In uniform flow

This solution gives unequivocally the effective control range of both unflanged and flanged openings when the exhaust flow rate and velocity of the idealized cross-draft are known. The distance from the hood opening to the dividing streamline for a hood in uniform flow perpendicular to its axis is thus... 

For this case the velocity equation is the same as (26), since the pressure term dp/dx in Eq. (4) disappears in uniform flow in which the free surface is in contact with the atmosphere at all points. Equations (5) and (6) reduce to... 

In a closed pipe conveying fluid under pressure, there is no relation between the slope of the pipe and the slope of the hydraulic gradient. In uniform flow in an open channel, the water surface must be parallel to the bed of the stream, and consequently S is then also the slope of the bed, S0 thus we arrive at the important relation, for uniform flow only, that... 

A general equation for frictional resistance in a pressure conduit was developed. The same reasoning may now be applied to uniform flow with a free surface. Consider a sloped channel of water flowing over a constant slope of angle 0, which shows the short reach of length L between stations 1 and 2 of a channel in uniform flow with area A of the water section. As the flow is neither accelerating nor decelerating,... 

A channel laid on a certain slope will carry a certain rate of discharge at critical velocity in uniform flow. The concepts of critical velocity and depth and alternate stages of flow, however, are of greater significance in cases of nonuniform flow because of the relation between the critical velocity and the celerity or velocity of propagation of the gravity wave. 

A rotating sphere in uniform flow will experience a lift which causes the particle to drift across the flow direction. This is called the Magnus effect (or force). The physics of this phenomenon are complex. 

H. Heat Transfer From a Solid Sphere in Uniform Flow for Re -C I and Pe I... 

H. HEAT TRANSFER FROM A SOLID SPHERE IN UNIFORM FLOW FOR Re < I AND Pe I... 

Lapidus, L., and N.R. Amundson. 1952. Mathematics of adsorption in beds. VI. The effects of longitudinal diffusion in ion exchange and chromatographic columns. J, Phys. Chem. 56 984-988. Li, W.H. 1972a. Effects of dispersion on DO-SAG in uniform flow. J. Sanit. Eng. 98 169-182. 

Much of the procedure for the analysis of jet stability has already been set down in connection with the discussion of undamped surface waves on deep water. A fundamental difference in the jet problem from plane deep water waves is that it is axisymmetric with an imposed characteristic length scale equal to the jet radius a. Since the undisturbed jet is considered to be inviscid and in uniform flow, it can be reduced to a state of rest simply by a Galilean transformation. With gravity neglected and only surface tension forces acting, the pressure at any point within the jet is -I- ala. This then describes the basic flow needed for the first step of the stability analysis. 

Most experimental data obtained to date have been interpreted on the basis of the Rubinow-Keller equation (216) for the lift force on a spinning, translating sphere in an unbounded fluid at rest (or in uniform flow) at infinity. The spin is assumed to be given by Eq. (253), whereas the velocity U appearing in Eq. (216) has usually been interpreted as the axial slip velocity. This gives rise to a lift force... 

Figure 7.9 Simplified remediation scenario extraction well in uniform flow field.

The unusually small volume ratio of gas to liquid makes stripping plate efficiencies low. Yokota s model of the process assumes that liquid travels across a plate in uniform flow with no transverse mixing but that vertical mixing is perfect. He then characterizes a plate by the length of linear travel of the liquid. Correlation of the experimental data is in terms of the length of a transfer unit. This is the distance that liquid must travel to undergo an amount of mass transfer equivalent to one transfer unit. A plate then provides a (normally fractional) number of transfer units given by... 

Saiki E, Biringen S. Numerical simulation of a cylinder in uniform flow application of a virtual boundary method. J Comput Phys 1996 123(36) 450-465. 

Example 3-1. Straight-line shale segment in uniform flow. 

A similar analysis can be performed for laminar flow past a stationary cylinder placed in uniform flow, which as implications for predicting particle or protein adsorption at fibers (filtration mat). It can be shown [87] that at small distances from the cylinder surface, the components of the fluid flow velocity can be approximated by [86,87]... 

This means that the axial (perpendicular) velocity profile in the RIJ cell closely resembles the flow in the vicinity of the sphere immersed in uniform flow. This suggests that the mass-transfer phenomena (e.g., colloid particle adsorption on the sphere surface) can be modeled well by the RIJ cell. However, a quantitative comparison becomes feasible if the flow parameter for the RIJ cell is known as a function of Re number. This parameter has been determined numerically and the results are plotted in Fig. 17. 

Analytical expressions for the limiting flux also can be derived for the nonuniformly accessible surfaces by using the similarity transformation [78]. For the sphere or cylinder in uniform, flow, the flux jq is given by... 

For practical purposes, the most important parameter is the extension of the region where the particle flux remains position independent, which means that the sirrface is rmiformly accessible for partiele transport. The uniformity of the flux distribution depends on the Reynolds number, as can be assessed from the results shown in Fig. 44. It can be deduced that for Re < 16, the uniform adsorption conditions prevail over distances r/R < 0.5, whereas for higher Re, this region shrinks to approximately 0.25r/R. It is also interesting to observe that for moderate Re (1 < Re < 16), the reduced flux distribution measured in the RIJ cell closely resembles the theoretical results for the sphere in uniform flow when theyW//o dependence in the limit of low Re is given by the function derived from Eq. (157) ... 

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