Fluid flow examples

Convective heat transfer is classified as forced convection and natural (or free) convection. The former results from the forced flow of fluid caused by an external means such as a pump, fan, blower, agitator, mixer, etc. In the natural convection, flow is caused by density difference resulting from a temperature gradient within the fluid. An example of the principle of natural convection is illustrated by a heated vertical plate in quiescent air. 

A final example of laser measurement techniques is measurement of the velocity of fluid flow (79) (see Flow measurement). If a laser beam is directed into a transparent fluid, some of the light may be scattered with a frequency shift zy given by... 

Normal Stress (Weissenberg Effect). Many viscoelastic fluids flow in a direction normal (perpendicular) to the direction of shear stress in steady-state shear (21,90). Examples of the effect include flour dough climbing up a beater, polymer solutions climbing up the inner cylinder in a concentric cylinder viscometer, and paints forcing apart the cone and plate of a cone—plate viscometer. The normal stress effect has been put to practical use in certain screwless extmders designed in a cone—plate or plate—plate configuration, where the polymer enters at the periphery and exits at the axis. 

Example Buckingham Pi Method—Heat-Transfer Film Coefficient It is desired to determine a complete set of dimensionless groups with which to correlate experimental data on the film coefficient of heat transfer between the walls of a straight conduit with circular cross section and a fluid flowing in that conduit. The variables and the dimensional constant believed to be involved and their dimensions in the engineering system are given below ... 

Examples Four examples follow, illustrating the apphcation of the conservation equations to obtain useful information about fluid flows. 

Example 1 Force Exerted on a Reducing Bend An incompressible fluid flows through a reducing elbow (Fig. 6-5) situated in a horizontal plane. The inlet velocity Vj is given and the pressures pi and measured. 

Example 3 Venturi Flowmeter An incompressible fluid flows through the venturi flowmeter in Fig. 6-7. An equation is needed to relate the flow rate Q to the pressure drop measured by the manometer. This problem can he solved using the mechanical energy balance. In a well-made venturi, viscous losses are neghgihle, the pressure drop is entirely the result of acceleration into the throat, and the flow rate predicted neglecting losses is quite accurate. The inlet area is A and the throat area is a. 

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. 

The galvanic potential of metals can vary in response to environmental changes such as changes in fluid chemistry, fluid-flow rate, and fluid temperature. For example, at ambient temperatures steel is noble to zinc (as in galvanized steel). In waters of certain chemistries, however, a potential reversal may occur at temperatures above 140°F (60°C), and the zinc becomes noble to the steel. 

Consider the example of fluid flow through a filter, where the objective is to maximize flow rate. Assume that the relevant control factors are filter, fluid viscosity and... 

Examples chosen for this category include the operations of vapor/liquid separation, heat transfer, and fluid flow. The Underwood method of estimating the... 

The Lapple charts for compressible fluid flow are a good example for this operation. Assumptions of the gas obeying the ideal gas law, a horizontal pipe, and constant friction factor over the pipe length were used. Compressible flow analysis is normally used where pressure drop produces a change in density of more than 10%. 

The column may be packed or it may be an open tube but in this example, a packed column will be specifically considered. The column is considered to have a length (L) and inlet and outlet pressures and inlet and outlet velocities of (Pi), (Po) (ui) and (uo), respectively. The pressure and velocity at a distance (x) from the front of the column is (Px) and (ux), respectively. According to D Arcy s equation for fluid flow through a packed bed, at any point in the column. 

Computational fluid dynamics (CFD) is the analysis of systems involving fluid flow, energy transfer, and associated phenomena such as combustion and chemical reactions by means of computer-based simulation. CFD codes numerically solve the mass-continuity equation over a specific domain set by the user. The technique is very powerful and covers a wide range of industrial applications. Examples in the field of chemical engineering are ... 

This example demonstrates the dimensioning of a duct with a frictional incompressible fluid flow. Now the Bernoulli equation can be written as... 

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. 

Computational fluid dynamics (CFD) is the numerical analysis of systems involving transport processes and solution by computer simulation. An early application of CFD (FLUENT) to predict flow within cooling crystallizers was made by Brown and Boysan (1987). Elementary equations that describe the conservation of mass, momentum and energy for fluid flow or heat transfer are solved for a number of sub regions of the flow field (Versteeg and Malalase-kera, 1995). Various commercial concerns provide ready-to-use CFD codes to perform this task and usually offer a choice of solution methods, model equations (for example turbulence models of turbulent flow) and visualization tools, as reviewed by Zauner (1999) below. 

An ideal plug flow reactor, for example, has no spread in residence time because the fluid flows like a plug through the reactor (Westerterp etal., 1995). For an ideal continuously stirred reactor, however, the RTD function becomes a decaying exponential function with a wide spread of possible residence times for the fluid elements. 

The total heat duty required to raise a substance from one temperature to another temperature must include an allowance for heat lost to the atmosphere during the process. For example, if the process fluid flows through a coil in a water bath, not only is the water bath exchanging heat with the process fluid, but it is also exchanging heat with the surrounding atmosphere. 

A similar action takes place in a fluid power system in which the fluid takes the place of the projectile. For example, the pump in a hydraulic system imparts energy to the fluid, which overcomes the inertia of the fluid at rest and causes it to flow through the lines. The fluid flows against some type of actuator that is at rest. The fluid tends to continue flowing, overcomes the inertia of the actuator, and moves the actuator to do work. Friction uses up a portion of the energy as the fluid flows through the lines and components. 

It was indicated earlier that the cathodic current was a poor indicator of adequate protection. Whilst, to a first approximation the protection potential is a function of the metal, the current required for protection is a function of the environment and, more particularly, of the cathodic kinetics it entails. From Fig. 10.4 it is apparent that any circumstance that causes the cathodic kinetics to increase will cause both the corrosion rate and the current required for full (/") or partial (1/ — /, ) protection to rise. For example, an increase in the limiting current in Fig. 10.5 produced by an increase in environmental oxygen concentration or in fluid flow rate will increase the corrosion rate and the cathodic protection current. Similarly, if the environment is made more acid the hydrogen evolution reaction is more likely to be involved in the corrosion reaction and it also becomes easier and faster this too produces an increased corrosion rate and cathodic current demand. 

Selection of inspection points therefore, should be based on a thorough knowledge of process conditions, materials of construction, geometry of the system, external factors and historical records. Some of these factors may not be present, for example, when new plant is commissioned. There is greater knowledge now available concerning hydromechanics of fluid flows which should be considered when installation is planned. 

A particular fluid flow problem must have an associated characteristic length L and characteristic velocity V. These values may be more or less arbitrarily specified, with the only constraint being that they represent some typical scales. For example, if the problem involves a flow past a sphere, L could be the diameter of the sphere and V could be the velocity of the fluid at infinity. The characteristic length and characteristic velocity also fix a characteristic time scale T = L/V. 

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