Fluid flow within pipes

To understand the mechanism of the turbulent mixing process occurring in pipe reactors, we have to consider first some of the properties of fluid flow in pipes. Resistance to fluid flow in a pipe has two components, the viscous friction of the fluid itself within the pipe, which increases as the fluid viscosity increases, and the pressure differential caused by a liquid level difference or a pressure difference between the two vessels. 

Osborn Re molds in 1883 in a classical experiment, observed two kinds of fluid flow within a pipe namely laminar or streamline flow (sometimes called viscous flow) and turbulent flow. In the former a thin filament of dye in the centre of the pipe remained coherent, whereas for turbulent flow the filament of dye was broken up by the action of the turbulence or turbulent eddies. 

Example 6-4 The double-pipe heat exchanger is essentially a set of concentric pipes. One fluid flows within the smaller pipe and the other in the torus or annulus. 

The pressure drop (AP) for fluids flowing through pipe lines of any diameter may be approximated by the following formula. I ve checked this correlation in the field. Caution This formula only applies if viscosity is low and flow is turbulent. By low viscosity, I mean something less than 2 or 3 cP, or perhaps 10 SSU (seconds saybolt universal). Water, warm diesel oil, and hot gas oil all fall within this category. 

High-pressure fluid flows into the low-pressure shell (or tube chaimel if the low-pressure fluid is on the tubeside). The low-pressure volume is represented by differential equations that determine the accumulation of high-pressure fluid within the shell or tube channel. The model determines the pressure inside the shell (or tube channel) based on the accumulation of high-pressure fluid and remaining low pressure fluid. The surrounding low-pressure system model simulates the flow/pressure relationship in the same manner used in water hammer analysis. Low-pressure fluid accumulation, fluid compressibility and pipe expansion are represented by pipe segment symbols. If a relief valve is present, the model must include the spring force and the disk mass inertia. 

Convection is the heat transfer in the fluid from or to a surface (Fig. 11.28) or within the fluid itself. Convective heat transport from a solid is combined with a conductive heat transfer in the solid itself. We distinguish between free and forced convection. If the fluid flow is generated internally by density differences (buoyancy forces), the heat transfer is termed free convection. Typical examples are the cold down-draft along a cold wall or the thermal plume upward along a warm vertical surface. Forced convection takes place when fluid movement is produced by applied pressure differences due to external means such as a pump. A typical example is the flow in a duct or a pipe. 

Conservation is a general concept widely used in chemical engineering systems analysis. Normally it relates to accounting for flows of heat, mass or momentum (mainly fluid flow) through control volumes within vessels and pipes. This leads to the formation of conservation equations, which, when coupled with the appropriate rate process (for heat, mass or momentum flux respectively), enables equipment (such as heat exchangers, absorbers and pipes etc.) to be sized and its performance in operation predicted. In analysing crystallization and other particulate systems, however, a further conservation equation is... 

Fluid power equipment is designed to reduce friction as much as possible. Since energy cannot be destroyed, some of the energy created by both static pressure and velocity is converted to heat energy as the fluid flows through the piping and components within a hydraulic system. As friction increases, so does the amount of dynamic and static energy that is converted into heat. 

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. 

Example 4-1 Manometer. The pressure difference between two points in a fluid (flowing or static) can be measured by using a manometer. The manometer contains an incompressible liquid (density pm) that is immiscible with the fluid flowing in the pipe (density pf). The legs of the manometer are connected to taps on the pipe where the pressure difference is desired (see Fig. 4-2). By applying Eq. (4-7) to any two points within either one of the fluids within the manometer, we see that... 

Flashing liquids escaping through holes and pipes require special consideration because two-phase flow conditions may be present. Several special cases need consideration.17 If the fluid path length of the release is short (through a hole in a thin-walled container), nonequilibrium conditions exist, and the liquid does not have time to flash within the hole the fluid flashes external to the hole. The equations describing incompressible fluid flow through holes apply (see section 4-2). 

If the fluid in the pipe is in turbulent flow, the effects of molecular diffusion will be supplemented by the action of the turbulent eddies, and a much higher rate of transfer of material will occur within the fluid. Because the turbulent eddies also give rise to momentum transfer, the velocity profile is much flatter and the dispersion due to the effects of the different velocities of the fluid elements will be correspondingly less. 

Mass transfer can be definnd simply as the movement of any identifiable species from one spatial location to another. Tha mechanism of movement can be macroscopic as in the flow of a fluid in a pipe (convection) or in the mechanical transport of solids by a conveyor belt. In addition, the transport of a panicolar species may be the result of madom molecular motion (molecular diffusion) or randum microscopic fluid motion (eddy or turbulent diffusion) in the presence of a composition gradient within a phase. This chapter is concerned primarily with mass transfer owing to molecular or microscopic processes. 

Because the conditions of flow at the entrance to a tube differ from those well downstream from the entrance, the velocity field and the associated temperature field may depend on the distance from the tube entrance. Also, in some situations the fluid flows through a preliminary length of unheated or uncooled pipe so that the fully developed velocity field is established before heat is transferred to the fluid, and the temperature field is created within an existing velocity field. 

When a fluid flows through an orifice plate, the static pressure within the pipe varies as illustrated in Figure 4.13. Notice that just upstream of the orifice plate the static pressure reaches a maximum value. When the fluid passes through the bore of the plate it accelerates. As the fluid jet exits the other side of the plate it continues to accelerate and decrease in cross-sectional area hence, the minimum flow area is actually smaller than the area of the orifice. The location where the jet reaches its minimum cross-sectional area is referred to as the vena contracta and is where the velocity is the highest and the... 

In Chapter 5 the need for a concentration gradient to drive the mass transfer process was discussed. Fig. 7.1 shows the particle concentration profile within a fluid flowing through a pipe under turbulent conditions. In terms of the rate of deposition the transport of particles to a surface can be defined by... 

Estimating the size of the smallest length scale is relatively simple. One could use computational fluid dynamic modeling techniques or estimate them based on the power input to the system (head loss) and the mass of the fluid being powered. For example, in pipe flow, the energy dissipation rate is a function of the total head loss in the flow h, the volumetric flow rate Q, the density of the solution p, and the mass of the solution m, which in this case is the mass of fluid contained within the pipe [Equation (4.1-3)]... 

The shear stresses within the fluid are responsible for the frictional force at the walls and the velocity distribution over the cross-section of the pipe. A given assumption for the shear stress at the walls therefore implies some particular velocity distribution. In line with the traditional concepts that have proved of value for Newtonian fluids, the turbulent flow of power-law fluids in smooth pipes can be considered by dividing the flow into three zones, as shown schematically in Figure 3.12. 

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