Final Report in Reynold's Number CheLab1

1. 1
1. INTRODUCTION
Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is
subjected to relative internal movement due to different fluid velocities. The concept was
introduced by Sir George Stokes in 1851,] but the Reynolds number was named by Arnold
Sommerfeld in 1908[3] after Osborne Reynolds (1842–1912), who popularized its use in 1883.
The inertial force and the viscous force is similar. This goes that they also have the
same units thus the Reynolds number is unitless. We can determine whether fluid flow is
laminar or turbulent based on the Reynolds number.
The objective of this experiment is 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. The
experiment gives insight on how to determine or the process of obtaining the Reynolds number
of a fluid. Also, the experiment uses a dye to help predict the type of flow of the fluid. If the
dye runs smoothly together with the fluid, then it is assumed to have a laminar flow. If the dye
flows in a violent manner then it is considered to be Turbulent. If the dye is in zigzag form but
is consistent in flow then it is in transient flow or between laminar and turbulent.
The Reynolds number is one of the basic quantity in fluid mechanics and is mostly
used in various computations. In production, the flow rate of the materials must be controlled.
It helps to predict the flow pattern of liquids. It may be laminar or turbulent depending on the
properties of the material. It is important to include the Reynolds number to avoid unnecessary
eddies or disturbances or to avoid extremely slow flow rate of the fluids.

2. 2
2. THEORETICAL BACKGROUND
The Reynolds number is the ratio of a fluid's inertial force to its viscous force. Inertial
force involves force due to the momentum of the mass of flowing fluid. Viscous forces deal
with the friction of a flowing fluid. I
In fluid mechanics, it is 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 less than that of 2100, the flow
is laminar while if it is more than that of 4000 then it is turbulent and for 2100<Re<4000 it is
in transition flow.
The Reynolds number is a function of the fluid’s velocity given a fixed setting and
material. Thus, it can also be expressed as a function of flowrate.
With respect to laminar and turbulent flow regimes:
• laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is
characterized by smooth, constant fluid motion;
• turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which
tend to produce chaotic eddies, vortices and other flow instabilities.
The dimensionless number can be determined by the equation:
𝑁 𝑅𝑒 =
𝜌𝐷𝑣
𝜇

3. 3
Equation 1
where:
• NRe is the Reynolds number, which is unitless
• ρ is the fluid density in kilograms-per-cubic-meter (kg/m3)
• v is the velocity in meters-per-second (m/s)
• D is the diameter of the pipe in meters (m)
• μ is the viscosity of the fluid in pascal-seconds (Pa⋅s)
This equation can also be expressed in terms of rate flow since
𝑄 = 𝐴𝑣
Equation 2
A = cross-sectional area of the pipe
Then
𝑁 𝑅𝑒 =
4𝜌𝑄
𝜋𝐷𝜇
Equation 3
Where the Reynolds number is a function of the flow rate of the fluid in a pipe.

4. 4
The apparatus that is used in the experiment is the Osbourne Reynolds apparatus. This
is equipped with a dye which can indicate the flow of the fluid. If the dye runs smoothly
together with the fluid, then it is assumed to have a laminar flow. If the dye flows in a violent
manner then it is considered to be Turbulent. If the dye is in zigzag form but is consistent in
flow then it is in transient flow or between laminar and turbulent. The concept of the apparatus
is shown below in Figure 2.1.
Figure 2.1

5. 5
3. EXPERIMENTAL SECTION
3.1 Materials and Apparatus
- Osbourne Reynolds Number Apparatus
- Dye
- Thermometer
- Stopwatch
- 1 Liter Graduated Cylinder
- 1 Digital Camera
3.2 Procedure
The apparatus was setup and the diameter and cross-sectional area was
determined. After setting up, the temperature of the water was recorded for the density
and viscosity of the water to be determined. The dye was mounted on top of the head
tank and the head tank was supplied with water and the control valve was opened
securing the flow rate of the water supplied and the flow rate of the control valve was
the same. The flow was stabilized for 30 seconds.
The dye was introduced slowly by adjusting the dye control valve and the
behavior of the dye was observed and a picture was taken. The dye is of importance
because it supports the calculations of the students. An amount of water was collected
in the discharge valve for 15 seconds in order for the actual flow rate to be determined
the Reynold’s number was computed. The same procedure was done for five different
flow rates.

6. 6
3.3 Specifications:
Diameter of pipe = 0.0254 m
Temperature = 31 degrees Celsius
Density of water at given temp = 995.337 kg/m3
Viscosity of water at given temp = 0.3355 x 10-3
kg/m.s

7. 7
4. RESULTS AND DISCUSSION
The experiment lasted for about 10 minutes. The students perfumed at least 5 trials for
the experiment. In the table 4.1, the first 3 columns are the data that were recorded in the
experiment. The succeeding columns were calculated using excel. The calculations can be
found in Appendix using equation 3.
Trial
Volume of
H2O
Collected
(mL)
Collection
Time
Volumetric
Flow rate
(m3/s)
Reynold’s
Number
Type of Flow
(sec) (NRe)
1 655 15 4.3667E-05 6493.86194 Turbulent
2 590 15 3.9333E-05 5849.43289 Turbulent
3 310 15 2.0667E-05 3073.43084 Transient
4 200 15 1.3333E-05 1982.85861 Laminar
5 150 15 0.00001 1487.14396 Laminar
Table 4.1
An amount of 15 seconds of time were the basis of the experiment. For 15 seconds the
volume from the flowrate were recorded. With this, the students identified the Reynolds
number. It is shown that with an increasing flowrate with the same time interval yields
increasing velocity thus also increasing the Reynolds number. This is true since the Reynolds
number is directly proportional to the velocity of the fluid which is water. Trial 1 and 2 were
recorded to be Turbulent flow since its Reynolds number is greater that 4000. This was also

8. 8
shown in the apparatus since the dye did not form a straight flow. Trials number 4 and 5 has a
flow of Laminar. The dye in these trials follows a smooth path with consistency, this is since
the flow is very smooth that forces acting on the dye is very small. Trial number 3 is in
Transient flow. This means that the Reynolds number is between 4000 and 2100. The dye in
this trial forms a zigzag path. This is also true since the dye did break but also did not form a
straight path.

9. 9
5. CONCLUSION
The experiment determined the relationship between the fluid’s Reynolds number and
volumetric flow. It is shown that as the volumetric flow rate increases in a constant diameter
pipe, its Reynolds number also increases. It is also shown in the behavior of the dye being
carried by the fluid. Though there were delays in performing of the experiment because of the
dye clogging, the students manage to obtain the data from another Osbourne apparatus thus
delaying the making of the final report. However, the apparatus is still liable since the data
obtained agrees with the theories making the experiment valid.
6. RECOMMENDATIONS
It is highly recommended to thoroughly clean the apparatus after experiment to avoid
clogging. It can be cleanse by HCl but it will take a long time if not cleaned immediately. Also
the apparatus needs to be handle properly specially in the dye section. A small opening in the
valve controlling the dye is sufficient enough since the needle where the dye is release into the
fluid has very little hole. Over opening the valve causes the dye to overflow.

10. 10
7. REFERENCES
[1] https://www.academia.edu/18747082/CHE241_-
_Lab_Report_Solteq_Osborne_Reynolds_Demonstration_FM11_2015_?auto=download
[2] https://www.nuclear-power.net/nuclear-engineering/fluid-dynamics/reynolds-
number/
[3] https://www.britannica.com/science/Reynolds-number
[4] https://www.simscale.com/docs/content/simwiki/numerics/what-is-the-
reynolds-number.html
Acquired:February24,2018
8. APPENDICES
8.1 Table
Trial
Volume of
H2O
Collected
(mL)
Collection
Time
Volumetric
Flow rate
Q
(m3/s)
Reynold’s
Number
Type of Flow
(sec) (NRe)
1 655 15 4.3667E-05 6493.86194 Turbulent
2 590 15 3.9333E-05 5849.43289 Turbulent
3 310 15 2.0667E-05 3073.43084 Transient

11. 11
4 200 15 1.3333E-05 1982.85861 Laminar
5 150 15 0.00001 1487.14396 Laminar
Table 4.1
8.2 Computations
8.2.1 Volumetric flow rate
𝑄1 =
655 𝑚𝐿
15 𝑠
×
1 𝐿
1000 𝑚𝐿
×
1 𝑚3
1000 𝐿
= 4.3667E − 05 𝑚3
𝑠⁄
𝑄2 =
590 𝑚𝐿
15 𝑠
×
1 𝐿
1000 𝑚𝐿
×
1 𝑚3
1000 𝐿
= 3.9333E − 05 𝑚3
𝑠⁄
𝑄3 =
310 𝑚𝐿
15 𝑠
×
1 𝐿
1000 𝑚𝐿
×
1 𝑚3
1000 𝐿
= 2.0667E − 05 𝑚3
𝑠⁄
𝑄4 =
200 𝑚𝐿
15 𝑠
×
1 𝐿
1000 𝑚𝐿
×
1 𝑚3
1000 𝐿
= 1.3333E − 05 𝑚3
𝑠⁄
𝑄5 =
150 𝑚𝐿
15 𝑠
×
1 𝐿
1000 𝑚𝐿
×
1 𝑚3
1000 𝐿
= 0.00001 𝑚3
𝑠⁄
8.2.2Reynolds Number
𝑁 𝑅𝑒 =
4𝜌𝑄
𝜋𝐷𝜇
Trial 1
𝑁 𝑅𝑒 =
4𝑥(995.337 𝑘𝑔
𝑚3⁄ )4.3667E−05
𝜋(0.0254𝑚)0.3355×10−3 𝑘𝑔
𝑚.𝑠⁄
=6493.86194

12. 12
Trial 2
𝑁 𝑅𝑒 =
4𝑥(995.337 𝑘𝑔
𝑚3⁄ )3.9333E−05
𝜋(0.0254𝑚)0.3355×10−3 𝑘𝑔
𝑚.𝑠⁄
=5849.43289
Trial 3
𝑁 𝑅𝑒 =
4𝑥(995.337 𝑘𝑔
𝑚3⁄ )2.0667E−05
𝜋(0.0254𝑚)0.3355×10−3 𝑘𝑔
𝑚.𝑠⁄
=3073.43084
Trial 4
𝑁 𝑅𝑒 =
4𝑥(995.337 𝑘𝑔
𝑚3⁄ )1.3333E−05
𝜋(0.0254𝑚)0.3355×10−3 𝑘𝑔
𝑚.𝑠⁄
=1982.85861
Trial 5
𝑁 𝑅𝑒 =
4𝑥(995.337 𝑘𝑔
𝑚3⁄ )0.00001
𝜋(0.0254𝑚)0.3355×10−3 𝑘𝑔
𝑚.𝑠⁄
=1487.14396