectangular duct may be described by... 

In time-of-flight (TOF) mass spectrometers, a pulse of ions is accelerated electrically at zero time. Having attained a maximum velocity, the ions drift along the flight tube of the analyzer. The times of arrival of ions at a detector are noted. 

Figure 5 shows the variation of the droplet mean axial velocity at the same axial location. The primary feature of this velocity profile is that the maximum velocity peaks at the centerline. The velocity magnitude and direction in the center region tend to be related to the hquid swid strength and axial distance. A reverse (recirculation) flow with negative velocity is possible if the swid is intense. Under such conditions, the maximum velocity tends to shift away from the centerline. 

Surface area, mVg Temperature, °C Residence time, s Maximum velocity, m/s... 

The maximum velocity at the axis is twice the average, whereas the velocity at the wall is zero. The effect of the burner wall is to cool the flame locally and decrease the burning velocity of the mixture. This results in flame stabilization. However, if the heat-transfer processes (conduction, convection, and radiation) involved in cooling the flame are somehow impeded, the rate of heat loss is decreased and the local reduction in burning velocity may no longer take place. This could result in upstream propagation of the flame. 

Maximum velocity tbrougb minimum free area between rows of tubes m/s ft/h... 

Rothfus, Monrad, Sikchi, and Heideger [Ind. Eng. Chem., 47, 913 (1955)] report that the friction factor/g for the outer wall bears the same relation to the Reynolds number for the outer portion of the anniilar stream 2(r9 — A, )Vp/r9 l as the fricBon factor for circular tubes does to the Reynolds number for circular tubes, where / is the radius of the outer tube and is the position of maximum velocity in... 

Equation (5-62) predicts the point of maximiim velocity for laminar flow in annuli and is only an approximate equation for turbulent flow. Brighton and Jones [Am. Soc. Mech. Eng. Basic Eng., 86, 835 (1964)] and Macagno and McDoiigall [Am. Inst. Chem. Eng. J., 12, 437 (1966)] give more accurate equations for predicting the point of maximum velocity for turbulent flow. 

Calculated from drag coefficient for single cylinders using maximum velocity — Experimental... 

Stichlmair uses the ratio of actual velocity to this maximum velocity together with a term that increases entrainment as the distance gets small between the hquid-vapor layer and the tray deck above. His correlation spans a 10 fold range in entrainment. He shows a sharp increase in entrainment at 60 percent of the maximum velocity and attributes the increase to a shift to the spray regime. 

Correlations can be extended to evaporators at lower velocities by assuming that E dechnes with (velocit) " between 60 percent and 10 percent of the maximi im velocity. At velocities below 10 percent of the maximum velocity, E can be assumed to change directly with velocity. 

General Characteristics Countercurrent flow is maintained by virtue of the difference in densities of the hquids and either the force of gravity (vertical towers) or centrifugal force (centrifugal extractors). Only one of the liquids may be pumped through the equipment at any desired velocity. Tne maximum velocity for the second is then fixed if it is attempted to exceed this limit, the second hquid will be rejected and the extractor will be flooded. 

Now for the snag of a soft bearing material - will it not fail to support the normal operating forces imposed on it by the crankshaft All bearing materials have a certain p - v envelope within which they function safely (Fig. 26.3). The maximum pressure, p, that the bearing can accept is determined by the hardness of the surface the maximum velocity, v, is determined by heating, and thus by the thermal conductivity... 

Flow distribution in a packed bed received attention after Schwartz and Smith (1953) published their paper on the subject. Their main conclusion was that the velocity profile for gases flowing through a packed bed is not flat, but has a maximum value approximately one pellet diameter from the pipe wall. This maximum velocity can be 100 % higher than the velocity at the center. To even out the velocity profile to less than 20 % deviation, more than 30 particles must fit across the pipe diameter. 

Across a control valve the fluid is accelerated to some maximum velocity. At this point the pressure reduces to its lowest value. If this pressure is lower than the liquid s vapor pressure, flashing will produce bubbles or cavities of vapor. The pressure will rise or recover downstream of the lowest pressure point. If the pressure rises to above the vapor pressure, the bubbles or cavities collapse. This causes noise, vibration, and physical damage. 

Nr = Rows of tubes per shell pass (Nr is always equal to the number of minimum clearances through which the fluid flows in series. For square staggered pitch the maximum velocity, Umax, which is required for evaluating Re may occur in the transverse clearances a or the diagonal clearances c. In the latter case Nr is one less than the number of tube rows.)... 

Figure 1. Maximum velocity for gases and vapors through heat exchangers on sheli-side.

The following table gives suggested maximum velocities in exchanger nozzles. The pressure drop through nozzles should be checked, especially where pressure losses are a problem such as in low pressure systems. 

For vapor/liquid separators, this is usually expressed in terms of maximum velocity which is related to the difference in liquid and vapor densities. The standard equation is... 

As discussed in 5-4.2 and 5-4.3, three different maximum velocity-diameter vd) products can be found in current recommended practices. Values... 

An important practical question is, what is the representative pipe diameter in loading circuits comprising different sizes of pipe This has a large effect on the values calculated for velocity and velocity-diameter product. As an example, static ignition of ester mist in a rail car (5-1.3.1) involved 1450 gpm through a 6-in. pipe (v = 5 m/s and vd = 0.76 mVs) followed by a short 4-in. dip pipe assembly (y = 11 m/s and vd = 1.15 mVs). Were nonconductive liquid flow rate restrictions applied to the semiconductive ester (time constant —0.01 s) involved in this fire, the flow rate based on the 4-in. pipe would be unacceptably large based either on a 7 m/s maximum velocity or a 0.80 mVs maximum vd product. However, based on the 6-in. pipe upstream the flow velocity is less than 7 m/s and also meets API s vd < 0.80 mVs criterion. 

Table 5-4 gives solutions for various tank filling criteria discussed in this chapter in which either a maximum velocity or a maximum velocity-diame-... 

Figure 1. Available pressure drop may in some cases dictate acceptance of a lower maximum velocity, but at least 75 m/s is recommended to insure good dispersion. Flare tips consisting of a simple open-ended pipe with a single pilot are subject to flame lift-off and noise problems at lower velocities, and should therefore be designed for a maximum velocity of 50 m/s.

The number of jets is based on gas velocity. For 25 mm standard pipe, the recommended maximum velocity permits a flow rate of 72.2 m /h (acmal or standard) of gas per jet. The following empirical equation can be used ... 

The determining factor in convection is the flow boundary layer. Outside the boundary layer, the fluid is considered to have achieved a maximum velocity at an infinite distance from the surface. 

Compact air jets are formed by cylindrical tubes, nozzles, and square or rectangular openings with a small aspect ratio that are unshaded or shaded by perforated plates, grills, etc. Compact air jets are three-dimensional and axisymmetric at least at some distance from the diffuser opening. The maximum velocity in the cross-section of the compact jet is on the axis. 

---