Critical Velocity of Flows

Some metals depend on formation of a protective film for corrosion resistance in sea water. A fresh supply of oxygen brought to the surface of the metal tends to promote the corrosion reaction in some cases, and in others it helps form desired protective films. If a critical velocity of flowing sea water is exceeded, the film may be eroded away. The velocity for useful corrosion resistance is low for copper, higher for aluminum, cupro-nickels, and aluminum bronzes, and highest for stainless steels, Hastelloy C, and titanium. 

Various parameters of speed determine whether a mixture may separate or continue to flow. In fact, the designer of a thickener or a mixer is often more interested in the sinking velocity of particles. On the other hand, the designer of a pipeline has to pay attention to the critical velocity of flow, setding speed, and whether the flow is vertical or horizontal, particularly in the case of heterogeneous flows. 

This is the minimum speed needed to maintain particles in suspension, particularly in a process of mixing or thickening. This velocity is not identical with the critical velocity of flow, and should not be confused with it. 

The decrease in film burn-out heat flux with increasing mass velocity of flow at constant quality has been explained by Lacey et al. in the following way. At constant quality, increasing total mass flow rate means increasing mass flow of vapor as well as liquid. It has been shown that above certain vapor rates increased liquid rates do not mean thicker liquid layers, because the increased flow is carried as entrained spray in the vapor. In fact, the higher vapor velocity, combined with a heat flux, might be expected to lead to easy disruption of the film with consequent burn-out, which seems to be what actually occurs at a constant steam mass velocity over very wide ranges of conditions—that is, the critical burn-out steam quality is inversely proportional to the total mass flow rate. 

Principally, investigations have been conducted of suitable linear velocities and power requirements. Slurries of 40-50 vol% solids can be handled satisfactorily, with particle sizes less than 24-48 mesh or so (0.7-0.3 mm). At low line velocities, particles settle out and impede the flow of the slurry, and at high velocities the frictional drag likewise increases. An intermediate condition exists at which the pressure drop per unit distance is a minimum. The velocity at this condition is called a critical velocity of which one correlation is... 

This paper reviews the results of investigations into low-frequency mechanical and high-frequency (ultrasonic) vibration effects upon flowable polymeric systems, primarily, on molten commercial thermoplastics. We tried to systematize possible techniques to realize vibration in molding of polymers. Theoretical and experimental corroboration is provided for major effects obtained at cyclic (shear and bulk) strains of molten polymers and compositions based thereon. It is demonstrated that combined stress of polymeric media is attained under overlapping vibrations and this results in a decreased effective viscosity of the melts, a drop i the pressure required to extrude them through molding tools, increased critical velocities of unstable flow occurrence and a reduced load on the thrust elements of extruder screws. 

The velocity and rate of discharge occurring at the critical depth are termed Vc and qc = qmax, the critical velocity and flow, respectively. On account of the greater area, the velocity of upper-stage flow is slower than the critical and is called subcritical velocity likewise, supercritical velocity occurs at lower-stage conditions. Combining Eqs. (10.110) and (10.113) yields a simple expression for critical velocity,... 

Critical Shear Rate - Fluoropolymers, and generally thermoplastic materials, must be processed below the velocity at which melt fracture occurs, referred to as the critical shear rate. Melt fracture in molten plastics takes place when the velocity of the resin in flow exceeds the critical velocity, the point where the melt strength of the polymer is surpassed by internal stresses. Critical velocity of most fluoropolymers is usually much lower than most thermoplastics. 

The maximum velocity of flow that can be attained is the speed of sound. It is reached for the critical pressure ratio Wi ji, and true as well if w < Wknt- The flow rate then only depends on the pressure inside the enclosure, pi, and not on the external pressure, p2. Equation (7.20) hence applies for discharge processes with velocities below the speed of sound and Eq. (7.23) for all other cases. The latter is usually required if gas under high pressure is discharged. 

Critical velocity of a slurry in horizontal pipes is the fluid velocity below which the solids begin to deposit at the bottom of the pipe. In vertical pipes, solids that would be deposited if the pipe were horizontal are easily transported because their settling velocity is usually much lower than normal flow velocities. In general ... 

In Chapters 3, 4, and 5 the mechanics of solid suspensions are described in detail. An im portant parameter to introduce in this chapter is the critical velocity of a slurry flow. Figure 1-8 plots the pressure loss per unit length on the y-axis, versus the velocity Kof a slurry flow on the x-axis. Five points are shown for flow at a constant volume concentration. For this slurry of moderate viscosity, the flow is stationary and the solids clog the pipeline below point 1. There is insufficient speed to move the particles. As the flow is accelerated, the speed reaches point 1, which is called the deposition critical velocity Vp, or minimum speed to start the flow. Between points 1 and 2, the bed builds up, dunes form, and the different phases are well separated. Between points 2 and 3 the flow is streaking but... 

The first and second critical velocities of the water and air flows as shown as functions of particle diameter in Fig. XI.7. As we should expect, the first critical velocity for wind erosion exceeds the velocity for erosion by a flow of water, owing to the difference between the adhesive forces in air and water. The broken line shows the change in the value of when the force of interaction between the particles exceeds their weight (see Fig. XI.5 and 31, 37, 38). In this case the first critical velocity produces the detachment of the adhering particles. The value of this velocity may exceed Vj 2> velocity required to produce actual flight... 

The velocity of flowing aqueous solutions becomes critical when it is sufficient to affect the protective hydroxide film (Loose, 1946). Faster corrosion is caused by... 

As the volume flow from the terrace into the well is larger than the supply rate of the disperse phase, necking near the end of the terrace takes place below a critical velocity of the disperse phase in the microchannel. Due to the small radius in... 

Darcy velocity for onset of upper Newtonian or shear-thickening flow, L/t, ft/D Darcy velocity where mechanical degradation begins, L/t, ft/D interstitial velocity, L/t, ft/D average interstitial velocity, L/t, ft/D critical velocity where flow regimes change, L/t, ft/D... 

These phenomena may affect hydraulic transport the critical velocity of the sand-water mixture (see Section 4.5.2) in the pipeline may be less than when pumping normal quartz sands, but when it drops below a certain threshold value the discharge pipe may choke up suddenly and rapidly. This problem may be aggravated by the tendency of the flow velocity to decrease with the development of a bed load in the pipeline. 

Use dimensional analysis to show that the critical velocity of a liquid with kinematic viscosity v, flowing in a channel of lateral dimension d, is proportional to vjd. 

Laminar and Turbulent Flow, Reynolds Number These terms refer to two distinct types of flow. In laminar flow, there are smooth streamlines and the fuiid velocity components vary smoothly with position, and with time if the flow is unsteady. The flow described in reference to Fig. 6-1 is laminar. In turbulent flow, there are no smooth streamlines, and the velocity shows chaotic fluctuations in time and space. Velocities in turbulent flow may be reported as the sum of a time-averaged velocity and a velocity fluctuation from the average. For any given flow geometry, a dimensionless Reynolds number may be defined for a Newtonian fluid as Re = LU p/ I where L is a characteristic length. Below a critical value of Re the flow is laminar, while above the critical value a transition to turbulent flow occurs. The geometry-dependent critical Reynolds number is determined experimentally. 

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