Effect of Pipe Inclination on the Pipe Flow Head Losses For

7/28/2019 Effect of Pipe Inclination on the Pipe Flow Head Losses For

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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 6308

(Print), ISSN 0976 6316(Online) Volume 4, Issue 3, May - June (2013), IAEME

45

EFFECT OF PIPE INCLINATION ON THE PIPE FLOW HEAD

LOSSES FOR DIFFERENT SAND CONCENTRATIONS

Mahmoud Ali Refaey EltoukhyFaculty of Engineering, Shobra, Banha University, Egypt

ABSTRACT

This paper presents results of an experimental study pertaining to the behavior of

sand-water (two-phase) flows in inclined pipes, a phenomenon that is generally witnessed atthe canal intakes which aligned at desert area, and dredging processes. The experiments were

conducted in a modern hydraulics laboratory to study the effect of sand concentration and

pipe inclination on the pipe flow head losses. The pipe inclination angle was varied from 0

to 90 in upward and downward directions and the sand concentration in water was regulated

up to 15% by volume. It was concluded that the head losses of the downward sloping pipe

flow are always lower than the head losses of the horizontal flow and these are always lower

than the head losses of the upward sloping pipe flow, regardless of the concentration and

inclination angle. The experiment results were analyzed in the light of earlier published data

and useful empirical correlations have been developed to determine the head losses of

horizontal flow, alongwith upward and downward sloping pipe flows.

Keywords: head loss, sand - water mixture, inclined pipes, sand concentration

INTRODUCTION

Most of the applications of hydraulic transport in the past have been in the minerals

industries. Generally, such industrial facilities are located in remote areas with insufficient

road or rail infrastructure. Therefore, pipeline transport has been preferred and recognized as

the most cost effective method of transporting huge quantities of minerals over long

distances, across difficult terrain. The solid particles invariably being heavier than the

conveying liquid are transported in lower part of the channel. This unique pattern has been a

subject of special study and is presented in this paper. The effect of flow velocity, sand

concentration and the sloping pipe inclination angle on the head loss were investigated. The

INTERNATIONAL JOURNAL OF CIVIL ENGINEERING ANDTECHNOLOGY (IJCIET)

ISSN 0976 6308 (Print)

ISSN 0976 6316(Online)

Volume 4, Issue 3, May - June (2013), pp. 45-56 IAEME:www.iaeme.com/ijciet.asp

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head losses determined for the horizontal portion of the pipeline were compared with

correlations found in the literature. A pipe loop system was built, allowing variation of flow

velocity, sand concentration and pipe inclination.

OVERVIEW OF THE PRIOR PUBLISHED DATA

Wasp et al., (1999) found that the flow of solid-liquid slurries in pipes differs from the

flow of homogeneous liquids in a variety of ways. The complete range of velocities is

possible with liquids, whereas nature of the flow, i.e., laminar, transition, or turbulent, can be

characterized based on the knowledge of physical properties of the fluid and the pipe system.

The characterization of slurry flow is not as simple as for liquid flow mainly for two reasons:

firstly the properties of the solid particles to be accounted for are superimposed on the

properties of the liquid, and also the effect of the particles on the mixture properties;

secondly, depending on the particular conditions, a range of slurry behavior is possible.

Kaushal et al (2005), and Kaushal and Tomita (2007) carried out experimental study for

concentration of distributions in slurry pipeline by using - ray densitometer. Theirmeasurements show that, pressure gradient profiles of equivalent fluid for finer particles were

found to resemble with water data except for 50% concentration, however, more skewed

pressure gradient profiles of equivalent fluid were found for coarser particles. Experimental

results indicate absence of near-wall lift for finer particles due to submergence of particles in

the lowest layer into the viscous sub layer and presence of considerable near-wall lift for

coarser particles due to impact of viscous-turbulent interface on the bottom most layer of

particles and increased particleparticle interactions.

Richardson, et al., (1999) found that, in homogenous flow systems, the presence of

the solids can have a significant effect on the system properties, usually resulting in a sharp

increase in viscosity as compared to that of the carrier fluid. In heterogeneous flow systems,

solids are not evenly distributed and in horizontal flow, pronounced concentration gradient

exists along the vertical axis of the pipe, even at high velocities. Particle inertial effects aresignificant, i.e., the fluid and solid phases to a large extent retain their separate identities, and

the increase in the system viscosity over that of the carrier liquid is usually quite small.

Heterogeneous slurries tend to be of lower solid concentrations and have larger particle sizes

than homogeneous slurries. Raudkivi, (1989), found that in vertical pipes the velocity of

solids for upward flow is less than the fluid velocity, but is greater for downward flow. The

difference is approximately the value of the settling velocity.

Coiado and Diniz, (2001), studied the solid-water flow in inclined pipes. Based on the

collected experimental data, the adopted methods and the experimental conditions, it was

concluded that the head losses values for the downward sloping pipes are always lower than

the head losses for the horizontal pipe, and these are always lower than the head losses for the

upward sloping pipes, regardless of the inclination angles and concentrations. Whereas, in

case of downward sloping length of water-sand slurry flow, the presence of sand decreases

the head losses values corresponding to the inclination angle and increasing concentration.

C. Kim et al, (2008), made an experimental study on the transport of sand-water

mixtures in circular and square pipelines, focusing on the economic transport of solid

particles. The measured data of the hydraulic gradient, solid effect, and deposition-limit

velocity for both circular pipe and square duct were compared and analyzed. The hydraulic

gradient of water in the circular pipe was found larger than that in the square duct because of

the secondary flow in the square duct. The hydraulic gradient of sand-water mixture in the


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square duct was larger than that in the circular pipe. It was found that the hydraulic gradient

of the slurry flow in the circular and square pipelines increases with the volumetric delivered

concentration and Reynolds number.

D.R. Kaushal, et al, (2012), simulated Pipeline slurry flow of mono- dispersed fineparticles at high concentration numerically using Mixture and Eulerian two-phase models. It

was found that, pressure drop predictions by both MIxture and Eulerian two-phase models for

flow of water show good agreement with the experimental data. Whereas, in case of

comparison between measured and predicted pressure drops at different concentrations,

namely, 30%, 40% and 50%, the Mixture model fails to predict pressure drops correctly, the

amount of error increasing rapidly with the concentration. However, Eulerian model gives

fairly accurate predictions for pressure drop at all the efflux concentrations and for flow

velocities considered in the present study.

The published materials about two-phase (solid-liquid) flow are mostly related to

horizontal pipe flow. There are a limited number of studies concerning the effect of pipe

inclination on two-phase flow energy loss. In htis backdrop, this paper studies the effect of

the pipe inclination on the pipe flow head losses for different sand concentrations, andpresents its results in the forms of curves and equations to compute the head loss, given the

sand water mixture flow velocity, the pipe angle of inclination, and the sand concentration in

volume.

EXPERIMENTAL APPARATUS

The general layout of the apparatus is shown in Fig. 1. This apparatus is used to reach

the objectives proposed in this paper. It consists of a pipe loop system, and was fabricated in

the professional Hydraulics Laboratory. The sand water mixtures were prepared in the main

tank, which had dimensions of 0.80 m length, 0.70 m width, and 0.80 m depth. The mixture

was maintained homogeneous in the main tank by the use of an auxiliary pump. Then, the

homogeneous mixture was pumped, through a pipeline with diameter of 0.75 m. The pipelinewas made up of horizontal and inclined pipes. The head loss measurements for the sand-

water mixture flow were carried out in the pipelines. The sand used in the experiment was

uniform with median grain size d50 = 0.20 mm, and relative density of 2.67, with

concentrations 15 % up in volume. The pipe inclination angle used was varied from 0o

(horizontal position) to 90o

(vertical position), for each upward and downward inclinations.

During the sand water mixture flow through the pipeline, for different velocities and

concentrations of the mixture, the following parameters were measured: a) the head losses in

the horizontal, upward, and downward inclinations; b) the discharge; and c) the concentration

of the sand in water. The discharge was measured by dividing a volume of the outlet mixture

by the corresponding time. The concentration of the mixture was determined using a tank to

measure the volume and one balance. Whereas, the head losses in the horizontal, upward, and

downward sloping lengths were measured by differential manometer.

EXPERIMENTAL WORK

The experimental work consists of two main sets of experiments. The first set consists

of 126 runs, and it used to measure the head losses through the upward inclination pipeline at

different mixture velocities and for different sand concentrations. The angles of the pipeline

inclination were 5o, 10

o, 25

o, 35

o, 45

oand


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Rubber pipe

Tank auxiliary pump main pump

Fig. 1. The Apparatus Layout

90o. The sand concentrations used for each angle of inclination are 5 %, 10 %, and 15 % in

volume. The second set of experiments consists of 118 runs, and the pipeline inclination

angles were as that of the first set except that, the pipeline inclination was downward. Fifty

runs were carried out to measure the head losses through the horizontal pipeline at three

different sand concentrations. The horizontal pipeline runs results, are analyzed with the

upward and downward pipeline inclination's results. In the light of above conclusions, the

sand water mixture velocity should be greater than the deposition limit (critical) velocity,

which is the mean mixture velocity at the limit of stationary deposition. From Durand (1953)

and Gibert (1960) for the used sand, the mixture velocity should be greater than 1.88 m/s in

all runs to maintain that the sand particles are always in suspension state.

RESULTS AND DISCUSSION

Two empirical equations were developed to calculate the head losses of the water-

sand mixture as a function of flow Froud's number, Fn, the sand concentration, C, and the

inclination angle, , of upward and downward flows in inclined pipes. The equations were

developed by several curve fittings. First of all, the apparatus was calibrated through

comparison of the measured head losses in a horizontal pipeline with that measured by E. M.

Coiado, (2001), Fig. (2), which shows that the measured and Coiado results are almost

identical.

FLOW THROUGH UPWARD INCLINATION PIPELINE

For the first set of experiments, the sand water mixture was pumped through the

pipeline which was laid in upward inclination positions. The used pipeline inclination angles

are 0o

(horizontal position), 5o, 10

o, 25

o, 35

o, 45

o, and 90

o(upward vertical position). The

head losses were measured in the pipeline in each inclination position for three sand

concentrations, i.e., 5%, 10%, and 15%.


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The results of the flows through upward inclination Pipeline were analyzed. The

effect of each sand-water mixture velocity represented in Froude's number, F n, the pipeline

angle of inclination, , and the sand

Fig. 2. Apparatus Calibration, for C = 10%, and pipe inclination angle 10o

upward

concentration, C on the head losses in the pipeline was developed. It was found that the

hydraulic gradient increases with increasing sand water mixture velocity. For example, for C

= 10% and = 35o, if the sand water mixture velocity increases from 3.3 m/s to 5.2 m/s, the

hydraulic gradient increases from 0.27 to 0.37, meaning thereby that increase of 57.5% in the

mixture velocity results in increasing 37% in the hydraulic gradient, as indicated in Fig. (3).

Another runs of experiments were carried out through varying the sand

concentrations up to 15%, to study the effect of sand concentration on the head losses in

upward pipeline inclination. It was found that increase in the sand concentration results in

increasing hydraulic gradient. For example, for pipeline inclination angle of 25o

and sand

water mixture velocity of 3.75 m/s, changing sand concentration from 10% to 15%, the

hydraulic gradient changes from 0.21 to 0.265, thereby showing that 50% increase in sandconcentration yields 26% increase in the hydraulic gradient in the pipeline, as shown in Fig.

(4).

The effect of pipeline inclination angle was studied by changing from 0o

(horizontal

pipeline) to 90o

(vertical pipeline). Experiments showed that the hydraulic gradient of the

pipeline increases as its upward angle of inclination increases, Fig. (5). For example, at sand

concentration C = 10 %, when the upward inclination angle increases from =10o

to 45o, the

hydraulic gradient increases from 0.199 to 0.296, implying that increase of 35% in upward

inclination angle of pipeline results into 49% increase in the hydraulic gradient.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

2 3 4 5 6 7

Froude's Number, Fn

Hydrau

licGradient,(i)

Present

Coiado, 2001


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Fig. 3 Variation of the hydraulic gradient with the sand water mixture velocity for C=

10% and = 35o

Fig. 4 Effect of sand concentration on the hydraulic gradient, for = 25o

and v = 3.75

m/s (Upward)

0

0.1

0.2

0.3

0.4

0.5

0.6

2 2.5 3 3.5 4 4.5 5 5.5 6

Froude's Number, Fn

Hydraulicgradient(i)

= 0

Up 5

Up 10

Up 25

Up 35

Up 45

Up 90

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5

Froude's Number, Fn

HydraulicGradient,(i)

C = 5 %

C = 10 %

C = 15 %


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Sin

Fig. 5 Effect of the upward pipe inclination angle on the hydraulic gradient, i for C=

10%

With a view to accomplish the objectives set for this study, several curve fittings were

done and sound relationship was established between hydraulic gradient and the affecting

parameters, i.,e., the Froude's number, the pipeline inclination, and the sand concentration,

Fig. (6). With parameters factor UPI on the horizontal axis and the hydraulic gradient on the

vertical axis:

0779.025.0sin1091.00574.0 += CgD

vIUP (1)

Where:

v : sand water mixture flow velocity, (m/s)

: pipeline angle of inclinationC: sand concentration in water (% in volume).

The hydraulic gradient, i , may be calculated for anyUP

I for a given sand water mixture

velocity, the pipeline inclination angle, and the sand concentration from Fig. (6). Through

curve fitting for data in Fig. (6), the following equation was obtained:

012.00669.1 =UP

Ii (2)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.2 0.4 0.6 0.8 1 1.2

HydraulicGradient,(i),


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UPI

Fig. 6 Upward pipe flow hydraulic gradient variation with the affecting parameters

By substituting the value of UPI from Equation 1 into Equation 2, the hydraulic gradient canbe directly calculated as under:

0951.02667.0sin1164.00612.0 += CgD

vi (3)

FLOW THROUGH DOWNWARD INCLINATION PIPELINE

In the second set of experiments, the sand water mixture was pumped through

the pipeline which was laid in downward inclination positions. The study parameter

encompassed pipeline inclination angles 0o

(horizontal position), 5o, 10

o, 25

o, 35

o, 45

o, and

90o (downward vertical position). Whereas, all measurements of head losses in the pipelinewere carried out in each inclination position for the three sand concentrations, 5%, 10%, and

15%.

The results were analyzed to determine the effect of each of sand water mixture

velocity represented in Froude's number, Fn, the pipeline angle of inclination, , and the sand

concentration, C on the head losses in the pipeline. The sand water mixture velocity effect on

the head loss is shown in Fig. (7). It was found that the hydraulic gradient increases as the

sand water mixture velocity increases. For example, for C = 10% and = 35o, if the sand

water mixture velocity increases from 3.28 m/s to 5.2 m/s the hydraulic gradient increases

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6



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Fig. 7 Variation of the hydraulic gradient with sand water mixture velocity for C= 10%

and = 35o

from 0.024 to 0.175, showing that increase of 58.5% in the mixture velocity results in

increase of 629% in the hydraulic gradient.

Another set of experiments was undertaken to study the effect of sand

concentration on head losses in downward pipeline inclination by varying sand

concentrations up to 15%. The results showed that the sand concentration is inverselyproportional with the hydraulic gradient. For example, for pipeline inclination angle of 25

o

and sand water mixture velocity of 3.75 m/s, changing sand concentration from 10% to 15%,

results in changing the hydraulic gradient from 0.0778 to 0.063, showing that 50% increase in

the sand concentration results in 19% decrease in the hydraulic gradient in the pipeline, Fig.

(8).

Also, the effect of the pipeline inclination angle on the pipeline hydraulic gradient

was studied by changing from 0o

(horizontal pipeline) to 90o

(vertical pipeline).

Experiments showed that the hydraulic gradient of the pipeline decreases as its downward

angle of inclination increases, Fig. (9). For example, at sand concentration C = 10 %, when

the downward inclination angle increases from =10o

to 45o, the hydraulic gradient

decreases from 0.129 to 0.048, showing that with downward inclination angle of the pipelineincreasing by 35%, the hydraulic gradient decreases by 63%.

The curve fittings were done for this set of parameters as well to determine

relationship between the hydraulic gradient and the affecting parameters, i.e, the Froude's

number, the pipeline inclination, and the sand concentration, which yielded promising results

as shown in Fig. (10) and the underlying relationship, taking Parameters factor DwnI on the

horizontal axis and the hydraulic gradient on the vertical axis:

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

2 3 4 5 6 7

Froude's Number, Fn


= 0

Dow 5

Dow 10

Dow 25

Dow 35

Dow 45

Dow 90


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Fig. 8 Effect of sand concentration on the hydraulic gradient, for = 25o

and v = 3.75

m/s (Downward)

Sin

Fig. 9 Effect of the Downward pipe inclination angle on the hydraulic gradient, i for C=

10%

0

0.05

0.1

0.15

0.2

0.25

2 3 4 5 6 7

Froude's Number, Fn


C = 5 %

C = 10 %

C = 15 %

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 0.2 0.4 0.6 0.8 1 1.2



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DwnI

Fig. 10 Downward pipe flow hydraulic gradient variation with the affecting parameters

1346.015.0sin0675.00585.0 += CgD

vIDwn (4)

The hydraulic gradient, i may be calculated for anyDwn

I for a given sand water

mixture velocity, the downward pipeline inclination angle, and the sand concentration. The

relationship established by curve fitting for data in Fig. (10), is given as under:

0031.09848.0 += DwnIi (5)

The following relationship is obtained by combining Equations (4) and (5), to calculate the

hydraulic gradient given the values of sand water mixture velocity, the pipeline inclination,and the sand concentration:

1295.0148.0sin0665.00576.0 += CgD

vi (6)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35



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CONCLUSIONS

This paper gives the results of an experimental study undertaken to determine the

effects of sand water mixture velocity, the pipeline inclination angle upward and downward,and the sand concentration on the head loss in the pipeline. Based on the experimental data,

the results of curve fitting, and the resulting mathematical expressions, the following

conclusions are reached:

1. The head losses for the downward inclination of the pipeline are always lower thanthe head losses for the horizontal pipe, and these are always lower than the head

losses for the upward sloping pipes, regardless of the inclination angles and

concentrations.

2. For the downward inclination of the pipeline, the presence of sand decreases the headlosses with increasing inclination angle and the sand concentration.

3. For the water-sand mixture flow in the horizontal pipe, the presence of sand increasesthe head losses as the concentration increases.

4. For the upward inclination of the pipeline water-sand mixture flow, the presence ofsand increases the values of the head losses with increase in inclination angle and theconcentration.

5. The curve fitting results and the corresponding equations developed can be used forcalculating the head loss in the pipeline for given sand water mixture velocity, the

pipeline inclination angle, and the sand concentration.

REFERENCES

1. E. M. Coiado and M. G. Diniz, (2001), "Two-Phase (Solid-Liquid) Flow in InclinedPipes", J. Braz. Soc. Mech. Sci. vol.23 no.3 Rio de Janeiro.

2. D.R. Kaushal, T. Thinglas, Y. Tomita, S. Kuchii, and H. Tsukamoto, (2012), " CFDmodeling for pipeline flow of fine particles at high concentration", International Journalof Multiphase Flow 43, 85100

3. Durand, R. (1953), " Basic solids in pipes Experimental Research", ProceedingsInternational Hydraulics Conference, Minneaplis, MN, pp. 89 103.

4. Gibert, R. (1960), "Transport Hydraulique et Refoulement des Mixtures en Conduit",Anna1es des Pontes et Chaussees, 130e Annee, No. 12, et No. 17.

5. Kaushal D.R., Kimihiko Sato, Takeshi Toyota, Katsuya Funatsu, Yuji Tomita (2005),"Effect of particle size distribution on pressure drop and concentration profile in

pipeline flow of highly concentrated slurry", International Journal of Multiphase Flow

Volume 31, Issue 7, July 2005, Pages 809823

6. Kaushal, D.R., Tomita, Y., 2007, "Experimental investigation of near-wall lift ofcoarser particles in slurry pipeline using -ray densitometer" Powder Tech nol. 172,

177187.

7. Raudkivi, A. J., 1989 "Loose Boundary Hydraulics", Pergamon Press, New York8. Richardson, J. F., Chhabra, R. P., Khan, A. R., 1999 "Multiphase flow ou non-

Nextonian fluids in horizontal pipes", Slurry Handling and Pipeline Transport.

Hidrotransport 14. Maastrich. Netherlands.

9. Wasp, E. J.; Kenny, J. P.; Gandhi, R. L. 1999. "Solid-Liquid Flow Slurry PipelineTransportation", Series on Bulk Materials Handling. International Standard Book

Number. Trans Tech Publications. Germany.

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Effect of Pipe Inclination on the Pipe Flow Head Losses For