# The Connotation Of Capsule Pipelines Biology Essay

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I feel very fortunate to be able to work under the supervision of Prof. Rakesh Mishra. Prof. Rakeshs constant help and support throughout the project has been deeply appreciated. Prof. Rakesh's help and support exceeded the formal relationship of supervisor and has often showed the warmth to help all his students and be a great deal of inspiration.

My deep appreciation for all the help and support provided to me by postgraduate researcher Taimoor Asim. Despite his own work pressure he has always showed patience to help me at every occasion. For all his efforts I cannot thank him enough.

In addition, I would like to thank my wife for showing the great deal of help and support throughout my project.

I appreciate the support and help of the University of Huddersfield student support staff that were very polite and friendly during the difficult time of war in my home country (Libya).

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## SUMMARY

The connotation of capsule pipelines has become increasingly common over time, the idea of hydraulic capsule pipeline (HCP), but still a fairly new phenomenon and there is relatively little research and study in this area. It was therefore selected as the focus of this research.

For the aims of this study, Computational Fluid Dynamics (CFD) was used. CFD is a useful tool for the analysis of pipe flow problems. Optimization and analysis of the capsule may be performed by problems such as FLUENT CFD packages.

The behaviour of a drop in pressure three, trains-capsule was studied under the effect of various bulk speed and the diameter of the capsule altered. The results obtained from the study concluded that the pressure drop in a tube increases as the concentration increases the size and capsules.

Using the results obtained from CFD, a mathematical correlation has been derived from the pressure drop in a capsule transport hydraulic line. The correlation is consistent with experimental data and theoretical. In addition, an effective method to optimize the tubes which carry the capsule has developed along the correlation with the pressure drop at constant density spherical capsule train in a hydraulic.

There are several recommendations for further studies and research from both CFD and experimental analysis of flow problems of the capsule.

## Chapter 1

## Introduction

## Chapter 1: Introduction

## Introduction to capsule Pipelines:

The capsule of transport refers to any system which involves the transport of goods (solids) capsules (containers or vehicles) driven by the fluid moves through a pipe.

This trend is commonly covered by department stores, hospitals and factories, in which the documents and the samples are often small cylindrical containers transported through tubes of small diameter, but are usually transported in a vacuum instead of being transported by the fluid. When used to push the fluid in a pipe of air or other gas , is known as a pipeline capsule tire (CFP), when the fluid to push the capsule is water or other liquid, which is known as a capsule tube hydropower(SHP).

Both the PCP and the PS have different characteristics and have windows of opportunity, this new technology can be used commercially

For the carriage of cargo, including coal, other minerals, solid waste, mail, packages and many other products. In PCR, capsules are introduced into the flow of water along a conduit.

When the water is moving at a low speed capsules slide along the floor

Of the tube, however, once the flow rate increases adequately, lift is generated (similar to that of an airplane) and the capsule becomes in waterborne. At this point , the transport of the capsule only require 10- 30% more energy than would be necessary for the flow of water of alone. The three main types of pipelines are carrying liquids, sludges and mineral filled capsules. The third type of tube is a recent invention and it is becoming increasingly common.

The capsules used in this type of pipe are empty containers of spherical or cylindrical. The capsules used in this type of pipe are empty containers of spherical or cylindrical. Industries related to hazardous liquids, minerals perishables, pharmaceuticals, cement powder can effectively use this means of transport to their advantage.

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The advantage of capsules tubes are many .For example, the fluid phase separation and of the transported materials is not necessary, transported materials are available in the original /dry on the target so that no additional cost incurred as a result of drying of materials, the carrier fluid is not contaminated and therefore, can recycled material to be transported being held back in its original properties, and piplines of the capsule were found to be generally more economical than slurry pipelines(1). The containers used as capsules generally rigid structures, however, can also have a flexible structure. Flexible can capsules negotiate the curves and go under the valve openings easily. The capsules can be loaded at different densities and thus the density of macro-capsules may be lower, equal to or higher than the carrier fluid. Such capsules are called lower density of density equal to or neutrally buoyant and increasing the density of the capsules, respectively.

There are many physical factors that influence the transport of a capsule inside of a pipeline. For example bends and branching points all affect the capsule flow in inclined or declined sections. therefore, it is necessary to determine various parameters to evaluate the hydraulic flow capsule. In addition, relations between the parameters and the ratio of capsule/liquid velocity ration and pressure gradient must be checked.

To determine and calculate the parameters that affect the flow of a capsule, a series of technical terms and formulas must be applied and understood. These are the following:

1-Newtonian Fluid.

2-Reynolds Number.

3-Friction Losses:

The Darcy- Weisbach Equation.

Blasius Equation.

Fanning Friction Factor.

The Colebrook- White Equation.

Moody's Chart.

4-Boundary Layer in pipes.

5-Magnus Effects.

Above Terms have Discuses again in Section 1.2:

## 1.2 Definition of Terms

## 1.2.1 Newtonian Fluid

Newtonian Fluids are Fluids whose stress versus rate of the strain curve is linear and The amount of the viscosity is independent of the speed of cut and can vary greatly with the temperature can be regarded as a constant for a certain fluid and a temperature passes through the origin. The constant of proportionality is known as the viscosity (2)

Simplified form of equation to explain Newtonian fluid behaviour is:

Where;

Is the shear stress applied by the fluid.

Is the fluid viscosity

(du/dx) Velocity gradient perpendicular to the direction of shear

In other terms, the fluid keeps on flowing, regardless of the forces acting on it. For example, the water is Newtonian, because it follows an example of fluid properties, regardless of the speed is stirred or mixed. This contrasts with the non-Newtonian fluid, in which stirring can leave a "hole" behind which fills gradually over time. This behaviour is seen in materials such as starch pudding in water to cause the fluid to be thinner and the drop in viscosity, making the flow more (3).

## 1.2.2 Reynolds Number

In fluid mechanics, the Reynolds number (Re) is a dimensionless number that dives shows of the ratio of inside forces to viscous forces, and therefore, amounts the relative importance of these two types of forces given flow conditions.

Reynolds number is defined as:

Reynolds Number =Inertia/Viscous forces

Re= (

(Ï) Density of fluid

(v) Velocity of fluid

(L)Length of the pipe in which the fluid is flowing (4).

Laminar flows are unstable to small disturbances, when the viscous forces are sufficiently small component of the force balance of the total. The laminar flow occurs at low Reynolds number, where the viscous forces are dominant, and is characterized by a smooth, constant fluid, whiles the turbulent flow, however, occurs at high Re and is dominated by the forces of inertia, producing vortices random fluctuations of the vortices and other flow(5).

## 1.2.3 Friction losses

When the fluid flows inside the pipe, the roughness of the wall of the inner the pipe can create local eddy currents within the fluid by adding a resistance to fluid flow. These eddy currents and the ratio of the roughness of the internal pipe diameter of the inner pipe should be considered to be able to determine the friction losses. This can be shown using the following equations:

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Examples of our work(a)The Darcy-Weisbach Equation

(b)Blasius Equation

(c) Fanning Friction Factor

(d) The Colebrook-White Equation

(e) Moody's Chart.

Every of the above has been discussed in feature below.

(a)The Darcy - Weisbach Equation

The Darcy-Weisbach in 1850 was to express the loss of pressure in a piping system.

The number of Velocity heads (V2/2*g) lost by a pressure drop DP is expressed by the product of the (f), the factor of friction and the geometric factor (L/D). The factor of friction for the velocity profile fully developed for both laminar and turbulent .On (f) on other hand can mean the factor of friction in the pipes, both smooth and rough. (F)Darcy-Weisbach is a complex function of Reynolds number and relative roughness. The pipe roughness is the ratio of the pipe surface roughness 'e' to its diameter (D) or

f=f (Re,

Pipe roughness is not a factor and expression for laminar flow where;

f=64/Re

(b)Blasius Equation

In turbulent flow for hydraulically smooth pipes (example glass, copper and plastic piping the Blasius equation is used for (f) :

f=0.3146 /Re0.25 (4,000 <Re < 100,000)

http://ars.els-cdn.com/content/image/1-s2.0-S0894177711000161-gr5.jpg

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## Figure 1: The experimental friction factor with the Blasius equation

(c)Fanning Friction factor

Using the following formula, the friction head loss in pipe flow with a full and appropriate Fanning friction factor can be calculated.

hf= ff (L/Rh)*(V2/2g)

Where;

hf=head loss (m)

ff= Fanning friction factor

L= length of pipe work (m)

Rh=hydraulic radius of pipe work (m)

V= Velocity of fluid (m/s)

g= acceleration due to gravity (m/s2)

The above formula is very similar to the Darcy-Weisbach formula but the hydraulic, radius of the pipe should be used not the diameter.The hydraulic radius calculation consists on dividing the cross-sectional area of flow through the wetted perimeter.

To around pipe with the total flow of the hydraulic radius is equal to aquarter of the diameter of the pipe, i.e.

Cross sectional area of flow/ Wetted perimeter= (Ï€

(d)The Colebrook-White Equation

It provides a mathematical method to calculate the friction factor (for the pipes which are neither totally smooth nor completely rough) is the factor of friction (f) term on both sides of the formula and is difficult to resolve without trial and error (ie mathematical iteration is usually necessary to find (f) (7). For conduits which is filled with fluid Reynolds number (R) greater than 4000, is defined as:

(e) Moody's chart

Moody's is used to calculate the friction in pipes(f) as shown in the figure 2 below.

http://maji.utsi.edu/courses/02_fluids/sheet_f6_Moody_chart.jpg

## Figure 2: Moody's chart of Friction Factor

## 1.2.4 Boundary Layer in Pipes

In the beginning as the flow enters a pipe of the boundary layer is laminar from.Other changes in the level depends on the ratio of inertial and viscous forces, i.e., if a higher viscous forces (laminar flow) or high inertial forces (turbulent flow).

http://www.cartage.org.lb/en/themes/sciences/physics/mechanics/fluidmechanics/RealFluids/BoundaryLayers/img00035.gif

http://nuclearpowertraining.tpub.com/h1012v3/img/h1012v3_40_1.jpg

## Figure: 3 Velocity profiles and Boundary Layers for Laminar and Turbulent Flow

If the flow is laminar only, the profile is parabolic, as only the first part of the diagram of growth of the boundary layer is used as shown in Figure 3(a). If the flow is turbulent (or transition), both the laminar and turbulent (transitional) areas of the diagram of growth of the boundary layer is used as shown in Figure 2 (b). Once the boundary layer has reached the middle of the flow pipe, it is called fully developed.

## 1.2.5 Magnus Effects

Named after the German physicist and chemist HG Magnus, who first (1853) studied experimentally the effect, Magnus effect, refers to the generation of lateral force in a spinning cylindrical or spherical solid immersed in a fluid (liquid or gas) when there is a relative movement between the rotating body and the fluid.

Rotation of an object moving through a fluid, out from its rectilinear path due to pressure differences that develop in the liquid as a result of speed variation induced by the rotating body. The Magnus effect is a particular demonstration of Bernoulli's theorem: the fluid pressure decreases at the points where the fluid velocity increases.

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F V

## Figure 4 effect of a capsule spinning in a fluid

When a body, such as a circular cylinder or sphere rotates in a fluid that creates a boundary layer around itself, and the boundary layer induces a circular motion largest of the fluid. If the body fluid moves by the (V) speed then the speed of the fluid near the body is slightly greater than (V) on one side, and slightly less than (V) on the other side. The reason being the velocity created by the boundary layer surrounding the rotating body is added onto (V) on one side, and is subtracted from the (V) on the other side. In accordance with Bernoulli's principle, if you increase the velocity of the fluid pressure decreases, and in which the velocity is low, the fluid pressure is higher. Effect of the difference in velocity of the fluid on each side of the body, fluid Pressure is different causing a force on the body as shown in Figure 4. The force acting in a direction to move the body perpendicular to the vector representing the velocity of the body is relative to the fluid (8).

## 1.3 Capsules Transport in a Hydraulic Pipeline

## 1.3.1 General Features of Hydro- capsule system

A transport system of capsules, either hydraulic or pneumatic, is generally composed of several common characteristics. The essential components are: a housing, means of transport (in solid form in bulk within the capsule), the pipeline, the fuel (gas or fluid), and some sort of conveying device. Booster pump stations and terminals are held in every system and share many of the advantages of the capsule system can provide compared to other forms of transport of solids. To transport the medium through a capsule, pipeline first must be enclosed in a capsule which can be cylindrical or spherical. The capsule is then introduced into the pipeline through the injection device and then transported by the fluid or gas already present inside the pipeline.

## 1.3.2 The capsules

The capsules used for hydraulic transport systems, as mentioned above can be cylindrical or spherical. It was recognized that the spherical capsules can exhibit favourable power requirements for the transmission of high-density materials. Capsules mostly have a diameter of up to 85% of the inside diameter of the pipe. The length can vary but is typically about five times the size of the diameter. The containers which are empty, generally used as a rigid structure, but these can also be flexible at times. Soft capsules have the advantage of overcoming the bends can pass under the openings of the valve easily. The capsules can be loaded at different densities depending on the needs and thus the macro -density of the capsules may be lower, equal to or greater than the carrier fluid. These capsules are called less density, equal to or neutrally buoyant and increasing the density of the capsules, respectively. Since the density of the propellant fluid (usually water) is relatively close to the actual density of the capsules, is usually a requirement for the capsules must be equipped with wheels. Some confusion regarding the use of the "word capsule applied to the solid cylinders or spheres made from the material to be transported, while hydrodynamic considerations generally not be influenced by the fact that the capsule is hollow or solid. Semi - hard capsules represent another approach to the movement of solids by means of hydraulic lines, flexible container is generally available in such a way that the problem of the return empty containers is eliminated and a single pipeline can be used.

## .

http://ars.sciencedirect.com/content/image/1-s2.0-S0301932206001947-gr4.jpg

## Figure 5 capsules in pipeline.

## 1.3.3 Pipeline

One reason that the hydro - transport system capsule has difficulty to compete with conventional mineral slurry is the need for two pipes between the terminal for loading and unloading, one for the completion of the filled capsules and one for which it is empty again. Not surprisingly, there has been considerable interest in alternative pipeline which will carry the advantages of a capsule to obtain with only a single pipe. For the transport of coal, it has been suggested that over short distances (less than 10 km) conveyor belts, trucks or pipelines dense suspension may be more convenient than a double hydraulic line - capsule system, and for long distances (500 km) the thin pipeline is likely to be the better option. Only in the mid range of 10 - 500 km double capsule pipeline system to be competitive, but if a system can be designed to use only a single pipeline, the capsules are much more attractive.

For the applications of short distance, it may be feasible to pump the capsules to a first side and then the other through a single pipeline. However, the "dead time", while the capsules are empty represents a significant loss, and the fleet size would be considerably larger to compensate temporarily out of capsules.

## 1.3.4 Water supply and pump system

The hydrodynamic movement of the capsule is quite complex. The water flow rate through the pipeline must be sufficiently high to ensure that the capsules are clear of the walls of the pipe. To achieve this goal, the speed of the capsule to exceed the value corresponding to lift "- off 'where the capsule reaches a nose - attitude, and off the pipe wall. In order to use a hydraulic pipeline for the transport of capsules over long distances, the pressure of the carrier fluid must be raised on various known intervals as 'booster stations'. The main challenge in these 'booster stations' is to increase the pressure with minimal disruption to transport the capsule. To overcome this there are two possible approaches for increasing water pressure with conventional pumps (taking the capsules in a provision of crash), or use a pump more complex through which the capsules can be passed with minimal disturbance.

## 1.3.5 Injection and Ejection of capsules

The capsules may be introduced into the pipeline through a series of different resources. A common example is that of a lock - injector which is similar in layout to the by - step scheme of booster stations. At the point of exit of the pipeline, the capsules naturally flow from the water pipe, so that no special equipment is needed to discharge them. However, an automated system is required for collecting capsules and transmits to the terminal in which its contents are emptied, cleaned and then either buffered or sent through the return pipe.

## 1.3.6 Size of Capsule Fleet

An important consideration in the design of a capsule pipeline, pneumatic or hydraulic, is the size of the total fleet of capsule required. This number should include capsules in active service, in addition to an adequate number of services either for routine maintenance, or in a state of alert in respect of scheduled maintenance or breakdown. The following analysis is a method for determining the size of the fleet of capsules, capsules-dependent design, i.e. line length, running speeds, terminal turn - round times, annual input and operating hours.

Given the (load) line overhang, if (N1) is the number of capsules in line of length (L), and (V1) is their velocity, which reach the destination at a speed of capsules per unit of time:

(V1*N1)/L

If the mass of the load in each capsule is mc, instantaneous flow rate of through the load line can be expressed as:

ms = (mc*v1*N1)/L

Capsules should be returned to the loading point at the same rate, and therefore, assuming that the output line and return have the same length:

(V2*N2)/L = (V1*N1)/L

Where N2 is the number of capsules in the line and V2 is its velocity. Therefore: N2=N1*(V1/V2)

And the total number of active capsule in the pipeline is given by:

NP = N1+N2 NP = N1+ {1+ (V1/V2)}

NP = {(ms*L)/(ms*V1)}*{1+(V1/V2)}

As regards in terms the required annual throughput (tons / year), the number of active capsules can be written as:

NP = {ma/ (3.6*ha)}*{L/ (mc*V1)}*{1+ (V1/V2)}

Where ha is the annual system operation (hours / year), taking into account downtime for regular maintenance, shutdown at weekend, and so on.

Active capsules will also be passed through the terminals and the number of capsules participate therefore depend on the proportion of the total cycle which is actually spent in the terminals. Now, the time required for a capsule to travel along the outlet pipeline is:

t1=L/V1

And for return line is:

t2=L/V2

So that the total time in the pipeline is:

t1+t2= (L/V1) + (L/V2) = (L/V1) + {1+ (V1/V2)}

So, if the time spent in the loading station and is ta in the unloading station is tb, the total cycle time is:

tcycle= ta+t1+tb+t2

The time number of active capsules in the system is:

Ntotal= Np*{tcycle/ (t1+t2)}

Ntotal= {ma/ (3.6*ha)}*{(L/mc*V1)}*{1+ (V1/V2)}*{tcycle/ (L1/V1)+(1+(V1/V2)}

Or: Ntotal= (ma*tcycle)/ (3.6*ha*mc)

The size of the capsule fleet exceeds this total by a small number to allow the standby mode in case of breakdowns.

## 1.4 Computational Fluid Dynamics:

## 1.4.1 Introduction

Computational fluid dynamics or CFD analysis or related systems of fluid flow, heat transfer and associated phenomena such as chemical reactions by means of computer - based on simulation. The technique is very powerful and covers a wide range of industrial and non - industrial application areas. Starting in 1960, onwards the aerospace industry has integrated CFD techniques in the design, R&D and development and production of jet engines. Additional in recent times, the method has been applied to the design of internal combustion engines, combustion chambers of gas turbines and furnaces. In addition, car manufacturers now routinely predict resistance drag forces, under - bonnet air flows and the in-car environment with CFD. Is increasingly CFD is becoming a vital element in the design of industrial products and processes. The variable cost of an experiment in terms of hiring structures and / or person - hour costs, is proportional to the number of data points and the number of test configurations. in contrast, CFD codes can produce very large volumes of results in practically no additional cost, and is very economical to perform parametric studies, for example, to optimise equipment performance (27).

## 1.4.2 Working of CFD Code.

CFD codes are structured around the numerical algorithms able to deal with the problems of fluid flow. In order to provide easy access to their solving power, all commercial, CFD packages include sophisticated user interfaces in the input parameters and problems to examine the results. Therefore, all the codes contain three main elements. These are:

Pre - Processor

Solver

Post - Processor

Pre - processing consists of the input of flow problem the CFD program through an operator. Friendly interface and the subsequent conversion use this input in a form suitable for use by the solver. User activity in the pre - processing includes defining the geometry of the region of interest. It is called the computational domain. Grid generation is the sub-division of the domain into a series of smaller, -overlapping sub-domains. It also called mesh. Selected physical or chemical phenomena that must be modelled, defining the properties of the fluid and the specification of the boundary conditions in the cells that overlap, with or touch the domain boundary is also included in pre-processing (27). There are three separate streams of numerical solution techniques. There are Finite differences, finite elements and spectral methods. Finite volume method, a special formulation of finite differences, is essential for a major - consolidated CFD. The numerical algorithms includes integration of the equations of fluid flow through all control volumes in the domain, or the conversion of discretization of the integral equations resulting in a system of algebraic equations and solve these equations by an iterative method. Due to the growing popularity of engineering workstations, many of which have excellent graphics capabilities, leading CFD packages are now equipped with versatile data visualisation tools. These include the geometry of the domain, grid display, vector graphics, contour plots land, 2D and 3D surface plots, particle tracking, view manipulations, colour post - script output etc. More recently, these structures may also include animations to display dynamic result, and in addition to all the codes produce graphic output and have confidence export alphanumeric codes for further manipulation outside. As in many other branches of the CAE, the ability of graphical output of CFD codes have revolutionized the communication of ideas for non - specialists (27).

## 1.4.3 Governing Equations of Fluid flow

The equation representing the flow of the fluid mathematical propositions of the conservation laws of physics:

The mass of a fluid is conserved

The rate of change of momentum equals the sum of the forces on a fluid particle. (Newton's second law).

The rate of change in the energy is equal to the sum of the rate of addition of heat and the working speed of a fluid particle. (First law of thermodynamics).The fluid is considered as continuous. For the analysis of fluid flow in macroscopic length scales, the molecular structure of the material and molecular motions can be ignored. The behaviour of the fluid is described in terms of macroscopic properties, such as velocity, pressure, density and temperature, etc. These are the averages more conveniently a large number of molecules. particle of fluid or point in a fluid is then the smallest element can, whose macroscopic properties of fluid are not influenced by the individual molecules.

## Mass conservation in 3D

The first step n the derivation of the mass conservation equation is to write down a mass balance equation for the fluid element:

Rate of increase of mass in = Net rate of flow of mass into

Fluid element fluid element

For fluids, as the density is constant, the mass conservation equation is:

Div u=0

This equation describes the net flow of mass through the element's borders. The above equation in the notation of writing can be written as:

This equation represents the unstable, three - dimensional conservation of mass or continuity at a point in an incompressible fluid.

## Momentum Equation in 3D

Newton's second law states that the rate of change of momentum of a fluid particle is equal to the sum of the forces acting on the particle:

Rate of increase of Momentum of = Sum of flow of forces on fluid particle fluid particle.

There are two types of forces acting on the fluid particles. These are surface forces and the body forces. Surface forces include the forces of pressure, viscosity and gravity while the Carioles forces include centrifugal body and electromagnetic forces.

And 'common practice to highlight the contributions due to surface forces as independent terms in the equations of motion and include the effects of the forces of the body as source terms. The x - component of the equation of motion is to determine the rate of change of x - momentum fluid particle equal to the total force in the x - direction in the element due to the surface tension and increase the rate of x - momentum due to the sources. The equation is as follows:

The y and z - component of momentum equation are given by:

The signal associated with the pressure is opposite to that associated with normal viscosity voltages because the usual sign convention performs a tensile stress such that the normal positive pressure, which by definition is a normal compressive force has a minus sign with it. The effects of surface stresses are accounted into account explicitly, source terms SMX, SMY and SMZ in above equations include contributions due to body forces only.

## Energy Equation in 3D

The energy equation is derived from the first law of thermodynamics which states that the rate of change of energy of a fluid particle is equal to the heat addition to the fluid particle plus the rate of work on the particle:

Rate of increase of Energy of fluid particle =

Net rate of heat added to fluid particle + Net rate of work done on fluid particle

Energy saving of fluid particle is ensured by equating the rate of change of energy of the particles of fluid to the sum of the net rate of work on the fluid particle, the net rate of addition of heat to the fluid and the rate of increase of energy due to the sources .The energy equation is:

## +

## Equations of state

The movement of a fluid in three dimensions is described using a system of partial differential equations five i.e. conservation of mass, motion equations x, y and z and energy equation. Among the thermodynamic variables are four unknowns that is, the energy density, pressure, temperature and internal. The relations between the thermodynamic variables can be obtained through the assumption of thermodynamic equilibrium.

Fluid velocity can be great, but they are generally so small that, even if the properties of a fluid particle moving quickly from one location to another, the fluid thermodynamic can adapt to the new conditions change so rapidly that are effectively instantaneous. Thus, the fluid always remains in thermodynamic equilibrium. The only exceptions are some flows with strong shock waves, but also some of those are often sufficiently approximated by the assumption of equilibrium. The state of a substance in thermodynamic equilibrium may be described by means of only two state variables. The equations of state that refers to another variable densities, two state variables and temperature. The equations of state are:

P =P (

And i=i(

Liquids and gases flowing at low speed behave as incompressible fluids. Unchanged density there is no connection between the energy equation, the equation of conservation of mass and momentum equations. The flow field can often be solved by considering mass conservation and momentum conservation equations only. The energy equation needs to be solved only with the other if the problem is related to heat transfer.

## Nervier- Stokes equations

In a Newtonian fluid, the viscous stresses are proportional to the rates of deformation. The liquids are incompressible; viscous stresses are just twice the local rate of linear deformation times the dynamic viscosity. The Nervier- Stokes equations are:

## Chapter 2

## Literature Review

## 2 Literature Review

## 2.1Historical Studies and Developments in Capsule Pipelines

Pneumatic capsule systems were initially established in England in the 1820, which came after an English engineer, George Midhurst, had suggested that the letters and the goods can be transmitted at high speed through small diameter pipes. This concept later became known systems often used in department stores, factories and hospitals, for documents and small objects are transmitted through cylindrical containers in small diameter pipes that often operate under a vacuum. During the 19th century, the Company Pneumatic despatch undertook considerable developments of the pneumatic capsule concept. They laid an experimental pipe along River Thames which carried parcels at a velocity of about 7.5 m/sec via wheeled capsules. Later the Pneumatic Despatch Company has been developed a system of tunnels in London for transporting letters and parcels. Other developments in pneumatic capsule pipelines include transportation of minerals and broken stone in the Soviet Union at the rate of 4 million tons / year over a distance of 6 km, and 2.4 million tons / year through a distance of 50 km, respectively. in contrast, ,hydraulic capsule transport has been developed more recently. Despite originated in the 1960 in Canada, currently extensively studied in the United States, Japan and South Africa, with a series of technical documents being published. Capsule pipelines have been studied in depth by various individuals prior to 1975; however, little work has been carried out on the actual design of a capsule pipeline. In most studies, researchers have developed various methods for sizing of hydraulic pipelines. The most obvious examples are Albertson et al. (9)Hathoot et al. (10) Cheremisinoff et al. (11), and Daugherty and Franzini (12). All these individuals optimised the size of the pipeline by minimizing the total cost (1). For studies on capsules, which were held for the first time in 1960 by researchers at the Research Centre in Alberta, Canada. Many studies have been carried out on materials that were or density greater than or equal to the fluid carrier. Studies in 1970 focused in the flow characteristics of the individual capsules were either cylindrical or spherical.

As these studies were carried out on a single capsule, it was found that the increase in the pressure gradient was small, therefore, the additional pressure gradient measurements have not been studied and instead is postponed may be studied in continuous flow systems with capsules started. These studies have been limited to measurements of the velocities of the liquid transport and distribution of the forces affecting the surface of the capsules. The carrier liquid in the studies was generally water, even if a polymer is added in some cases, to increase the viscosity of the carrier fluid(13)(14). The addition of surfactants or polymers generally decreased pressure drop (drag reduction effect) (15). Kruyer & Ellis (13) carried out speed measurements in a Plexiglass pipe with a length of 10 m and an internal diameter of 0.04 m. on single spherical capsule flow with equal density (16). It has been found that the speed of the capsules (vc) with a higher speed between 0.06 and 3.7 m / s is 1.05 to 1.5 times the speed bulk (vm). Govier and Aziz [17] have defined the relationship between the velocity of the capsule and the flow velocity in the upper spherical capsule by a coefficient (VC = coVm). They have stated that this distribution coefficient might assume a co value between 1.0 and 1.2 when the capsule is in concentric position and have a capsule to pipe diameter ratio of 0.8-0.9 (17). The results of studies in individual capsules cannot be assumed to reflect the results of the measurements made on capsule trains. Therefore considered necessary to conduct studies addressing trains capsule, which were conducted in 1970s. Previous studies involved a capsule train suspended inside a pipe. The mechanism of flow and the train behaviour has been studied. Studies revealed that the gradient of pressure increase, as the density of the capsule increased (13). Until the 1970 have been developed mathematical models to calculate the pressure drop in the flow of a spherical capsule train whose density is lower than the carrier liquid inside horizontal pipes. Some empirical expressions presented in experimental studies involving the internal capsule flows from vertical tubes (18) (19) (20). Flow in a horizontal pipe is different from flow in a vertical pipe. Capsules movement within a vertical pipe, the results of the movement of the carriage simply exerted by the water on horizontal pipes; however, there is no oscillating movement or loss of friction surface. Developed empirical expressions for pressure drops in the flow of the capsules in a vertical tube, thus cannot be used for the capsule flowing in a horizontal pipe. Govier and Aziz [21] performed on the theoretical analyses friction factor, flow properties and characteristics of the pressure drop observed in the flow of the capsule in a pipe. The preceding studies and their results were reviewed to develop models that cover both concentric and non-concentric flows capsule for practical applications. It draws attention to the fact that until 1972 no study was done in spherical capsules hydraulic whose density is close to or below the water and has not carried out a theoretical analysis of the pressure drop in the flow of concentric spherical capsules or concentric. An analogy was made with the Taylor bubbles in vertical pipes at normal velocities and for 0.8-0.9 values of the diameter ratio, so that it was calculated that Rv Â¼ 1.2 for the expression Vc Â¼ RvVb. Govier and Aziz was shown that [21] by using the density of the mixture and the mixing rate can be determined pressure drop as a pressure drop caused by single- phase liquid flow.

Agarwal and Mishra [1] conducted a study on the optimal size and the optimal distance between two pumping stations for a spherical capsule pipeline. They found that as the capsule density increased, the friction coefficient increased too. The friction coefficient decreases whenever the Re value increases. Their study suggests that the mixture of liquid capsule as a homogeneous single-phase current according to the conclusions reached by Govier and Aziz [21] in the pressure drop and velocity of spherical capsules.

## Figure 6: Pressure drop expressions for different flow conditions developed by various authors (24).

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## Prediction of single phase pressure dropÂ fromÂ variousÂ correlations.

Teke and Ulusarslan have conducted deeply studies on the works of previous researchers in the field of spherical capsule trains. From these studies, and studies have been conducted a number of conclusions, a summary of the results on mathematical expressions of the pressure gradient is shown in Figure6. An experimental setup, related to actual capsule pipelines, was formed by Ulusarsalan and Teke (22). The test part was created using horizontal Plexiglas pipes that were 6m in length and had an internal diameter of 0.1m. Measuring the pressure drop was carried out on the 4m section of the Plexiglas pipe. Two pressure taps were associated through piezometric hoses to the ends of a degree of difference pressure transmitter used for measuring pressure drops with a space of 4m between them. The capsules are rigid structure, spherical in shape, with a exact gravity of 0.87 and a diameter ratio of 0.8. Pressure drops were measured at 1.2x104 <Re <1.5x105 and transport at low concentrations of 5-30% (23). In addition to the observations of pressure drop, Ulusarsalan and Teke also studied several other trains spherical capsules. These include:

Experimental investigations of the speed of the capsule, the concentration ratio and the space between the capsules.

Comparison between the gradient of correlation pressure for the flow of train spherical capsule.

Statistical expression of pressure inclines in the flow of spherical capsules.

Relationship between the friction coefficient and Reynolds number for the train spherical capsule in a horizontal pipe.

## 2.2 Current Applications

HCP has generated the concept of Coal Log Pipelines (CLP). These use the same principles, except capsule HCP is constituted by a "log" of the load itself, without membrane that encloses. Coal is crushed and compressed into a capsule form. After that the capsule is fed into a pipeline containing a flow of water. Upon arrival at destination, the coal is crushed registered.