EXPERIMENT 1
Reynolds’ Number
Presented to the
Faculty of the Department of Chemical Engineering
School of Engineering and Architecture
Saint Louis University
In Partial Fulfillment of the Requirements for the Course:
CHE 3251L: Chemical Engineering Laboratory 1
by:
Luis, Shaira Mae R.
Manoguid, Phoebe Kate U.
Marna, Conaya F.
Masilungan, Angelica L
September 2022
Department of Chemical Engineering
School of Engineering and Architecture
Saint Louis University
LABORATORY REPORT EVALUATION SHEET
Laboratory Course: CHE 3251L
Schedule: 7:30-10:30 ThF
Experiment Number: 1
Experiment Title: Reynolds’ Number
Group Number: 4
Group Members: Luis, Shaira Mae R.
Manoguid, Phoebe Kate U.
Marna, Conaya F.
Masilungan, Angelica L
Date Performed: August 19, 2022
CONTENTS
I.
II.
III.
IV.
V.
VI.
VII.
Introduction
Equipment/Materials Needed
Procedures
Data and Results
Discussion
Conclusion
References
(APA format)
Appendices:
a. Computations
b. Answers to
Questions/Problems
c. Documentation
Format and Neatness
TOTAL POINTS:
Evaluated by: Engr. Genevive S. de Vera
Date Submitted: September 2, 2022
TOTAL
POINTS
10
3
3
15
25
15
REMARKS
3
10
10
3
3
100 pts
SCORE:
Date: _____
SCORE
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CHE 3251L LABORATORY REPORT
Experiment No: 1
Title: REYNOLD’S NUMBER EXPERIMENT
At the end of this experiment, the student should be able to:
TLO# 1: Reproduce the classical experiment conducted by Osborne Reynolds concerning the
fluid flow conditions.
TLO #2: Observe the laminar, transition and turbulent velocity profiles as related to Reynolds’
number.
I.
INTRODUCTION
In the 19th century, Osborne Reynolds was honored with the term "Reynolds’ Number."
Two distinct forms of flow have been established in an experiment by Osborne Reynolds. In order
to conduct the experiment, a long, clear water-flowing tube was filled with a thin stream of a
colored fluid that had the same density as water. Numerous elusive fluid characteristics, including
flow rate, fluid density, pipe diameter, and fluid viscosity, affect the Reynolds number.
𝑅𝑒 =
VDρ
μ
Reynolds’ number (Re) is also defined as a ratio of inertial or destabilizing force to the
viscous damping or stabilizing force. With the increase in the value of Re, the fluid flow gets into
full-blown turbulence as the inertial flow becomes relatively larger. The Reynolds’ number has
many practical applications, as it provides engineers with immediate information about the state
of flow throughout pipes, streams, and soils, helping them apply the proper relationships to solve
the problem at hand. It is also very useful for dimensional analysis and similitude. As an example,
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if forces acting on a ship need to be studied in the laboratory for design purposes, the Reynolds’
number of the flow acting on the model in the lab and on the prototype in the field should be the
same.
Fluid mechanics deals with the study of all fluids under static and dynamic situations. Fluid
mechanics is a branch of continuous mechanics which deals with a relationship between forces,
motions, and statical conditions in a continuous material. This study area deals with many and
diversified problems such as surface tension, fluid statics, flow in enclose bodies, or flow round
bodies (solid or otherwise), flow stability, etc.
Flow behavior in natural or artificial systems depends on which forces (inertia, viscous,
gravity, surface tension, etc.) predominate. In slow-moving laminar flows, viscous forces are
dominant, and the fluid behaves as if the layers are sliding over each other. Laminar flow is also
referred to as streamline or viscous flow. These terms are descriptive of the flow because, in
laminar flow, (1) layers of water flowing over one another at different speeds with virtually no
mixing between layers, (2) fluid particles move in definite and observable paths or streamlines,
and (3) the flow is characteristic of viscous (thick) fluid or is one in which viscosity of the fluid
plays a significant part. In turbulent flows, the flow behavior is chaotic and changes dramatically,
since the inertial forces are more significant than the viscous forces. Turbulent flow is
characterized by the irregular movement of particles of the fluid. There is no definite frequency as
there is in wave motion. The particles travel in irregular paths with no observable pattern and no
definite layers. Laminar and turbulent flow can occur in two quite different regimes in both nature
and laboratory research. When fluid particles move in laminar flows, they do so in layers that slide
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over one another, resulting in a little energy exchange between the layers. When fluids move
slowly and with high viscosity, laminar flow develops. The fluid's particles move and mix
randomly in a turbulent flow, on the other hand, and there is a significant energy exchange within
the fluid. Low viscosity, high-velocity fluids exhibit this sort of flow. Reynolds’ number, which
has no dimensions, is used to categorize the flow condition. A well-known experiment called the
Reynolds’ Number Demonstration involves slowly and gradually introducing dye into a pipe to
see flow characteristics.
II.
EQUIPMENT/ MATERIALS NEEDED
Table 1.1 List of apparatus used with their specific functions in the experiment
Apparatus
Use
It is used to measure the
Thermometer
temperature.
It is used for containing
1000 mL Beaker
and measuring liquids.
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It is used to measure the
time interval of an event,
Stopwatch
which is the filling the
beaker with 1000 mL of
water and ink solution.
It is used to give a visual
demonstration of laminar,
Reynolds’ Apparatus
transition, and turbulent
flow.
III.
PROCEDURES
The dye injector was placed within the glass cylinder. Then hose is connected to the water
outlet allowing the water to flow through the inner part of the glass cylinder. The plastic outlet
valve is opened so that the water will flow to the canal. Potassium permanganate solution is poured
into the ink station and its flow is regulated through the equipment. When the ink flow has
stabilized as well as the water flow, the ink inflow line and the plastic gate valve was closed slowly.
By gradually opening the exit valve, to give successively higher velocities, the time it takes to fill
a 1000 mL beaker is measured. While Reynolds’ number in x-axis vs. velocity in y-axis is plotted.
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IV.
DATA AND RESULTS
Outer diameter of the pipe, m:
Thickness of the pipe, m:
Inner diameter of the pipe, m: 0.0134 m
Density of the fluid, kg/m3: 997.2113 kg/m3
Viscosity of the fluid, Pa·s: 1.0115 x 10˗3 Pa·s
Temperature of the Fluid, K: 293.15 K
Table 1.2 Time, velocity, and Reynolds’ number for each trial
FLOW REGIME
LAMINAR
TRANSITION
TURBULENT
TRIAL
TIME (s)
VELOCITY (m/s)
REYNOLD’S NUMBER
1
186 s
0.0381 m/s
503.3280
2
152.4 s
0.0465 m/s
614.2979
3
147 s
0.0482 m/s
636.7561
1
30 s
0.2364 m/s
3123.0114
2
36 s
0.1970 m/s
2602.5095
3
44 s
0.1612 m/s
2129.5662
1
20.77 s
0.3414 m/s
4510.1358
2
20.10 s
0.3528 m/s
4660.7379
3
20.53 s
0.3454 m/s
4562.9786
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V.
DISCUSSION
The data presented above shows the results obtained by the students, specifically the time
it took for the fluid to flow during the three fluid flow regimes. To solve the Reynolds’ number in
every trial per flow regime, it requires the inner diameter of the outlet pipe. It also requires the
velocity, density, and the viscosity of the fluid, which is water. The values taken from the table of
Properties of Water of the Perry's Handbook were the following: for the density, 997.2113kg/m 3,
and for the viscosity of the fluid, 1.0115x10-3 Pa·s. Using the inner diameter to get the area, the
students have computed a value of 1.4103x10-4 m2. Now using this, the students were able to
compute the following values of velocity; for Laminar flow trials one to three: 0.0381 m/s, 0.0464
m/s, and 0.0482 m/s, respectively. For Transition flow trials one to three, respectively: 0.2364 m/s,
0.1970 m/s, and 0.1612 m/s. And lastly for turbulent flow trials one to three: 0.3414 m/s, 0.3528
m/s, and 0.3452 m/s. Now for the Reynolds' number, the students have computed the values using
the formula given. The values computed for the three trials for Laminar flow are the following:
503.3280, 614.2979, 636.7561. Moreover, for transition flow trials one to three, 3123.0114,
2602.5095, and 2129.5662. And lastly, for the turbulent flow trials one to three, 4510.1358,
4660.7379.
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Reynolds' Number vs. Velocity
0.4
Velocity (m/s)
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
1000
2000
3000
4000
5000
Reynolds' number (Re)
Figure 1.1 Reynolds’ Number vs. Velocity
To observe laminar, transition, and turbulent velocity profiles related to Reynolds' Number
is the learning outcome of this first experiment. By plotting the Reynolds’ Number and the velocity
of the fluid, we can observe that there is an existing direct relationship that is proportional between
the two variables. Hence, we can say that as the Reynolds’ Number increases, the velocity
increases as well. As a result, it can also be emphasized that 0.0381 m/s as the slowest flow velocity
and 503.3280 as the smallest value of Reynolds’ Number shows that the fluid flows smoothly,
which then, therefore, is laminar. On the other hand, the turbulent flow having the highest velocity
of 0.3528 m/s and Reynolds’ Number which is 4660.7379 indicates a rapid flowrate, and can be
seen in the apparatus by the naked eye. The transition flow, moreover, pertains to the between
status of the laminar and the turbulent flow, having a value of 0.2364 m/s as its velocity and
3123.0114 as its Reynolds’ Number.
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VI.
CONCLUSION
Three different flow types were observed in the experiment: laminar, transition, and
turbulent. In the experiment, the students observed that laminar flow occurred when the ink moved
slowly in a straight line parallel to the tube. When the formation of eddies occurs, there are
turbulent outbursts, and the ink travels in a waveform, it is in the transition region. Its velocity
exceeds that of the laminar flow. On the other hand, it is a turbulent flow when there is already
lateral mixing and no discernible ink streamline.
The fastest velocity is found in a turbulent flow. The longest time was recorded to attain
laminar flow, while the shortest time for turbulent flow. It is a laminar flow when the Reynolds'
number (Re) is less than 2100. Reynolds' number for transition flow is greater than or equal to
2100 and lesser than or equal to 4000. The value of Reynolds' number of turbulent flow is above
4000.
The experiment's results are in line with the stated conditions. The computed Reynolds’
numbers for the laminar flow are 503.3280, 614.2979, and 636.7561. The transition flow's
calculated Reynolds' numbers are 3123.0114, 2602.5095, and 2129.5662. Lastly, the computed
Reynolds' numbers for turbulent flow are 4510.1358, 5660.7379, and 4562.9786.
It is recommended to ensure that the flow is stable before filling the beaker and recording
the time. The beaker must be filled and the time must be recorded synchronously. Filling the beaker
up to 1 liter and recording the time must be done carefully and correctly; the persons in charge
must be alert and fast. To minimize problems identifying the type of flow seen in the tube, it is
also advised to read about the theory and experiment before experimenting.
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VII. REFERENCES
1.1: What is Fluid Mechanics? (2016, July 31). Engineering LibreTexts.
https://eng.libretexts.org/Bookshelves/Civil_Engineering/Book%3A_Fluid_Mechanics_(
BarMeir)/00%3A_Introduction/1.1%3A_What_is_Fluid_Mechanics%3F
Ahmari, H., & Kabir, S. M. I. (2019, August 14). Experiment #7: Osborne Reynolds’
Demonstration. Uta.pressbooks.pub; Mavs Open Press.
https://uta.pressbooks.pub/appliedfluidmechanics/chapter/experiment-7/
BYJU'S. (2022, April 26). Reynolds number - definitions, formulas and examples - Byju's.
BYJUS. Retrieved August 29, 2022, from https://byjus.com/physics/reynolds-number/
Laminar and Turbulent Flow | Engineering Library. (n.d.). Engineeringlibrary.org.
https://engineeringlibrary.org/reference/laminar-and-turbulent-fluid-flow-doe-handbook
Sharma, C. (2021, June 15). 8 laminar flow examples in real life. StudiousGuy. Retrieved August
29, 2022, from https://studiousguy.com/laminar-flow-examples/
What is Reynolds number and why is it important? Cadence. (2022, January 14). Retrieved
August 29, 2022, from https://resources.system-analysis.cadence.com/blog/msa2022what-is-reynolds-number-and-why-is-it-important
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VIII.
APPENDICES
A. Definition of Terms:
1.
Laminar Flow - It is a type of flow pattern of a fluid in which all the particles are flowing in
parallel lines, opposed to turbulent flow, where the particles flow in random and chaotic
directions.
2.
Reynolds’ Number - It is the ratio of inertial forces to viscous forces occurring in a fluid flow.
3.
Transitional Flow - It is a mixture of laminar and turbulent flow, with turbulence in the center
of the pipe, and laminar flow near the edges.
4.
Turbulent Flow - It is a type of flow of fluid in which the fluid travels in irregular path. In this
type of flow, the speed of the fluid at a point undergoes changes continuously in both
magnitude and direction.
B. Computations:
A=
π 2
π
Dinner = (0.0134m)2 = 1.4103 × 10−4 m2
4
4
For Laminar
Trial 1:
q=
V
1L
1m3
m3
=
×
= 5.3763 × 10−6
t 186s 1000L
s
3
−6 m
5.3763
×
10
q
s = 0.0381 m
υ= =
−4
A 1.4103 × 10 m2
s
kg
m
Dυρ (0.0134m) (0.0381 s ) (997.2113 m3 )
Re =
=
= 503.3280
μ
1.0115 × 10−3 Pa. s
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Trial 2:
1L
1m3
×
q
m
υ = = 152.4s 1000L
= 0.0465
−4
2
A 1.4103 × 10 m
s
kg
m
Dυρ (0.0134m) (0.0465 s ) (997.2113 m3 )
Re =
=
= 614.2979
μ
1.0115 × 10−3 Pa. s
Trial 3:
1L
1m3
×
q
m
υ = = 147s 1000L
=
0.0482
A 1.4103 × 10−4 m2
s
kg
m
Dυρ (0.0134m) (0.0482 s ) (997.2113 m3 )
Re =
=
= 636.7561
μ
1.0115 × 10−3 Pa. s
For Transition
Trial 1:
1L
1m3
×
q
m
υ = = 30s 1000L
= 0.2364
−4
2
A 1.4103 × 10 m
s
kg
m
Dυρ (0.0134m) (0.2364 s ) (997.2113 m3 )
Re =
=
= 3123.0114
μ
1.0115 × 10−3 Pa. s
Trial 2:
1L
1m3
×
q
m
υ = = 36s 1000L
= 0.1970
−4
2
A 1.4103 × 10 m
s
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kg
m
Dυρ (0.0134m) (0.1970 s ) (997.2113 m3 )
Re =
=
= 2602.5095
μ
1.0115 × 10−3 Pa. s
Trial 3:
1L
1m3
×
q
m
υ = = 44s 1000L
= 0.1612
−4
2
A 1.4103 × 10 m
s
kg
m
Dυρ (0.0134m) (0.1612 s ) (997.2113 m3 )
Re =
=
= 2129.5662
μ
1.0115 × 10−3 Pa. s
For Turbulent
Trial 1:
1L
1m3
×
q
m
υ = = 20.77s 1000L
=
0.3414
A 1.4103 × 10−4 m2
s
kg
m
(997.2113
)
(0.0134m)
(0.3414
)
Dυρ
s
m3
Re =
=
= 4510.1358
μ
1.0115 × 10−3 Pa. s
Trial 2:
1L
1m3
×
q
m
υ = = 20.10s 1000L
= 0.3528
−4
2
A 1.4103 × 10 m
s
kg
m
Dυρ (0.0134m) (0.3528 s ) (997.2113 m3 )
Re =
=
= 4660.7379
μ
1.0115 × 10−3 Pa. s
Trial 3:
1L
1m3
×
q
m
υ = = 20.53s 1000L
= 0.3454
−4
2
A 1.4103 × 10 m
s
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kg
m
Dυρ (0.0134m) (0.3454 s ) (997.2113 m3 )
Re =
=
= 4562.9786
μ
1.0115 × 10−3 Pa. s
C. Answers to Questions:
A. Give 3 real-life situations each where laminar and turbulent flows are observed. Describe
briefly.
Laminar:
a. Rivers/canals- The water flowing in calm rivers or other bodies of water is slow
and smooth. Because there are no waves or swirls in the water body, the different
layers of water do not interfere with each other and follow a straight path parallel
to each other.
b. Taps- When water flows through the tap, there is no turbulence. When water is
dispensed from taps, the moment pressure and viscosity become the same at all
points in the water.
c. Viscous fluid- Fluids such as honey, glycerin, and other syrups exhibit laminar
flow. Because the pressure, viscosity, and other physical parameters of a viscous
fluid remain constant at each point of the fluid, the laminar flow appears.
Turbulent:
a. Blood Flow in Arteries- The aortic curve bends the blood flow, causing the blood
cells to mix. A bulge in the arteries can sometimes cause turbulent blood flow. This
raises radial pressure and shear stress on the artery wall.
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b. Air from Fan/AC- The air from a fan or air conditioner is circulated throughout the
room by the fan's rotating blades. The airflow inside the room is chaotic. The
particles or dust and the air mix together.
c. Car Exhaust- The smoke particles from a car's exhaust pipes do not remain
separated; instead, they mix and flow in a random zig-zag pattern, displaying
turbulent flow.
B. Define Reynolds number and identify what its value implies.
Reynolds number is defined by the ratio of inertial forces to viscous forces. Reynolds
number is a dimensionless quantity used to determine the type of flow pattern as laminar or
turbulent while flowing through a pipe. The flow is laminar if the Reynolds number is less
than 2100. The flow through the pipe is turbulent if the Reynolds number is greater than 4000.
A transition flow is defined as Reynold's number between 2100 and 4000, indicating a
combination of laminar and turbulent flow.
C. What is the importance of identifying the Reynolds number in flowing fluids?
Reynolds number facilitates the prediction of flow behavior. Identification of flow
regime with Reynolds number facilitates the creation of an ideal flow model for efficient fluid
system design. Some practical applications include:
•
Simulation of aircraft or vehicle models in laminar and turbulent flow conditions.
•
Developing correlation between the heat transfer and friction factor within the
flow system.
•
Prediction of the onset of turbulence can help facilitate large-scale prediction of
flow behavior.
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•
Identify pressure requirements with flow rate calculations.
D. Documentation:
Fig. 1.2 Reynolds’ Apparatus
Fig. 1.4 Laminar Flow
Fig. 1.3 Adjusting the Valve
Fig. 1.5 Filling 1 L Beaker with Water
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Fig. 1.6 Controlling the Valve
Fig. 1.7 Laminar Flow
Fig. 1.8 Measuring the Temperature