This experiment aimed to determine the Reynolds number (NRe) as a function of flow rate for liquid flowing through a circular pipe. NRe was calculated for 6 trials with increasing flow rates. All trials had NRe below 2100, indicating laminar flow as observed by the smooth movement of dye in the pipe. As flow rate increased, NRe also increased but remained in the laminar flow regime. The results show that flow type depends on NRe, with laminar flow occurring at low velocities (NRe < 2100).

1. REYNOLD’S NUMBER
ELECCION, NICELY JANE R.
Department of Chemical Engineering
College of Engineering and Architecture
Cebu Institute of Technology – University
N. Bacalso Ave., Cebu City 6000
This experiment’s objective is to be able to determine the Reynolds Number, NRe, as a
function of flow rate and to characterize the type of flow of liquid in a circular pipe.
Reynold’s number in Geankoplis (2009) is used to characterize the regimes of flow. The
types of flow characterized are laminar, transitional and turbulent flow. The flow is laminar
when the fluid is flowing slowly, and turbulent when the fluid flows fast and transitional
when the flow switches between laminar and turbulent. It was observed that at laminar
flow where the velocity is low, the dye forms a thin thread line then it slightly swirls as
velocity is increased and at further increase of velocity which characterizes turbulent flow,
the flow of dye fully swirls then disperses. This shows that as the water flow rate
increases, the calculated Reynolds number also increases.

2. 1. Introduction
Reynolds (1883) was the first to propose a criterion for differentiation between
laminar and turbulent flows in his classic dye visualization with the equation: NRe = Dvρ/μ
and suggested a critical value of NRe = 2100 for the upper limit of laminar flow.. Fluid flow
can be classified to three regimes: laminar, transitional and turbulent. The laminar regime
is a where the flow is characterized by fluid particles moving in the form of lamina sliding
over each other. It is a flow characterized by smooth streamlines and highly ordered
motion. The turbulent regime is where the flow is characterized by constant agitation and
intermixing of fluid particles such that their velocity changes from point to point and even
at the same point from time to time. It is characterized by velocity fluctuations and highly
disordered motion. The transitional regime is where the flow fluctuates between laminar
and turbulent before it becomes fully turbulent.
The objective of this experiment is to be able to determine the Reynolds Number
as a function of flow rate and to characterize the type of flow of liquid in a circular pipe.
In fluid mechanics, a number that indicates whether the flow of a fluid is steady
(laminar flow) or on the average steady with small, unsteady changes (turbulent flow) is
the Reynolds number. In case of flow through pipe for values of Re<2100 the flow is
laminar while Re>40000 it is turbulent and for 2100<Re<4000 it is transition flow.
The critical velocity averaged over the cross section at which laminar pipe flow
changes to transitional flow or transitional flow changes to turbulent, is believed to be a
function primarily of the pipe diameter, the fluid density and the fluid dynamic viscosity.

3. 2. Materials and Methods
2.1 Equipment and Materials
 Osbourne Reynolds Number Apparatus
 Dye
 Thermometer
 Stopwatch
 1 L Graduated Cylinder
 1 Digital Camera
2.2 Methods
The diameter of the pipe was determined in order to compute the cross-
sectional area of the pipe. The temperature of the water was obtained to determine
the viscosity and density. The dye reservoir was mounted on top of the head tank.
The head tank was continuously supplied with water from the faucet and at the same
time the control valve was opened at the end of the visualization pipe. The flow was
allowed to stabilize for thirty seconds or more. The dye was slowly introduced by
adjusting the dye control valve. The behavior of the dye was then observed. An
amount of water was collected for each change observed from the dye inside the
pipe. The amount of water collected was measured using a graduated cylinder. The
volumetric flow rate of water was observed and its corresponding Reynolds number
during the course of the change from Laminar-Transition flow and Transition-
Turbulent flow was computed. A picture of the dye behavior for each analysis was
taken to support the computed Reynolds number.

4. 3. Result
Table 3.1 Data obtained from Reynold’s Appartus
4. Calculations
Diameter of ther pipe = 0.008m
ρ = 996.24
𝑘𝑔
𝑚3
µ = 0.008817
𝑘𝑔
𝑚.𝑠
Cross-sectional Area =
𝜋𝑑2
4
=
𝜋(0.008)2
4
= 5.0265 x 10−5
𝑚2
Solving for volumetric flowrate, Q=
𝑉
𝑡
Solving for Velocity, V=
𝑄
𝐴
Solving for Reynolds’ Number, NRe =
𝐷𝑉𝜌
𝜇
Trial 1:
Q1=
(125 𝑚𝐿)(
1𝑐𝑚3
1𝑚𝐿
)(
1𝑚
100𝑐𝑚
)3
16.03𝑠
= 7.7979x10-6 m3/s
V1 =
7.7979 𝑥 10 −6
𝑚3
/𝑠
5.0265 𝑥 10−5 𝑚2 = 0.1551 m/s
Trial
No.
Temp
(°C)
Density
(kg/m3)
Viscosity
(Pa s)
Volume of
Water
Collected
(mL)
Time
(sec)
Volumetric
flow rate, Q,
(m3/s)
Reynolds
Number,
NRe
(dimensio
nless)
Type
of
Flow
1 25 996.24 0.008817 125 16.03 7.7979 x 10-6 140.1990 Laminar
2 25 996.24 0.008817 195 14.04 1.3889 x 10-5 249.7549 Laminar
3 25 996.24 0.008817 235 12.11 1.9405 x 10-5 349.0060 Laminar
4 25 996.24 0.008817 220 9.16 2.4017 x 10-5 431.8961 Laminar
5 25 996.24 0.008817 295 7.64 3.8613 x 10-5 694.3963 Laminar
6 25 996.24 0.008817 135 7.85 1.7197 x 10-5 309.2333 Laminar

5. NRe1 =
(0.008𝑚)(996.24
𝑘𝑔
𝑚3)(0.1551
𝑚
𝑠
)
(0.008817
𝑘𝑔
𝑚.𝑠
)
= 140.1990
Trial 2:
Q2=
(195 𝑚𝐿)(
1𝑐𝑚3
1𝑚𝐿
)(
1𝑚
100𝑐𝑚
)3
14.04𝑠
= 1.3889x10-5 m3/s
V2 =
1.3889 𝑥 10−5
𝑚3
/𝑠
5.0265 𝑥 10−5 𝑚2 = 0.2763 m/s
NRe2 =
(0.008𝑚)(996.24
𝑘𝑔
𝑚3)(0.2763
𝑚
𝑠
)
(0.008817
𝑘𝑔
𝑚.𝑠
)
= 249.7549
Trial 3:
Q3=
(235 𝑚𝐿)(
1𝑐𝑚3
1𝑚𝐿
)(
1𝑚
100𝑐𝑚
)3
12.11𝑠
= 1.9405x10-5 m3/s
V3 =
1.9405 𝑥 10−5
𝑚3
/𝑠
5.0265 𝑥 10−5 𝑚2 = 0.3861 m/s
NRe3 =
(0.008𝑚)(996.24
𝑘𝑔
𝑚3)(0.3861
𝑚
𝑠
)
(0.008817
𝑘𝑔
𝑚.𝑠
)
= 349.0060
Trial 4:
Q4=
(220 𝑚𝐿)(
1𝑐𝑚3
1𝑚𝐿
)(
1𝑚
100𝑐𝑚
)3
9.16𝑠
= 2.4017x10-5 m3/s
V4 =
2.4017 𝑥 10−5
𝑚3
/𝑠
5.0265 𝑥 10 −5 𝑚2 = 0.4778 m/s
NRe4 =
(0.008𝑚)(996.24
𝑘𝑔
𝑚3)(0.4778
𝑚
𝑠
)
(0.008817
𝑘𝑔
𝑚.𝑠
)
= 431.8961
Trial 5:

6. Q5=
(295 𝑚𝐿)(
1𝑐𝑚3
1𝑚𝐿
)(
1𝑚
100𝑐𝑚
)3
7.64𝑠
= 3.8613x10-5 m3/s
V5 =
3.8613 𝑥 10−5
𝑚3
/𝑠
5.0265 𝑥 10 −5 𝑚2 = 0.7682 m/s
NRe5 =
(0.008𝑚)(996.24
𝑘𝑔
𝑚3)(0.7682
𝑚
𝑠
)
(0.008817
𝑘𝑔
𝑚.𝑠
)
= 694.3963
Trial 6:
Q6=
(135 𝑚𝐿)(
1𝑐𝑚3
1𝑚𝐿
)(
1𝑚
100𝑐𝑚
)3
7.85𝑠
= 1.7197x10-5 m3/s
V6 =
1.7197 𝑥 10−5
𝑚3
/𝑠
5.0265 𝑥 10−5 𝑚2 = 0.3421 m/s
NRe6 =
(0.008𝑚)(996.24
𝑘𝑔
𝑚3)(0.3421
𝑚
𝑠
)
(0.008817
𝑘𝑔
𝑚.𝑠
)
= 309.2333

7. 5. Sketch

8. 6. Discussion
The Reynolds number of each trial was calculated using the obtained data and
then tabulated in Table 3.1. Also, displayed in the aforementioned table is the type of flow
as observed with the naked eyes. All six trials showed laminar and smooth flow and their
Reynolds Numbers were both calculated to be below 2100. Laminar Flow occur at low
velocities, where the layers of fluid seem to slide by one another without eddies or swirls
being present; on the other hand, turbulent flow occurs at higher velocities, where eddies
are present giving the fluid a fluctuating nature.
Possible errors arrived in the experiment especially when expecting a turbulent
flow as the velocity was increased might be possible due to a defective equipment and
the instability of the area where it was situated.
7. Conclusion
The flow of a fluid can be characterized to be laminar, turbulent, or transitional. In
laminar flow, the motion of the particles of a fluid is very orderly with particles close to a
solid surface moving in straight lines parallel to that surface. Flow is laminar at Reynolds
Numbers of below 2100. In turbulent flow, the motion of the particles is chaotic and there
is lateral mixing. Flow is turbulent at Reynolds Numbers of above 4000. Between
Reynolds Numbers of 2100 and 4000, flow is in transition.
In this experiment, the Reynolds Number as a function of flow rate was
determined. It was found out that as the water flow rate increases, the calculated
Reynolds number also increases.

9. 8. Recommendation
In this experiment, it is best to use the highest quality of an Osbourne Reynolds
Apparatus, have proper execution of the experiment by the people assigned to it and
setting the experiment in the best atmosphere where there are no distractions and the
like that may alter results in order to achieve accurate data especially in getting the
determining whether the flow is laminar or turbulent as seen in the naked eye.
9. References
[1] Geankoplis, C.J. (2009) Principles of Transport Processes and Separation
Processes. 1st edition. Pearson Education South Asia PTE. LTD.
10.Web References
[1] Reynolds Number: Introduction and Definition of the Dimensionless Reynolds
Number. Retrieved from https://www.engineeringtoolbox.com/reynolds-number-
d_237.html
[2] Reynolds Number. (2016, September 7). Retrieved from
https://byjus.com/physics/reynolds-number/
[3] What is the difference between laminar flow and turbulent flow?. Retrieved from
http://www.physlink.com/education/askexperts/ae464.cfm
[4] Laminar Flow. Retrieved from http://hyperphysics.phy-
astr.gsu.edu/hbase/pfric.html