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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 6, June 2011
VISUALIZATION OF FLUID FLOW PATTERNS IN
HORIZONTAL CIRCULAR PIPE DUCTS
Olagunju, Mukaila,
Department of Computer Science, Taiwo, O. A (Ph.D)
Kwara State Polytechnic, Ilorin, Nigeria Department of Mathematics
olamukaila@yahoo.com University of Ilorin, Nigeria.
Oataiwo2002@yahoo.com
Abstract— This paper developed a visualization model for Visualization has a lot of definition which depend on it
determination of frictional Head loss in a circular pipe ducts. Head application. Visualization according to [1], is the systematic
loss is due to friction when the liquid or gases come in contact with and focus visual display of information in form of tables,
wall of the pipe. To determine the loss at each duct, modified Hagen diagrams and graphs. Previous authors were concerned with
postulates equation was used in visualization. Frame work stages representative and process of information by the brain in their
were developed which consists of data generation framework stages,
data enrichment framework stages, data rendering framework stages,
definitions [2] where they tried to distinguish between Visual
visualization development stages and output representation perception as meaning the image, an object achieved and as it
framework stages. Based on the model of visualization stages, can be seen as visual imagery, the mental production of an
MATLAB program was used to determine head loss due to pressure object in its absence and spatial imagery as represented by
drop and represented in tabular form and 2D representation. This tactile meaning. A linkage was established between brain
model greatly assist the learners and instructors in determine the activities with the uses of phrase “mental imagery” instead of
flow patterns especially the head loss of fluid in a pipe wall by visual imagery [3].
considering different points or ducts, this model serve as a reusable Also [5], visualization is also described as internal,
for both learner and instructors by assist in determine the region mental construct i.e. mental models, thought to be in the mind
along the wall of the pipe where the head loss is very great.
and use in mental imagery and to solve problems.
Keywords: Step Wise Visualization, Patterns, circular, pipe ducts,
fluid flow. Visualization is also described as the act or process of
interpreting in visual terms or putting into visual form [4.
Introduction Fluid according to [5] is defined as a substance
For centuries, fluid flow researchers have been studying fluid which cannot with stand a shear force or stress without
flows in various ways, and today fluid flow is still an moving as can a solid. It was further classified fluids as liquids
important field of research. The areas in which fluid flow or gases. A liquid has intermolecular forces which hold it
plays a role are numerous. Gaseous flows are studied for the together so that it possesses volume but no definite shape.
development of cars, aircraft and spacecrafts, and also for the They also classified fluid by the types of their flow into
design of machines such as turbines and combustion engines. laminar and turbulent flow.
Liquid flow research is necessary for naval applications, such
as ship design, and is widely used in civil engineering projects
such as harbor design and coastal protection. In chemical Characteristics of Good Visualization.
engineering, knowledge of fluid flow in reactor tanks is Before visualization can be categorized as a good
important; in medicine, the flow in blood vessels is studied. Visualization, it must have these qualities:-
Numerous other examples could be mentioned. Fluid is always 1. It serves a clear purpose
flow in pipe. 2 Show the data without distorting it.
The pipeline and pumping designers are always concern with 3 Cause the viewer to think about the substance of the
flow patterns especially in preventing the losses of fluid in data.
when the pressure drop play major role 4 Present large quantities of data in smallest space.
As fluid flows inside the pipe, the pressure drop or losses
occur due to fluid contact with pipe wall and try lead to Materials and Methods
friction loss which also called the head loss velocity is one of The material use in this paper is based on data that ware
the factors loss in pipe the size of pipe diameter (inside) also generated from modify Hagen postulate equation. The
cause friction loss. There two factors mentioned about ,which method used is based on development of mathematical
can only be demonstrated as factors causing head loss or model and visualization by develop taxonomy framework
stages.
friction loss function, model, stimulation and visualization
approach which is the
Focus of this work. Visualization is hereby proposed to
predetermine the flow trends. Taxonomy of Visualization Model (TVM)
164 http://sites.google.com/site/ijcsis/
ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 6, June 2011
Taxonomy according to [7], in his paper title. “A principled of
taxonomy of software “ Defined taxonomy as a common
language or terminology that facilitates communication about B = -pe2,where 0 < e < r
ideas or discoveries. 4k
“An early step towards understanding any set of phenomena (2)
= + −
is to develop taxonomy” [9]. Substitute 2 into 1 to get
The importance of taxonomy for visualization includes:
To make the thinking way and application goals clear
1. To discover the shortage of visualization
research.
In this work, in order to illustrate the Taxonomy U=p ( r2-e2)
of Visualization Model (TVM), the frame work 4k
stages were developed for visualization process. (3)
The frame work stages consist of different stages 3 can be rewritten as
and these include: Pe2 ( r2– e2)
1. Data generation frame work stage. 4k e2 e2 for a particular duct.
2. Data Enrichment and Enhancement frame
work stage. (4)
1− − + ⋯− 1−
3. Visualization mapping frame work stage. Also the total velocity is given as
4. Rendering frame work stage. 2
1-
5. Display frame work stage. pe 1
Based on stages of visualization process, (5)
different computer aided visualization
experiment can be develop with the
mathematical formulations.
=
Also Reynolds number along the ducts is given as
=− ∗
r
2 2
Mathematical formulations
1−
This work was developed based on Visualization process
4k ei2
model and each stage is developed as follow:
Data generation:- For this work, the model equation to be µ.
=−
Visualized shall be based on Hagen’s equation
The derivation is as follows from Equation 1 below and the Where
assumptions before the model include:
1. Flow starts from rest = Kinematic viscosity
2. The flow is taken place inside the boundary wall K= Dynamic viscosity
3. Parameters A and B are constants D= Diameter of the pipe
4. The flow is taking place at a particular temperature
e.g. 200c And the total hand loss along the pipe is give as
The Heagen Equation which is equation is given as
u=pr2+loge r+B
4k
(1)
Where
Where: hf = head loss
P = Pressure of pipe λ = Frictional loss of the fluid
u = Velocity l = Length of the pipe
e = Various point of eccentricity u = Velocity of the moving object in the pipe
r = Radius of the pipe g = Acceleration due to gravity
A = Parameter constant d = Diameter of the pipe when the fluid is moving
k= Dynamic viscosity
The Equation (1) above is modified with the following
assumptions
When u = 0, r = e, parameter constant A = 0
Then 0 = pe2+B
4k
165 http://sites.google.com/site/ijcsis/
ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 6, June 2011
0.08 688.05 345.85 251630.15
0.10 671.93 337.75 245732.57
0.12 652.22 327.84 238524.42
Table 1: HEAD LOSS ALONG THE WALL OF 0.14 628.92 316.13 230005.69
THE PIPE
0
Output at 0 c 0.16 602.04 302.62 220176.38
Length of the pipe 4m
Radius of the pipe 0.4m 0.18 571.58 287.31 209036.51
Point of Velocity Discharge Head lost 0.20 537.54 270.20 196586.06
eccentricity rate
0.22 499.91 251.28 182825.03
-0.40 -0.00 -0.00 NaN
0.24 458.70 230.57 167753.44
-0.38 69.88 35.13 2556.19
0.26 413.91 208.05 151371.26
-0.36 136.18 68.45 49801.80
0.28 365.53 183.73 133678.52
-0.34 198.89 99.97 72736.84
0.30 313.57 157.61 114675.20
-0.32 258.02 129.69 94361.31
0.32 258.02 129.69 94361.31
-0.30 313.57 157.61 114675.20
0.34 198.89 99.97 72736.84
-0.28 365.53 183.73 133678.52
0.36 136.18 68.45 49801.80
-0.26 413.91 208.05 151371.26
0.38 69.88 35.13 25556.19
-0.24 458.70 230.57 167753.44
0.40 -0.00 -0.00 NaN
-0.22 499.91 251.28 182825.03
-0.20 537.54 270.20 196586.06
Figure1: Graphical representation of the velocity
-0.18 571.58 287.31 209036.51 versus varying points on the radius of 0.4m
Velocity versus points of eccentricity
-0.16 602.04 302.62 220176.38 800
-0.14 628.92 316.13 230005.69 600
-0.12 652.22 327.84 238524.42
velocity
400
-0.10 671.93 337.75 245732.57
-0.08 688.05 345.85 251630.15 200
-0.06 700.59 352.16 256217.16 0
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
-0.04 709.55 356.66 259493.60 points of eccentricity
-0.02 714.93 359.36 261459.46
0.00 NaN NaN NaN
0.02 714.93 359.36 261459.46
0.04 709.55 356.66 259493.60
0.06 700.59 352.16 256217.16
166 http://sites.google.com/site/ijcsis/
ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 6, June 2011
-0.14 351.98 176.93 72120.56
-0.12 365.02 183.48 74791.69
-0.10 376.05 189.02 77051.88
Figure 2: Graphical representation of Reynolds
constant versus points of eccentricities -0.08 385.08 193.56 78901.12
5 Reynolds constant Versus points of eccentricity
x 10 -0.06 392.09 197.09 80339.42
3
-0.04 397.11 199.61 81366.78
2.5
-0.02 400.12 201.12 81938.20
2
0.00 NaN NaN NaN
Head loss
1.5 0.02 400.12 201.12 81983.20
1 0.04 397.11 199.61 81366.78
0.5 0.06 392.09 197.09 80339.42
0.08 385.08 193.56 78901.12
0
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
points of eccentricity 0.10 376.05 189.02 77051.88
0.012 365.02 183.48 74791.69
Table 2: HEAD LOSS ALONG THE WALL OF 0.14 351.98 176.93 72120.56
THE PIPE
Output two at 200c 0.16 336.94 169.36 69038.48
length of the pipe 4m
Radius of the pipe 0.4 0.18 319.89 160.80 65545.46
0.20 300.84 151.22 61641.50
Point of Velocity Discharge Head lost
eccentricity rate
0.22 297.78 140.63 57326.60
-0.40 -0.00 -0.00 NaN
0.24 256.72 129.04 52600.75
-0.38 39.11 19.66 8013.40
0.26 256.72 129.04 47463.96
-0.36 76.21 38.31 15615.85
0.28 204.57 102.83 41916.22
-0.34 111.31 55.95 22807.36
0.30 175.49 88.21 35957.54
-0.32 144.40 72.58 29587.92
0.32 144.40 72.58 29587.92
-0.30 175.49 88.21 35957.54
0.34 111.31 55.95 22807.36
-0.28 204.57 102.38 41916.22
0.36 76.21 38.31 15615.85
-0.26 231.65 116.44 47463.96
0.38 39.11 19.66 8013.40
-0.24 256.72 129.04 52600.75
0.40 -0.00 -0.00 NaN
-0.22 279.78 140.63 57326.60
-0.20 300.84 151.22 61641.50
-0.18 319.89 160.80 65545.46
-0.16 336.94 169.36 69038.48
167 http://sites.google.com/site/ijcsis/
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Vol. 9, No. 6, June 2011
Table 3: HEAD LOSS ALONG THE WALL OF -0.28 1407.98 2830.81 721205.57
THE PIPE
Output three at 200c -0.26 1435.01 2885.25 735074.91
length of pipe 4m
-0.24 1460.08 2935.66 747916.89
Radius of the pipe 0.8
-0.22 1483.14 2982.03 759731.51
Point of Velocity Discharge Head lost
eccentricity -0.20 1504.20 3024.37 770518.78
Rate
-0.18 1523.25 3062.68 780278.68
-0.80 -0.00 -0.00 NaN
-0.16 1540.30 3096.96 789011.23
-0.78 79.22 159.28 40580.66
-0.14 1555.34 3127.20 796716.41
-0.76 156.44 314.53 80133.95
-0.12 1568.38 3153.41 803394.24
-0.74 231.65 465.75 118659.89
-0.10 1579.41 3175.59 809044.71
-0.72 304.85 612.94 156158.47
-0.08 1588.44 3193.74 81366.83
-0.70 376.05 756.09 192629.69
-0.06 1595.45 3207.85 817263.58
-0.68 445.24 895.21 228073.56
-0.04 1600.47 3217.93 819831.98
-0.66 512.43 1030.30 262490.06
-0.02 1603.48 3223.98 821373.01
-0.64 577.61 1161.36 295879.21
0.00 MaN NaN NaN
-0.62 640.79 1288.38 328241.00
0.02 1603.48 3223.98 821373.01
-0.60 701.96 1411.37 359575.43
0.04 1600.47 3217.93 819831.98
-0.58 761.13 1530.33 389882.50
0.06 1595.45 3207.85 817263.58
-0.56 818.28 1645.26 419162.21
0.08 1588.44 3193.74 813667.83
-0.54 873.44 1756.15 447414.57
0.10 1579.41 3175.59 809044.71
-0.52 926.59 1863.01 474639.57
0.12 1568.38 3153.41 803394.24
-0.50 977.73 1965.84 500837.20
0.14 1555.34 3127.20 796716.41
-0.48 1026.87 2064.64 526007.48
0.16 1540.30 3096.96 789011.23
-0.46 1074.00 2159.40 550150.41
0.18 1523.25 3062.68 780278.68
-0.44 1119.12 2250.13 573265.97
0.20 1504.20 3024.37 770518.78
-0.42 1162.25 2336.83 595354.17
0.22 1483.14 2982.03 759731.51
-0.40 1203.36 2419.50 616415.02
0.24 1460.08 2935.66 747916.89
-0.38 1242.47 2498.13 636448.51
0.26 1435.01 2885.25 735074.91
-0.36 1279.57 2572.73 655454.64
0.28 1407.93 2830.81 721205.57
-0.34 1314.67 2643.30 673433.41
0.30 1378.85 2772.34 706308.88
-0.32 1347.76 2709.84 690384.82
0.32 1347.76 2709.84 690384.82
-0.30 1378.85 2772.34 706308.88
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ISSN 1947-5500
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Vol. 9, No. 6, June 2011
0.34 1314.67 2643.30 673433.41
Figure3: Graphical representation of head loss
0.36 1279.57 2572.73 655454.64 versus points of eccentricities
0.38 1242.47 2498.13 636448.51 5 Reynolds constant Versus points of eccentricity
x 10
10
0.40 1203.36 2419.50 616415.02
0.42 1162.25 2336.83 595354.17 8
0.44 1119.12 2250.13 573265.97
6
Head loss
0.46 1074.00 2159.40 550150.41
0.48 1026.87 2064.64 526007.48 4
0.50 977.73 1965.84 500837.20
2
0.52 926.59 1863.01 474639.57
0
0.54 873.44 1756.15 447414.57 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
points of eccentricity
0.56 818.28 1645.26 419162.21
Discussion of the Results
0.58 761.13 1530.33 389882.50
MATLAB (Matrix Laboratory) program version 2007a was
0.60 701.96 1411.37 359575.43 used to develop a Taxonomy of Visualization Model System
(TVMS) for determination of flow patterns of water. Table 1,2
0.62 640.79 1288.38 328241.00 and 3 above show the tabular representation of points
eccentricities (ducts), velocities, discharge rate and head losses
0.64 577.61 1161.36 295879.21 at zero and twenty degree centigrade respectively. It was
discovered that velocity is higher at neighborhood of the
0.66 512.43 1030.30 262490.06 centre of and also the discharge rate and head loss follow the
same pattern. The temperature effects was clearly shown that
0.68 445.24 895.21 228073.56
at increase in temperature, the head loss, discharge rate are
0.70 376.05 756.09 192629.69 also reduce. Figure 1 to 3, shown the flow pattern of fluid
especially water by consider velocity, discharge rate and
0.72 304.85 612.94 156158.47 Reynolds. The three graphs clearly shown that the flow does
not take place at the wall and the centre of the pipe.
0.74 231.65 465.75 118659.89
Conclusion and Recommendations
0.76 156.44 314.53 80133.95 With the (TVMS) that was developed, we concluded with the
following:
0.78 79.22 159.28 40580.66 1. Temperature always has effect on fluid flow
patterns.
0.80 -0.00 -0.00 NaN
2. The radius of the pipe also determine the flow
rate and the higher the radius the higher the flow
pattern.
3. The neighborhood of the centre of the pipe
always has the higher discharge rate.
4. The centre of the pipe must always be protected
in other to avoid spillage of the fluid.
5. The flow of fluid is in parabolic shape in which
the flow does not take place in centre and edges.
Also recommended the following:
1. The learners can use (TVMS) as a guide to
determined the flow patterns of any fluid.
2. The flow pattern of different fluid can be
compare easily.
169 http://sites.google.com/site/ijcsis/
ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 6, June 2011
3. (TVMS) can assist designers of pipe option in computer science, he is currently undergo
especially when the determination of head his PhD. In computer science. His area of study
loss is need to quantify the economy wise. include Data Mining and visualization graphics.
Dr. O.A Taiwo is an Associate professor of
Mathematics and Ph.D Supervisor to the first author.
Further Study He has published many articles both in the National
The research work should be carried out further by compare and International Journals and his area of study
the flow patterns with emphasis on head loss by compare include numerical computing.
smooth pipe and rough pipe of different material.
Acknowledgment
I wish to acknowledg the following people with, thanks
professor J.S Sadiku of Department of Computer Science,
Faculty of Communication and Information Sciences,
university of Ilorin, Ilorin, Nigeria and also DR. R.G Jimoh of
the same Department and faculty. I also appreciate Mr. A.O
Ameen and Rasheed Tomori of university of Ilorin, Nigeria.
Finally I thank the management and staff of kwara state
polytechnic Ilorin, for their support at all time.
References
1) L. R, Turfle (2001): Visualization of Quantitative
Information, (2nd ed), Graphics Press, Cheshine
2) D, Reisherg (1997): Cognitive thinking of
visualization, Oxford University Press, New-
York
3) M. S, Kosslyn, (1994) Seeing and Imagining in the
Cerebral Hemisphere Computational Approach
Psychological Review, 94, 148-175
4) G: Domink, (2007): Computer Generated
Visualization, http.//www.Un Paderbom.d cs/
tutorial/ in dex, Access 2007.
5) L, Johnson (1985): The crucible of creation, Oxford
University Press, London
6) R Kasma, and J Rusell, (1997): Multimedia and
Under Standing, Expert and Novice
Responses to Different Representation, of Chemical
Phenomena, Journal in Research Science Teaching;
34(9), 949-968
7) E.L et al, Bruce, (2009): Hydraulic of pipeline
systems, Library of congress cataloging in
publication data, New York.
8) D.H Brian, and T.V Danel, (2007): Essential
MATLAB for Engineers and Scientists, 3rd
edition, published by Elsevier New- York.
9) H.A Simon, (1969): The Sciences of Artificial,
Published MITI Press, London.
Author’s Profile
Olagunju Mukaila, was born on the 19th of
September, 1966 in offa, kwara state Nigeria.
He obtained his first degree in mathematics
and computer science (combined honor) from federal
University of Technology Minna, Nigeria. He
obtained his secondary degree in mathematics with
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ISSN 1947-5500
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