Velocity decrease

In the case of a packed column, the terms on the right-hand side should each be divided by the voidage, ie, the volume fraction not occupied by the soHd packing (71). In unpacked columns at low values of the sHp velocity approximates the terminal velocity of an isolated drop, but the sHp velocity decreases with holdup and may also be affected by column internals such as agitators, baffle plates, etc. The sHp velocity can generally be represented by (73) ... 

Boundary layer flows are a special class of flows in which the flow far from the surface of an object is inviscid, and the effects of viscosity are manifest only in a thin region near the surface where steep velocity gradients occur to satisfy the no-slip condition at the solid surface. The thin layer where the velocity decreases from the inviscid, potential flow velocity to zero (relative velocity) at the sohd surface is called the boundary layer The thickness of the boundary layer is indefinite because the velocity asymptotically approaches the free-stream velocity at the outer edge. The boundaiy layer thickness is conventionally t en to be the distance for which the velocity equals 0.99 times the free-stream velocity. The boundary layer may be either laminar or turbulent. Particularly in the former case, the equations of motion may be simphfied by scaling arguments. Schhchting Boundary Layer Theory, 8th ed., McGraw-HiU, New York, 1987) is the most comprehensive source for information on boundary layer flows. 

Turbulent velocity fluctuations ultimately dissipate their kinetic energy through viscous effects. MacroscopicaUy, this energy dissipation requires pressure drop, or velocity decrease. The ener dissipation rate per unit mass is usually denoted . For steady ffow in a pipe, the average energy dissipation rate per unit mass is given by... 

Hindered Settling When particle concentration increases, particle settling velocities decrease oecause of hydrodynamic interaction between particles and the upward motion of displaced liquid. The suspension viscosity increases. Hindered setthng is normally encountered in sedimentation and transport of concentrated slurries. Below 0.1 percent volumetric particle concentration, there is less than a 1 percent reduction in settling velocity. Several expressions have been given to estimate the effect of particle volume fraction on settling velocity. Maude and Whitmore Br. J. Appl. Fhys., 9, 477—482 [1958]) give, for uniformly sized spheres,... 

In the nonadiabatic limit ( < 1) B = nVa/Vi sF, and at 1 the adiabatic result k = k a holds. As shown in section 5.2, the instanton velocity decreases as t] increases, and the transition tends to be more adiabatic, as in the classical case. This conclusion is far from obvious, because one might expect that, when the particle loses energy, it should increase its upside-down barrier velocity. Instead, the energy losses are saturated to a finite //-independent value, and friction slows the tunneling motion down. 

This reaction is carried out in tall fluidized beds of high L/dt ratio. Pressures up to 200 kPa are used at temperatures around 300°C. The copper catalyst is deposited onto the surface of the silicon metal particles. The product is a vapor-phase material and the particulate silicon is gradually consumed. As the particle diameter decreases the minimum fluidization velocity decreases also. While the linear velocity decreases, the mass velocity of the fluid increases with conversion. Therefore, the leftover small particles with the copper catalyst and some debris leave the reactor at the top exit. 

Vane thickness. Because of manufacturing problems and physical necessity, impeller vanes are thick. When fluid exits the impeller, the vanes no longer contain the flow, and the velocity is immediately slowed. Because it is the meridional velocity that decreases, both the relative and absolute velocities decrease, changing the exit angle of the fluid. 

Profiles with indefinite boundaries" with air velocity decreasing with distance from the axis asymptotically approaching zero... 

Since the throw of a jet is a function of the velocity, and since the rate of velocity decrease is dependent on the rate of induction that occurs, the quantity of air induced into the discharge from an outlet is a direct function of the perimeter of the cross section of the primary airstream. 

It is quite easy to disturb the flow in a jet either by inserting a small surface at right angles close to the outlet or by using a small air velocity far from the outlet. Usually the latter needs a large flow rate, but a small flow rate with high velocity may also change the direction of the jet, especially as jet velocity decreases. 

For this safety criterion, we consider the fact that as the velocity decreases with increasing distance from the surface of the tank, it will reach some critical velocity, at which the induced movement of air will be insufficient to overcome the effects of crossdrafts or the buoyancy velocity At this point, we must ensure that the concentration is at, or below, some critical allowable concentration, Qfj,. The values of the critical concentration and velocity will depend (tn particular circumstances, but it is worth noting that must be at least equal to I g in order to overcome the effects of buoyancy, and the appropriate value will depend on the crossdrafts, which typically vary between 0.05 m to 0.5 in s F For the sake of providing examples, we have chosen to be the maximum of the buoyancy velocity and the typical cross-draft velocity. For the critical concentration we have chosen two values, C = 0.05 and C = 0.10. The actual value used by a designer would depend on the toxicity of the contaminant in question. 

Examination of equation 2.43 shows that the mass flux initially increases as concentration increases but then passes through a maximum and finally declines as velocity decreases due to hindered settling (Figure 2.8). 

Mechanism 1 of Figure 8-122B [209] is dominant when the underflow clearance at a given liquid rate is increased, the underflow velocity decreases and the severity of recirculation decreases. 

A sharp velocity decrease is seen for the water-base muds. Assuming a threshold detection of 500 ft/s, the alarm could be given for 0.5% of free gas or 1.1 to 1.4% of total gas (dissolved and free). 

The oil-base muds having no free gas behave differently and the 500-ft/s threshold is not reached before approximately 5% of gas is dissolved. Then the velocity decrease is almost as fast as with the water-base mud. 

There are two points of the cycle at which velocity decreases very rapidly from a high value to zero. To give a.familiar analogy, the van der Pol oscillator for this value of y. behaves not as a decent oscillator but rather as a pneumatic hammer, which idles for some time while the air pressure builds up, delivers a hammer blow, losing its kinetic energy, and then begins a similar half-cycle. 

Fluids whose behaviour can be approximated by the power-law or Bingham-plastic equation are essentially special cases, and frequently the rheology may be very much more complex so that it may not be possible to fit simple algebraic equations to the flow curves. It is therefore desirable to adopt a more general approach for time-independent fluids in fully-developed flow which is now introduced. For a more detailed treatment and for examples of its application, reference should be made to more specialist sources/14-17) If the shear stress is a function of the shear rate, it is possible to invert the relation to give the shear rate, y = —dux/ds, as a function of the shear stress, where the negative sign is included here because velocity decreases from the pipe centre outwards. 

The superficial air velocity required to give the minimum drag ratio increases as the liquid velocity decreases. 

For an ice sheet of thickness H in equilibrium with a climate supplying accumulation at a rate a (thickness of ice per imit time), the vertical velocity near the ice-sheet surface is a and this velocity decreases to zero at the ice-sheet bed. A characteristic time constant for the ice core is H/a. The longest histories are therefore obtained from the thick and dry interiors of the ice sheets (particularly central East Antarctica, where H/a = 2 X 10 yrs). Unfortunately, records from low a sites are also low resolution, so to obtain a high-resolution record a high a site must be used and duration sacrificed (examples are the Antarctic Peninsula (H/a = 10 ) and southern Greenland H/a = 5 x 10 )). 

G Particle velocity decreased over the gray arrow particle velocity increased over the black arrow... 

Tapered plates, prepared with a gradual increase in thiclcness of the layer from 0.3 nm to 1.7 am, can be used to improve resolution of the sample [215]. On the tapered layer the solvent front velocity decreases as the thickness of the layer increases. This results in the formation of a negative velocity gradient in the direction of solvent migration. As a result the lower portion of a zone moves faster than the top portion, keeping each component focused as a narrow band. Plates with concentrating zones are useful for optimizing sample application. 

In Section 7.2 we presented one method for determining E T from the effects of apparent enzyme concentration on the measured value of IC50 for tight binding inhibitors. Another convenient way to determine [E T derives from the nature of Morrison s equation. When the ratio E T/A (PP equals or exceeds 200, the fractional velocity decreases very steeply with increasing inhibitor concentration, in an essen-... 

As the fluid flows over the forward part of the sphere, the velocity increases because the available flow area decreases, and the pressure decreases as a result of the conservation of energy. Conversely, as the fluid flows around the back side of the body, the velocity decreases and the pressure increases. This is not unlike the flow in a diffuser or a converging-diverging duct. The flow behind the sphere into an adverse pressure gradient is inherently unstable, so as the velocity (and lVRe) increase it becomes more difficult for the streamlines to follow the contour of the body, and they eventually break away from the surface. This condition is called separation, although it is the smooth streamline that is separating from the surface, not the fluid itself. When separation occurs eddies or vortices form behind the body as illustrated in Fig. 11-1 and form a wake behind the sphere. 

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