MEASUREMENT TECHNIQUE OF REYNOLDS NUMBER USING CYLINDRICAL TUBE AND COLORED FLUID INJECTION

MEASUREMENT TECHNIQUE OF REYNOLDS NUMBER USING
CYLINDRICAL TUBE AND COLORED FLUID INJECTION

Oleh :
Agustin Eka Budhi Rahayu
NIM : 192012021
TUGAS AKHIR
Diajukan Kepada Program Studi Pendidikan Fisika, Fakultas Sains dan Matematika
guna memenuhi sebagian dari persyaratan untuk memperoleh gelar Sarjana Pendidikan
Program Studi Pendidikan Fisika

FAKULTAS SAINS DAN MATEMATIKA
UNIVERSITAS KRISTEN SATYA WACANA
SALATIGA
2017

MOTTO

Boleh jadi kamu membenci sesuatu, padahal ia amat baik bagimu, dan boleh jadi (pula) kamu
menyukai sesuatu, padahal ia amat buruk bagimu, Allah mengetahui,
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(Q.S Al-Baqarah 216)
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(Q.S Al-Insyirah 6-7)

KATA PENGANTAR
Segala puji dan syukur penulis panjatkan kepada Allah SWT dan junjungan Nabi besar
Agung Muhammad SAW karena karunia-Nya penulis dapat menyelesaikan tugas akhir dengan
judul “Measurement Technique Of Reynolds Number Using Cylindrical Tube And Colored
Fluid Injection”, telah dipublikasikan dalam Seminar “The 2nd IConSSE Fakultas Sains dan
Matematika, Universitas Kristen Satya Wacana pada tanggal 30-31 Agustus 2017 di Universitas
Kristen Satya Wacana Salatiga.
Laporan penelitian ini disusun untuk tugas akhir dan sebagai salah satu syarat untuk
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1. Allah SWT yang telah melimpahkan Rahmat dan Karunia-Nya sehingga terleselainya
2.

3.

4.

5.

6.

7.

Skripsi.
Dr. Suryasatriya Trihandaru, M.Sc.nat selaku pembimbing utama yang dengan sabar
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Salatiga, 18 September 2017

Penulis

Agustin Eka Budhi Rahayu

DAFTAR ISI

HALAMAN JUDUL............................................................................................................... i
LEMBAR PENGESAHAN................................................................................................... ii
LEMBAR PERNYATAAN KEASLIAN............................................................................. iii
LEMBAR PERSETUJUAN AKSES.................................................................................... iv
MOTTO.................................................................................................................................

v

KATA PENGANTAR..........................................................................................................

vi

DAFTAR ISI........................................................................................................................ vii
ABSTRAK............................................................................................................................ 1
PENDAHULUAN ................................................................................................................ 2
METODE............................................................................................................................... 5
HASIL DAN PEMBAHASAN ............................................................................................. 6
KESIMPULAN .................................................................................................................... 9
DAFTAR PUSTAKA.......................................................................................................... 10
LAMPIRAN

MEASUREMENT TECHNIQUE OF REYNOLDS NUMBER USING
CYLINDRICAL TUBE AND COLORED FLUID INJECTION
Agustin E. B. Rahayu *, Marmi Sudarmi, Suryasatriya Trihandaru **
Physics Department, Faculty of Science and Mathematics, Satya Wacana Christian University,
Diponegoro St. No. 56-60, Salatiga 50711 Indonesia
*192012021@student.uksw.edu
**Corresponding Author: suryasatriya@staff.uksw.edu

ABSTRACT

In this paper we give the result of the study of several types of flow of liquid in the vertical cylindrical
tube, those are divided into three kinds of flow ; laminar, transitional, and turbulent flow, depending on
the Reynolds number (Re). The fluid flow in the cylindrical tube is studied by adding colored dilute liquid
in the middle-top of the cylindrical such that it shows a thin track of colored fluid inside the fluid flow.
The laminar, transitional or turbulent flow can be realized by controlling the faucet aperture that gives
different values of Reynolds numbers. The flow is captured by the Kodak digital camera Easyshare M863
8.2 mega pixel. Reynolds numbers are obtained by measuring its volumetric flow rate divided by the
cross-sectional area of the tube. The fluid flow images as indicate that a stream with a Reynolds number
less than 2000 appears as a laminar flow, between 2000-4000 as a transitional stream, and above 4000 as

turbulent flow.

Keywords: laminar, Reynolds number, transition, turbulent

*

Corresponding author. Tel.: +62 822 2744 8884; E-mail address: suryasatriya@staff.uksw.edu

1

2

The purpose of this research is to visualize fluid flow with various Reynolds values, to
measure the Reynolds number of fluid flow in the vertical pipe, and to find the limit of Reynolds
value which still shows the laminar flow.
Theoretical Basis
The fluid flow with constant density  and constant viscosity  satisfy the Naiver Stokes
equation as follows (F. M. White, 1999):



dv
 p   2v
dt

(1)

From Eq. (1) p is ) pressure, v is the fluid velocity,  is the density of the substance
(liquid), t is time,  is the dynamic viscosity, and  is the gradient. Since fluid moves in
cylinders it is used Laplacian  2 in the cylindrical coordinate system, so the Naiver Stokes
Equation can be written by:



 1  v 1  2v  2v 
dv
 p   
 2
(r ) 
2

z 
dt
 r r r r 

(2)

Eq. (2) is a general fluid mobility equation whose solution cannot be derived analytically so
that it must use the numerical methods. However, for a simple flow that is the flow of fluid
laminar in a pipe or so-called Poiseuille flow, the solution can be derived analytically. Poiseuille
flow is derived from Naiver Stokes equation assuming that its flow is laminar in long enough
pipe, so the variation of velocity on z axis can be ignored as follows:

 2v
0
z 2

(3)

The variation of the velocity from the angle,  is ignored:

 2v
0
 2

(4)

The pressure p is assumed vary on the z axis only:

p
0
r

p
0

3

(5)

(6)

Thus, the Naiver Stokes equation assuming (3), (4), (5) and (6) becomes:



v
p
1  v
   (
r )
t
z
r r r

(7)

In Eq. (7), the unit of measurement for each variable is as follows. Variable t in seconds, r in
meters, p in Pascal,  in Ns/m2 and  in kg/m3. To show the important parameters in Eq. (7), a
non-dimensionalized method is required. The trick is to introduce the dimensionless variables as in
Table 1. (Peixinho, J., Nouar, C., Desaubry, C. & Theron, B. 2005 )and (L. I. Sedov. 1959):
Table 1. The dimensionless variables
Variable

Unit

Dimensionless Variable

t

second

r

meter

v

meter/second

z

meter

p

Ns/m

t* 

t
D / vref

r
r 
D
*

v* 

v
vref

z*  z

2

p* 

Note

t

= time

r

= position

D

= pipe diameter

v

= velocity

vref = refered velocity



= liquid density

p

= pressure

pD
 vref

By including the dimensionless variable in Table 1. the equation becomes

dv*
p*

1  * v*


(
r
)
dt *
z  Dvref r * r * r *

(8)

In Eq. (8) has been collected important parameters as the multiplier factor of the both on
the right side. This factor will determine the flow profile, which is referred to as Reynolds
number (Re) (1883) which is defined as follows:

Re 

with



 vref D vD






4

(9)

Re is the Reynolds number, vref is the speed of reference, v is the measured velocity, D is the
diameter,  is the density of the substance,  is the dynamic viscosity, and  is the kinematic
viscosity. It is further assumed that the fluid flow has reached a steady state so that the velocity
derivative over time is zero. Thus obtained Poiseuille equation

1 * v
p*
(r * )  Re
r*
r
z

(10)

1 p* *2 1
(r  )
v*   Re
4
4
z

(11)

Which has the following solutions:

1.

Materials and Methods
This research is performed by an experimental method which is done with the modeled
instrument as in Figure. 1.

Dye Injector

Discharge control valvic
Constant head tank
Thermometer
Overflow pipe
Marbles
Water Supply
Overflow to drain
Shroud

Glass test pipe

Discharge control valvic

Measuring glass

Figure.1. Reynolds number measurement instrument

5

The working principle of the instrument is the measurement of fluid flow discharge in the
transparent pipe by dividing the volume of fluid in the measuring glass against time. In this
modeled instrument, (1) a color injector is used to provide color to the flowing fluid in order to
show fluid flow patterns, in which the color injector is provided with an opening valve to drain
the dye to the fluid, (2) a thermometer for measuring The fluid temperature in the tank, (3) the
tank which is used as fluid shelter, which has 3 holes for the inlet of the fluid inlet pipe, for the
transparent pipe port, and the fluid output, (4) the marbles in the tank are used for removing
the water ripple, (5) transparent pipes used for visualizing fluid flow, the tube is provided with a
valve, (6) a 0.2 liter measuring glass is used for volume measurement. The instrument used has
the following specifications: tank maximum volume is 15 liters, transparent pipe diameter is 2.
92x10-2 m, transparent pipe length is 0.8 m, and has a stop valve with 3. 81x 10 -2 m in diameter.
The measurement experimental steps of the Reynolds number are as follows. First was
performed by measuring the discharge with the Eq. (12):

Q=

V
t

(12)

From Eq. (12) Q is the fluid discharge, V is the fluid volume measured by the measuring
glass, t is the fluid flow time. After obtaining the value of the discharge then calculated the
velocity of the fluid through the equation:

v

Q
A

(13)

From Eq. (13), A is the transparent cross-sectional area. By the obtained value of v , the
magnitude of the Reynolds number can be calculated by Eq. (9). This v value is used as the
referred velocity in Eq. (9).
Visualization of fluid flow was obtained by photographs when the fluid is flowing through
the transparent pipe using Kodak Easyshare M863 8.2 mega pixel digital camera. In this study,
the final results of the experiments are attached by the experimental module of the Reynolds
number experiments.

2.

Results and Discussion
The obtained results in the Reynolds number measurement was then analyzed from fluid
flow visualization and experimental data. Visualization of the fluid flow obtained by taking fluid
flow photographs and is displayed in several images as follows:

6

3. Lamninar fluid flow (Re 184)
Figure 2a.

Figure 2d. Lamninar fluid flow (Re 810)

Figure 2b. Lamninar fluid flow (Re 486)

Figure 2e. Lamninar fluid flow (Re 1575)

7

Figure 2c. Lamninar fluid flow (Re 719)

Figure 2f. Lamninar fluid flow (Re 1905)

Figure 2a -2f. shows the visualization of the laminar fluid flow. The flow is characterized by
a steady state in which all flow lines follow a relatively straight path without any movement of
turn or curl. In the fluid flow observation, the factors that affect the fluid flow velocity (and the
Reynolds number) are the width of valve hole (stop faucet) on the color injector and also the
valve underneath the transparent pipe.

Figure 4. Turbulent fluid flow (Re 4078)

Figure 3. Transition fluid flow (Re 2728)

Figure 3. shows the visualization of fluid flow that is characterized as transition flow by its
flow form that still looks straight at the top of the track then the trajectory which is further
characterized by the irregularity that occurs in the path trajectory. The transition flow is a
transition from the laminar flow to the turbulent flow.
Figure 4. shows the turbulent fluid flow. The flow is characterized by its flow that
resembles a swirling vortex and intermittent flow line causing a broken flow pattern and a
mixing of fluid with dye occurs (in this case, the dye dissipates when the fluid mixing is taking
place).
Figure 3. and Figure 4. do not show laminar flow, this can be explained theoretically
because the used assumptions in the equations in laminar flow are not met, i.e. (1) the angular
velocity turns out to vary in the z axis (at points 1 and 2 in Fig. 3, the v must be different,
indicated by the motion of the dye), (2) the pressure varies on r and  that shown by the
dispersed dye.

8

The data result of the Reynolds number experiment are shown in Table 2.
Table 2. Calculation results from Reynolds number experiments Reynolds number data value



Temperature
(0C)

9,34. 10-7

184

23

1,6. 10-2

9,8. 10-7

486

21

6,7. 10-4

2,4. 10-2

9,8. 10-7

719

21

2,9. 10-2

6,7. 10-4

2,7. 10-2

9,57. 10-7

810

22

3,3. 10-5

2,9. 10-2

6,7. 10-4

4,9. 10-2

9,13. 10-7

1575

24

9,68

4,1. 10-5

2,9. 10-2

6,7. 10-4

6,1. 10-2

9,34. 10-7

1905

23

8,2. 10-4

14,36

5,7. 10-5

2,9. 10-2

6,7. 10-4

8,5. 10-2

9,13. 10-7

2728

24

1,8. 10-3

21,32

8,5. 10-5

2,9. 10-2

6,7. 10-4

1,3. 10-1

9,13. 10-7

4078

24

time (s)

1

2,1. 10-4

53,23

3,9. 10-6

2,9. 10-2

6,7. 10-4

5,9. 10-3

2

2,4. 10-4

21,99

1,1. 10-5

2,9. 10-2

6,710-4

3

2,8. 10-4

17,34

1,6. 10-5

2,9. 10-2

4

2,8. 10-4

15,98

1,8. 10-5

5

3,1. 10-4

9,4

6

4,0. 10-4

7
8

No.

(m2/s)
Re

volume
(m3)

3

Q (m /s)

D (m)

2

A (m )

v (m/s)
(viscopedia)

Table 2. shows the calculation results of the Reynolds number experiments using the
modeled instrument. The laminar flow calculation is shown in Table 2. by the 1 st to 6th with the
values of each Reynolds number obtained under 2000 that match to the Reynolds value limit
which shows the laminar flow and is shown before in Figures 2a to 2f. The Reynolds number at
7th is between 2000 to 4000 that shows the transition flow and shown in Figure 3. While at 8th
the Reynolds number is over 4000 that indicates the turbulent flow and shown in Figure 4.

4. Conclusion and Remarks
With a measured discharge, the fluid flow rate can be calculated, and then the result can
be used to calculate the Reynolds number by entering the fluid velocity value into Eq. (9). By the
taken photographs, the various images are obtained, and it represents the value each Reynolds
number. By the obtained results in this study, it is can be concluded that the laminar flow occurs
at Reynolds number below 2000, the shift of fluid flow from the laminar flow to turbulent flow
occurs when the Reynolds number reaches the value between 2000 to 4000 and when the
Reynolds number is over 4000, the fluid flow shift into turbulent flow.

9

References
B. R. Munson, D.F Young and T. H. Okiisshi, 1998. Fundamentals of Fluid Mechanics, John Wiley and
Sons, Inc. .
F. M. White, 1999. Fluid Mechanics, McGraw-Hill.
L. I. Sedov. 1959. Similarity and Dimensional Methods in Mechanics,Academic, New York.
Moin, P. & Kim, J. 1982. Numerical Investigation of Turbulent Channel Flow. Journal of Fluid Mechanics,
118, 341-377.
http://aeroMultigrid
Navier-Stokes
Calculations
for
Three-Dimensional Cascades
comlab.stanford.edu/Papers/AIAA-11850-730.pdf
Orianto, M. Ir. BSE dan Pratikto, W.A. Ir. M. Sc. 1995. Mekanika Fluida 1, BPFE:Yogyakarta
Peixinho, J., Nouar, C., Desaubry, C. & Theron, B. 2005. Laminar transitional and turbulent flow of yield
stress fluid in a pipe. Journal of Non-Newtonian Fluid Mechanics, 128, 172-184.
Reynolds, O. 1883. An experimental investigation of the circumstances which determine whether the
motion of water shall be direct or sinous, and of the law of resistances in parallel channels. Phil
Trans Roy Soc London, 174, 935-982.
Reynolds, O. 1895. On the Dynamical theory of Incompressible Viscous Fluids and the Determination of
the Criterion. Phil. Trans. Roy. Soc. (London), 186A, 123-164.
Ridwan. (1982). Mekanika Fluida, Universitas Gunadarma, Depok.
Salwen, H., Cotten, F. W. & Grosch, C. E. 1980. Linear stability of Poiseuille flow in a circular pipe. J. Fluid
Mech., 98, 273.
Tutorial on Scaling Analysis of Navier-Stokes Equations: Linear and Non-linear Dynamics of FluidStructure-Interaction
https://www.asdjournal.org/index.php/asd/article/viewfile/15/dowell_asdj2011.pdf
Viscosity Tables Water IAPWS , 2008. http://viscopedia.com/viscosity-table/substances/water/

10

ATTACHMENT

11

EXPERIMENT MODULE
I.

Purpose
Visualize the laminar flow and calculate the Reynolds number.

II. Instruments and materials
Note :
1. Dye Injector

1

2. Discharge control valve
2

3. Constant head tank

3
4

4. Thermometer

5

5. Overflow pipe

6
7
8
9

6. Marbles
7. Water Supply
8. Overflow to drain

10

9. Shroud
11

10. Glass test pipe
11. Discharge control valves
12. stopwatch
13. Measuring glass

12

13

Figure 1. Reynolds Number Experiment Instrument

III. PROCEDURES OF EXPERIMENT
a. Prepare the experimental instruments by placing the Reynolds number experiments
according to Figure 1.Reynolds number experimental instrument.
b. Fill the Reservoir (1) with the dye (ink), and lower the dye injector until it reaches the
upper inlet mouth.
c. Open the inflator valve on water supply (7) and let the liquid enter the tank. Try to
achieve a constant fluid surface, do not exceed
d. Leave the fluid for 5 minutes and measure the fluid temperature by putting the
thermometer into it (4).
e. Open the flow control valve (2) gradually and arrange the dye-controlling valve until it
reaches the slow flow with clear dye.
12

f.

Determine the magnitude of the discharge Q by accommodating the flowing liquid
through the tube during certain time into the measuring glass.

g. Enter the obtained discharge Q into Table. 1, then calculate the Reynolds number
value.
h. Take a picture of the flowing fluid through the transparent tube (10) while the
measurement of the discharge value taking place.
i.

At each end of the experiment, measure the temperature again.

j.

Repeat the procedure above for varying Q from small magnitude until each laminar,
transition and turbulent fluid flow is achieved.

IV. Observation table
Reynolds number

No.

volume
(m3)

time
(s)

3

Q (m /s)

D (m)

 (m2/s)

2

A (m )

v (m/s)

Re
(viscopedia)

1
2
3
4
5
6
7
8

13

Temperature
(0C)

LAMPIRAN

14

15