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Laminar velocity, steady

Figure 1. No slip boundary condition steady laminar velocity profile for fluid sheared between two plates. Figure 1. No slip boundary condition steady laminar velocity profile for fluid sheared between two plates.
Mass transport in laminar flow is dominated by diffusion and by the laminar velocity profile. This combined effect is known as dispersion and the underlying model for the theoretical derivation of a kinetic study had to be derived from the dispersion model, which Taylor [91] and Aris [92] developed. Taylor concluded that in laminar flow the speed of an inert tracer impulse initially given to a channel will have the same speed as the steady laminar carrier gas flow originally prevailing in this channel. [Pg.118]

Now, for convenience, we assume that the barrel surface is stationary and that the upper and lower plates representing the screws move in the opposite direction, as shown in Fig. 6.57, but for flow rate calculations, it is the material retained on the barrel rather than that dragged by the screw that leaves the extruder. We assume laminar, isothermal, steady, fully developed flow without slip on the walls of an incompressible Newtonian fluid. We distinguish two flow regions marked in Fig. 6.57 as Zone I and Zone II. In the former, the flow is between two parallel plates with one plate moving at constant velocity relative to... [Pg.312]

Turbulent flow is described by conservation equations of continuity and momentum, known as the Reynolds-averaged Navier-Stokes (RANS) equations. Laminar velocity terms in conservation equations are replaced by the steady-state mean components and time-dependent fluctuating components defined by Equation 6.100. [Pg.217]

Entrance flow is also accompanied by the growth of a boundary layer (Fig. 5b). As the boundary layer grows to fill the duct, the initially flat velocity profile is altered to yield the profile characteristic of steady-state flow in the downstream duct. For laminar flow in a tube, the distance required for the velocity at the center line to reach 99% of its asymptotic values is given by... [Pg.91]

Example 4 Plnne Poiseuille Flow An incompressible Newtonian fluid flows at a steady rate in the x direction between two very large flat plates, as shown in Fig. 6-8. The flow is laminar. The velocity profile is to he found. This example is found in most fluid mechanics textbooks the solution presented here closely follows Denn. [Pg.635]

For steady-state laminar flow of any time-independent viscous fluid, at average velocity V in a pipe of diameter D, the Rabinowitsch-Mooney relations give a general relationship for the shear rate at the pipe wall. [Pg.639]

In a steady-state situation when gas flows through a porous material at a low velocity (laminar flow), the following empirical formula, Darcy s model, is valid ... [Pg.138]

Laminar Versus Turbulent Flames. Premixed and diffusion flames can be either laminar or turbulent gaseous flames. Laminar flames are those in which the gas flow is well behaved in the sense that the flow is unchanging in time at a given point (steady) and smooth without sudden disturbances. Laminar flow is often associated with slow flow from small diameter tubular burners. Turbulent flames are associated with highly time dependent flow patterns, often random, and are often associated with high velocity flows from large diameter tubular burners. Either type of flow—laminar or turbulent—can occur with both premixed and diffusion flames. [Pg.271]

In the present discussion only the problem of steady flow will be considered in which the time average velocity in the main stream direction X is constant and equal to ux. in laminar flow, the instantaneous velocity at any point then has a steady value of ux and does not fluctuate. In turbulent flow the instantaneous velocity at a point will vary about the mean value of ux. It is convenient to consider the components of the eddy velocities in two directions—one along the main stream direction X and the other at right angles to the stream flow Y. Since the net flow in the X-direction is steady, the instantaneous velocity w, may be imagined as being made up of a steady velocity ux and a fluctuating velocity ut, . so that ... [Pg.60]

Below we consider a quasi-one-dimensional model of flow and heat transfer in a heated capillary, with hydrodynamic, thermal and capillarity effects. We estimate the influence of heat transfer on steady-state laminar flow in a heated capillary, on the shape of the interface surface and the velocity and temperature distribution along the capillary axis. [Pg.351]

This system produces a steady laminar flow with a flat velocity profile at the burner exit for mean flow velocities up to 5m/s. Velocity fluctuations at the burner outlet are reduced to low levels as v /v< 0.01 on the central axis for free jet injection conditions. The burner is fed with a mixture of methane and air. Experiments-described in what follows are carried out at fixed equivalence ratios. Flow perturbations are produced by the loudspeaker driven by an amplifier, which is fed by a sinusoidal signal s)mthesizer. Velocity perturbations measured by laser doppler velocimetry (LDV) on the burner symmetry axis above the nozzle exit plane are also purely sinusoidal and their spectral... [Pg.82]

The steady states of such systems result from nonlinear hydrodynamic interactions with the gas flow field. For the convex flame, the flame surface area F can be determined from the relation fSl = b zv, where Sl is the laminar burning velocity, the cross-section area of the channel, and w is the propagation velocity at the leading point. [Pg.103]

For axial capillary flow in the z direction the Reynolds number, Re = vzmaxI/v = inertial force/viscous force , characterizes the flow in terms of the kinematic viscosity v the average axial velocity, vzmax, and capillary cross sectional length scale l by indicating the magnitude of the inertial terms on the left-hand side of Eq. (5.1.5). In capillary systems for Re < 2000, flow is laminar, only the axial component of the velocity vector is present and the velocity is rectilinear, i.e., depends only on the cross sectional coordinates not the axial position, v= [0,0, vz(x,y). In turbulent flow with Re > 2000 or flows which exhibit hydrodynamic instabilities, the non-linear inertial term generates complexity in the flow such that in a steady state v= [vx(x,y,z), vy(x,y,z), vz(x,y,z). ... [Pg.514]

The assumption of a steady state corresponds to laminar flow of the liquid. This is fulfilled only under certain conditions (limited velocity of the liquid, smooth phase boundary between the flowing liquid and the other phase, etc.). Otherwise, turbulent flow occurs, where the local velocity depends on time, pulsation of the system, etc. Mathematically the turbulent flow problem is a very difficult task and it is often doubtful whether, in specific cases, it is possible to obtain any solution at all. [Pg.148]

To describe the velocity profile in laminar flow, let us consider a hemisphere of radius a, which is mounted on a cylindrical support as shown in Fig. 2 and is rotating in an otherwise undisturbed fluid about its symmetric axis. The fluid domain around the hemisphere may be specified by a set of spherical polar coordinates, r, 8, , where r is the radial distance from the center of the hemisphere, 0 is the meridional angle measured from the axis of rotation, and (j> is the azimuthal angle. The velocity components along the r, 8, and (j> directions, are designated by Vr, V9, and V. It is assumed that the fluid is incompressible with constant properties and the Reynolds number is sufficiently high to permit the application of boundary layer approximation [54], Under these conditions, the laminar boundary layer equations describing the steady-state axisymmetric fluid motion near the spherical surface may be written as ... [Pg.175]

Ret < 150 Steady laminar inertial flow in which pressure drop depends nonlinearly on interstitial velocity and and boundary layers in the pores become pronounced with an inertial core appearing in the pores ... [Pg.335]

We consider steady-state, one-dimensional laminar flow (q ) through a cylindrical vessel of constant cross-section, with no axial or radial diffusion, and no entry-length effect, as illustrated in the central portion of Figure 2.5. The length of the vessel is L and its radius is R. The parabolic velocity profile u(r) is given by equation 2.5-1, and the mean velocity u by equation 2.5-2 ... [Pg.330]

Determine the shear stress distribution and velocity profile for steady, fully developed, laminar flow of an incompressible Newtonian fluid in a horizontal pipe. Use a cylindrical shell element and consider both sign conventions. How should the analysis be modified for flow in an annulus ... [Pg.38]

The velocity profile for steady, fully developed, laminar flow in a pipe can be determined easily by the same method as that used in Example 1.9 but using the equation of a power law fluid instead of Newton s law of viscosity. The shear stress distribution is given by... [Pg.119]

Some of the simplifications that may be possible are illustrated by the case of steady, fully-developed, laminar, incompressible flow of a Newtonian fluid in a horizontal pipe. The flow is assumed to be axisymmetric with no swirl component of velocity so that derivatives wrt 6 vanish and vg = 0. For fully-developed flow, derivatives wrt z are zero. With these simplifications and noting that the flow is incompressible, the continuity equation (equation A. 11) reduces to... [Pg.327]

Plot laminar and turbulent velocity profiles for steady state flow in a cylindrical pipe for a maximum velocity gm = 5 m/s using the radial positions 2r d - 0, 0.2, 0.4, 0.6 and 0.8. [Pg.334]

The laminar flow velocity profile in a pipe for a power law liquid in steady state flow is given by the equation... [Pg.335]

FIGURE7-1 Schematic of flow in daughter brandies of bifurcation model for steady inspiratory flow with flat profile in parent bran<. Velocity profiles in plane of bifurcation (—) and in normal plane (—) are indicated in right branch. Orientation of secondary flows and position of laminar boundary layer are shown in left branch. Redrawn wifo permisnon from Bdl. ... [Pg.289]

An incompressible fluid flows in a laminar steady fashion through a long pipe with a linear pressure gradient. Describe the velocity profile and determine the relationship for the Darcy-Weisbach friction factor. [Pg.80]

Consider the steady, laminar flow of an incompressible fluid in a long and wide closed conduit channel subject to a linear pressure gradient, (a) Derive the equation for velocity profile, (b) Derive the equation for discharge per unit width and cross-sectional mean velocity, and compare this with the maximum velocity in the channel, (c) Derive the equation for wall shear stress on both walls and compare them. Explain the sign convention for shear stress on each wall. [Pg.95]

The velocity of advance of the front is super sonic in a detonation and subsonic in a deflagration. In view of the importance of a shock process in initiating detonation, it has seemed difficult to explain how the transition to it could occur from the smooth combustion wave in laminar burning. Actually the one-dimensional steady-state combustion or deflagration wave, while convenient for discussion, is not easily achieved in practice. The familiar model in which the flame-front advances at uniform subsonic velocity (v) into the unburnt mixture, has Po> Po> an[Pg.249]

Accdg to remarks of Dunkle (Ref 8), an ideal detonation can be visualized as a steady-state process, in a frame of reference in which the detonation zone is stationary and time-invariant, with the undetonated explosive being "fed into the front at the detonation velocity D and with laminar flow of the products away from the C-J plane the rear boundary of the reaction zone is at velocity (D-u), where u is the particle velocity of the products in stationary coordinates. By the Chapman-Jouguet rule, D-u = c, the local sonic velocity at the C-J plane. That is, the velocity of the products with respect to the detonation front is sonic at the C-J temperature and pressure. Thus, even if the products were expanding into a vacuum, the rarefaction wave would never overtake the detonation front as long as any undetonated explosive remains... [Pg.390]

It is possible to derive an expression for the pressnre profile in the x direction using a simple model. We assnme that the flow is steady, laminar, and isothermal the flnid is incompressible and Newtonian there is no slip at the walls gravity forces are neglected, and the polymer melt is uniformly distribnted on the rolls. With these assnmptions, there is only one component to the velocity, v dy), so the equations of continuity and motion, respectively, reduce to... [Pg.765]

In order to familiarize the reader with Prandtl s evaluation procedure [3-5] on which the algebraic method is based, let us examine the steady laminar motion of a fluid along a plate and denote by x the coordinate along the plate, by y the distance to the plate, by u and v the x and y components of the velocity, and by p the pressure. The equations of motion of an incompressible fluid of density p and kinematic viscosity v have the form... [Pg.15]

Turbulent mass transfer near a wall can be represented by various physical models. In one such model the turbulent flow is assumed to be composed of a succession of short, steady, laminar motions along a plate. The length scale of the laminar path is denoted by x0 and the velocity of the liquid element just arrived at the wall by u0. Along each path of length x0, the motion is approximated by the quasi-steady laminar flow of a semiinfinite fluid along a plate. This implies that the hydrodynamic and diffusion boundary layers which develop in each of the paths are assumed to be smaller than the thickness of the fluid elements brought to the wall by turbulent fluctuations. Since the diffusion coefficient is small in liquids, the depth of penetration by diffusion in the liquid element is also small. Therefore one can use the first terms in the Taylor expansion of the Blasius expressions for the velocity components. The rate of mass transfer in the laminar microstructure can be obtained by solving the equation... [Pg.49]


See other pages where Laminar velocity, steady is mentioned: [Pg.7]    [Pg.89]    [Pg.518]    [Pg.673]    [Pg.256]    [Pg.61]    [Pg.438]    [Pg.338]    [Pg.390]    [Pg.203]    [Pg.130]    [Pg.18]    [Pg.246]    [Pg.9]    [Pg.11]    [Pg.105]    [Pg.779]   
See also in sourсe #XX -- [ Pg.281 ]




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Velocity laminar

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