Critical flow velocity

Consider the case of the simple Bunsen burner. As the tube diameter decreases, at a critical flow velocity and at a Reynolds number of about 2000, flame height no longer depends on the jet diameter and the relationship between flame height and volumetric flow ceases to exist (2). Some of the characteristics of diffusion flames are illustrated in Eigure 5. 

Turbulent flow occurs if the Reynolds number as calculated above exceeds a certain critical value. Instead of calculating the Reynolds number, a critical flow velocity may be calculated and compared to the actual average flow velocity [60]. 

In the above equation, the critical flow velocity is in ft/min and all other quantities are specified above. 

Velocity Accelerated Corrosion This phenomenon is sometimes (incorrecdy) referred to as erosion-corrosion or velocity corrosion. It occurs when damage is accelerated by the fluid exceeding its critical flow velocity at that temperature, in fliat metal. For that system, fliis is an undesirable removal of corrosion products (such as oxides) which would otherwise tend to stifle the corrosion reaction. 

Fines production from untreated test sands and permeability damage observed in untreated cores indicated that the laboratory test flow rates were above the critical flow velocity required to initiate fines migration. 

It is important to note that the reaction conditions (temperature and pressure) under which the various input streams are introduced into the SCWO system are of key importance in controlling phase separations. For waste streams that are highly complex and require upper-limit operation of the SCWO system, appropriate flow velocities can be used to minimize the solid deposition on the reactor components. The critical flow velocities required for solids are found in Refs. 117 and 118. 

These forces are very small compared with typical colloidal forces, which can be of the order of 1000-2000 pN in dilute electrolyte solutions. Figure 3 shows an example of colloidal forces calculated between a fine quartz particle and a sandstone grain. To be of the same order of magnitude as the colloidal forces, a superficial velocity of the order of 200 cm/h would be required in some reservoirs (23, 27). This is not to say that mechanically induced fines migration does not occur in some reservoirs at lower velocities. Critical flow velocities below which fines migration does not occur have been reported to span the range from about 14 to 900 cm/h (31). Recognizing that there will be exceptions, as a first approximation it may be appropriate to consider fine particle mobilization to be independent of fluid velocity and consider simply the influence of solution and interfacial chemistry on the colloidal forces. 

Fines are migrated in the medium if the salinity of the aqueous phase, CSjW, is below a critical value or if a critical flow velocity is surpassed (u > iqc). The critical salinity concept does not apply to fines migration in the oleic phase, therefore ki0dl = 0. It is assumed that the rate at which fines are trapped at pore throats is proportional to the mass flux of the particles, Furthermore, for fines that... 

In externally imposed inhomogeneous magnetic fields (TO 0) the rotational forces may generate sufficiently strong vortices in the solid/liquid interface sublayers to destroy the layer structure on account of large MHD-stresses appearing on the capillary walls (also on the surface of microscopic particles and entrapped gas bubbles in the flow, if impurities are present). The critical flow velocity for structure destruction is [125]... 

Metal/alloy Critical flow velocity, m/s Temperature, C°... 

In previous works, it has been experimentally established that mass transfer is very disturbed starting from a critical flow velocity U for the cylinder [11, or from a critical angular velocity for the disc [21 those critical values were shown to depend on the physicochemical parameters of the polymer solution. 

Zvonkov extended the concept of the four critical flow velocities to the process of wind erosion. In Fig. XII.13 we show the dependence of the forces Fdr and Fiif on the air-flow velocity for soil particles with a diameter of 0.058... 

Certain metals corrode at an abnormally high rate when the flow velocity in the turbulent flow regime exceeds a critical value. The phenomenon is well known for copper and its alloys used in domestic hot water systems and in heat exchanger tubes. Table 10.26 indicates empirical values for the critical flow velocity of seawater in condenser pipes made of different alloys. Similar values apply for fresh water. 

The occurrence of a critical flow velocity can be explained in two ways by the action of shear stress on corrosion product films covering the pipe walls or by mass transport considerations. We first consider the role of shear stress. 

Using equation (10.50) we can relate the critical flow velocity for erosion corrosion. Vent lo a critical shear stress... 

The data of Table 10.26 can now be interpreted in terms of mass transport. Above a critical flow velocity, which depends on pipe diameter, the rate of mass transport becomes sufficiently fast to carry away dissolved corrosion products without forming a salt film. In other words, their surface concentration remains below saturation. Under these conditions scales that are formed by precipitation of corrosion products at lower flow velocity can not exist and the corrosion rate therefore will be higher. An example in case is carbon dioxide corrosion of carbon steel that occurs in fluids containing... 

The critical shear stress that causes erosion corrosion of copper in a pipe containing sea water under turbulent flow conditions is taken to be 9.6 N/m. What would be the critical flow velocity in pipes of 5 cm and 20 cm respectively We assume that the friction coefficient is given by the Blasius relation ... 

I have discussed in this chapter the effect of reaching sonic velocity, also called the critical flow velocity or choke flow. 

Fig. 33 Critical flow velocity Vm of the discocyte-to-parachute transition of elastic vesicles and of the discocyte-to-prolate transition of fluid vesicles, as a function of the bending rigidity for IdRl/ksT =110 (left), and of the shear modulus ju for k/UbT = 10 (right). From [187]...

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