Laminar flow fluids

Let us look at an incompressible, constant-property fluid flowing laminarly inside a circular tube in regions away from the inlet where the velocity profile is fully developed. The continuity equation gives... 

In configurations more complex than pipes, eg, flow around bodies or through nozzles, additional shearing stresses and velocity gradients must be accounted for. More general equations for some simple fluids in laminar flow are described in Reference 1. 

The shear stress is hnear with radius. This result is quite general, applying to any axisymmetric fuUy developed flow, laminar or turbulent. If the relationship between the shear stress and the velocity gradient is known, equation 50 can be used to obtain the relationship between velocity and pressure drop. Thus, for laminar flow of a Newtonian fluid, one obtains ... 

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. 

If force P is greater than zero, the particle will be in motion relative to the continuous phase at a certain velocity, w. At the beginning of the particle s motion, a resistance force develops in the continuous phase, R, directed at the opposite side of the particle motion. At low particle velocity (relative to the continuous phase), fluid layers running against the particle are moved apart smoothly in front of it and then come together smoothly behind the particle (Figure 14). The fluid layer does not intermix (a system analogous to laminar fluid flow in smoothly bent pipes). The particles of fluid nearest the solid surface will take the same time to pass the body as those at some distance away. 

The steady, laminar, incompressible fluid flow in cyclone collectors is governed by the Navier-Stokes equations ... 

Laminar flow Fluid flow in which the fluid particles move in straight lines parallel to the axis of the pipe or duct. 

The basis for single-phase and some two-phase friction loss (pressure drop) for fluid flow follows the Darcy and Fanning concepts. The exact transition from laminar or dscous flow to the turbulent condition is variously identified as between a Reynolds number of 2000 and 4000. 

This is the basis for establishing the condition or type of fluid flow in a pipe. Reynolds numbers below 2000 to 2100 are usually considered to define laminar or thscous flow numbers from 2000 to 3000-4000 to define a transition region of peculiar flow, and numbers above 4000 to define a state of turbulent flow. Reference to Figure 2-3 and Figure 2-11 will identify these regions, and the friction factors associated with them [2]. 

Equation 2-25 is valid for calculating the head loss due to valves and fittings for all conditions of flows laminar, transition, and turbulent [3], The K values are a related function of the pipe system component internal diameter and the velocity of flow for v-/2g. The values in the standard tables are developed using standard ANSI pipe, valves, and fittings dimensions for each schedule or class [3]. The K value is for the size/type of pipe, fitting, or valve and not for the fluid, regardless of whether it is liquid or gas/vapor. 

The energy to drive the fluid through a static mixer comes from the fluid pressure itself, creating a loss in pressure (usually small) as the fluid flows through the unit. For laminar flow... 

Fluid flow is also critical for proper operation of a hydraulic system. Turbulent flow should be avoided as much as possible. Clean, smooth pipe or tubing should be used to provide laminar flow and the lowest friction possible within the system. Sharp, close radius bends and sudden changes in cross-sectional area are avoided. 

Flashing liquids, 134-146 Flow coefficients, Gv, for valves, 81 Friction loss, 68 Incompressible fluid, 71 Laminar flow, 77, 78, 86 Liquid lines, chart, 92 Long natural gas pipe lines, 120 Non-water liquids, 99 Pipe, 71... 

When a fluid flowing at a uniform velocity enters a pipe, the layers of fluid adjacent to the walls are slowed down as they are on a plane surface and a boundary layer forms at the entrance. This builds up in thickness as the fluid passes into the pipe. At some distance downstream from the entrance, the boundary layer thickness equals the pipe radius, after which conditions remain constant and fully developed flow exists. If the flow in the boundary layers is streamline where they meet, laminar flow exists in the pipe. If the transition has already taken place before they meet, turbulent flow will persist in the... 

For a power-law fluid in laminar flow at a velocity /. in a pipe of length /. the pressure drop -APL will be given by ... 

Lelea et al. (2004) investigated experimentally fluid flow in stainless steel microtubes with diameter of 100-500 pm at Re = 50-800. The obtained results for the Poiseuille number are in good agreement with the conventional theoretical value Po = 64. Early transition from laminar to turbulent flow was not observed within the studied range of Reynolds numbers. 

For single-phase fluid flow in smooth micro-channels of hydraulic diameter the Poiseuille number is independent of the Reynolds number. For single-phase gas flow in micro-channels of hydraulic diameter 16.6 to 4,010 pm, Knudsen number of Kn = 0.001-0.38, Mach number of Ma = 0.07-0.84, the experimental friction factor agrees quite well with theoretical one predicted for fully developed laminar flow. 

Sedov LI (1993) Similarity and dimensional methods in mechanics, 10th edn. CRC, Boca Raton Shah RK, London AL (1978) Laminar flow forced convection in duct. Academic, New York Shapiro AK (1953) The dynamics and thermodynamics of compressible fluid flow. Wiley, New York... 

In our analysis, we discuss experimental results of heat transfer obtained by previous investigators and related to incompressible fluid flow in micro-channels of different geometry. The basic characteristics of experimental conditions are given in Table 4.1. The studies considered herein were selected to reveal the physical basis of scale effect on convective heat transfer and are confined mainly to consideration of laminar flows that are important for comparison with conventional theory. 

As is well known, fluid dynamics is the study of motion and transport in liquids and gases. It is primarily concerned with macroscopic phenomena in nonequilibrium fluids and covers such behavior as diffusion in quiescent fluids, convection, laminar flows, and fully developed turbulence. 

Consider a situation where a fluid flows past a solid surface from which a component A is being transferred. Such a situation can be encountered in simple processes like drying or dissolution. The bulk of the fluid can be considered to be in turbulent flow, while there is a laminar film adjacent to the solid surface. The major change in the concentration of component A occurs across this laminar film. It is found that the rate of transfer of A (denoted by dNA/di) is proportional to the surface area, S, and to the difference in the concentration of A in the fluid adjacent to the solid surface and that in the bulk of the fluid. Denoting these concentrations as CAs and CAb respectively (Figure 3.23), one can write... 

Laminar flow Fluid flow pattern at low flow rate and/or high viscosity. 

Shah and Nelson [33] introduced a convective mass transport device in which fluid is introduced through one portal and creates shear over the dissolving surface as it travels in laminar flow to the exit portal. They demonstrated that this device produces expected fluid flow characteristics and yields mass transfer data for pharmaceutical solids which conform to convective diffusion equations. 

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