University of Southern Indiana
Flow Characteristics
& Reynolds Number
Laboratory Report
Arnold-Banschbach-Wallace-Webster
12/18/2013
Flow Characteristics & Reynolds Number
Arnold-Banschbach-Wallace-Webster
Objective
The objective of this lab will be to model laminar flow through a pipe. The flow will increase in
velocity and thus increase the Reynolds number with its given characteristics. Through many
different states of increasing velocity, the group will find at which Reynolds number the flow
begins to deviate from the laminar flow model.
Background Information
For this experiment the question being asked is "At which Reynolds number will the flow
through the pipe start to deviate from the laminar flow model?" To answer this question a few
items need to be addressed first. From our background knowledge of different fluid flows the
group knows to find the difference between laminar flow and turbulent flow is essentially the
Reynolds number equation.
𝑅𝑒 =
𝑉𝐷
𝑣
From this unique relationship, the main determining factor in classifying the fluid flow is the 'V'
term which is the average velocity of the fluid. Other factors are: Diameter of the pipe (D) and
the Kinematic viscosity of the fluid (μ). In this experiment the density, diameter and the dynamic
viscosity will remain constant throughout the data collection. So the only parameter that is
changing will be the velocity of the fluid. Thus, as the group increases the system’s flow rate, the
Reynolds number increases.
The fluid that will be used in this experiment will be water at room temperature. There is no
exact Reynolds number at which the flow will transition from laminar flow to turbulent flow. The
key word is transition. Most information that the group has been taught is that fluid flow
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remains laminar for the corresponding Reynolds number of 2000-2300. There is then a
transitional stage of the fluid until it reaches turbulent flow with the corresponding Reynolds
number around 4000.
To best illustrate this, the group will be referencing a graph better known as the Moody Diagram
which can be seen in the Reference section. This diagram shows different flow states that plot
values based on the friction factor as a function of Reynolds number and relative roughness of
the pipe. Briefly, the friction factor is found using two dimensionless terms, Reynolds number
and the relative roughness. The relative roughness in short, describes how rough the pipe
material is. Since the group is concerned with laminar flow the relative roughness of the pipe is
not as important as the friction factor (f) will be. The friction factor is to be determined using the
following equation:
𝑓=
64
𝑅𝑒
The group will be able to plot all of the data points knowing the friction factor (within laminar
flow) and the Reynolds number. And for clarity, the plot will be done in log-log scale. The
objective will be to see how far past the laminar flow the group can get the fluid to flow and at
which Reynolds number the data points no longer want to conform to the model.
Experimental Setup & Procedure
Materials List:

TecQuipment Gravimetric Hydraulic Bench
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Arnold-Banschbach-Wallace-Webster

TecQuipment H7 Friction Loss Apparatus

Safety Glasses

500 ml Beaker

Stopwatch
Setup & Procedure:
For this lab the apparatus was already set up for the group to begin the first portion of the
experiment. The second part of the lab would require us to redirect how the flow of water
would interact with the apparatus. In previous labs the group encountered issues with the top
of the gravimetric hydraulic benches not wanting to seat properly on the bench itself. The result
would be the apparatus rocking back and worth after we had initially leveled it. To combat this,
the bottom of the apparatus was shimmed on one end to prevent the rocking. After that had
been completed the apparatus was also level. The end result was that both the bench top and
device were stable thus allowing for more accuracy by means of repeatability.
Procedure Steps (Part 1)
1. Ensure the apparatus is level, the outflow hose from hydraulic bench leads to the
elevated tank and the outflow hose from the tank hooks into the apparatus.
2. Allow water to flow into elevated tank and fill tank as close to the top as possible
without the water spilling out.
3. Once the proper flow rate is established, leave the hydraulic bench valve alone and
begin making changes to the needle valve on the apparatus.
4. Start with the needle valve closed and manometer valve in the position shown in Figure
1.
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5. With a one half turn of the needle valve, monitor and collect the change in height from
the water manometer tubes.
Note: Turning the needle valve a consistent one half turn will lead to more exacting
data points.
6. Without turning the needle valve, find the volumetric flow rate using a beaker and a
stop watch.
7. Repeat Steps 2-6 with increasing turns on the needle valve until 8-9 data points have
been recorded.
Procedure Steps (Part B)
1. Ensure the apparatus is level and that the outflow hose from the hydraulic bench leads
directly to the inflow portion of the apparatus.
2. Open valve on the hydraulic bench fully
3. Just as in Part A, repeat steps 4-7 with the only exceptions being to record the change in
height from the Mercury manometer tubes and the manometer valve in position shown
in Figure 2.
Figure 1
Figure 2
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For the first part of the experiment the group would be running water through the apparatus
using an elevated tank, as seen in Figure 3. What this tank does is uses the effects of gravity to
allow the water to flow down the outflow tube into the apparatus at a constant velocity. In
previous experiments the group has found that the pump in the hydraulic bench has trouble
keeping the velocity constant at low flow rates due likely to the pump’s cyclic nature. The flow
rate in Part A will be quite lower than in Part B of the experiment.
Part B of the experiment will have the outflow hose from the hydraulic bench hooked directly up
to the apparatus to increase the flow rates through the main tube. When increasing the flow
rate the Reynolds number will also be increasing. Due to this, the flow will then be leaving the
laminar flow range, going through the transitional range and beginning to become turbulent.
Based on our previous knowledge from the Venturi Tube lab the group knows that with a higher
flow rate the pressure will increase. Thus the changes in pressure head will be greater. So much
so, that the water manometer readings will be off the scales and a “heavier” liquid will need to
be used. At this point, it will be necessary to move from the use of water to mercury for Part B.
Figure 3
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Arnold-Banschbach-Wallace-Webster
Experimental Data & Statistical Analysis of Data
Data:
Table 1
Mercury (Δh), meters
Water (Δh),meters
Volume (m^3)
0.0001
0.038
0.0002
E
l
e
v
a
t
e
d
T
a
n
k
0.007
0.097
0.014
0.189
0.021
0.301
0.0002
0.0002
0.0002
0.025
0.372
0.0002
0.028
0.407
0.029
0.434
0.031
0.456
0.0002
0.0002
0.0004
0.104
0.0004
0.121
D
i
r
e
c
t
l
y
0.0004
0.132
0.0004
0.139
0.0004
0.145
P
u
m
p
e
d
0.0004
0.157
0.0004
0.171
0.0004
0.180
0.0004
0.184
Time (s)
75.00
74.00
75.00
63.14
63.30
63.30
41.80
41.30
41.10
35.10
35.16
35.50
30.30
31.40
31.85
29.70
29.70
29.80
28.82
28.60
28.59
27.79
27.70
27.60
27.98
27.70
28.40
25.50
25.60
25.58
23.70
24.10
23.90
23.40
23.36
23.34
22.84
22.80
22.70
21.30
21.73
21.68
20.52
20.90
20.57
20.47
20.20
20.18
19.60
20.06
19.81
Flow Rate(m^3/s)
Velocity (m/s)
H_F
delta P
Reynold's Number friction factor
1.33929E-06
0.18947017
0.038
372.78
5.68E+02
0.11890247
3.16222E-06
0.447362898
0.097
951.57
1.34E+03
0.054442841
4.83092E-06
0.683435075
0.189
1854.09
2.05E+03
0.04545234
5.67322E-06
0.802596788
0.301
2952.81
2.41E+03
0.052488073
6.41368E-06
0.907350468
0.372
3649.32
2.72E+03
0.050755344
6.72646E-06
0.951599062
0.407
3992.67
2.85E+03
0.050486512
6.97593E-06
0.986892644
0.434
4257.54
2.96E+03
0.05005401
7.22109E-06
1.021574634
0.456
4473.36
3.06E+03
0.049081024
1.42721E-05
2.019092205
1.4092
13824.252
6.06E+03
0.038828383
1.56495E-05
2.213944609
1.63955
16083.9855
6.64E+03
0.037573369
1.67364E-05
2.367716494
1.7886
17546.166
7.10E+03
0.03583792
1.71184E-05
2.421758525
1.88345
18476.6445
7.27E+03
0.036072928
1.75593E-05
2.484127489
1.96475
19274.1975
7.45E+03
0.035764199
1.85443E-05
2.623478174
2.12735
20869.3035
7.87E+03
0.034719464
1.9358E-05
2.738591267
2.31705
22730.2605
8.22E+03
0.034703233
1.97206E-05
2.78989766
2.439
23926.59
8.37E+03
0.035198506
2.01782E-05
2.854637172
2.4932
24458.292
8.56E+03
0.034367208
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Figure 4
Statistical Analysis:
Table 1 shows the statistical data collected in lab as well as the calculations for flow rate,
Reynold’s number, and friction factor. This data will then be used to formulate a plot of friction
factor as a function of Reynold’s number for each of the data points (blue points in Figure 4).
Also, another set of data is shown. This data is that of another group conducting the same
experiment (green on the plot). This was done not only for a more thorough evaluation but also
worked well as to ensure the group was on the correct patch. As can be seen from the graph, at
roughly a Reynold’s number of 2000 is where the values begin to spike up.
The red line in Figure 4 is the theoretical value of f=64/Re. This theoretical line should only hold
true up to about a Reynold’s number of 2000 where you should then start to see the
experimental data begin to deviate from that lineal region. This is why the line is not extended
throughout the rest of the graph.
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Results, Conclusions & Recommendations
Results:
The experimental data that was obtained was changed in height of either mercury or water, the
volume of a beaker, and the time it took to fill that beaker up. Three values were used to
calculate the rest of the chart seen in Figure A. To calculate flow rate, Equation 1 was used. In
previous labs the group used the hydraulic bench to measure the flow rate. Because the volume
of water leaving the apparatus was so minimal, a 500ml beaker was used instead. Instead of
starting from the bottom of the beaker, the time on the stop watch was started when the fluid
reached a level of 100ml and stopped at 500ml. This let the group have time to react in the time
collection and lead to more accurate times, thus more accurate volumetric flow rates.
The group was then able to take that information and the given diameter of the main pipe and
find the average velocity. By using the method of pressure change with elevation that was
derived in class earlier in the semester, it was possible to calculate the change in pressure due to
the height difference in the monometer multiplied by the specific gravity of that fluid. Now that
the change in pressure is known, Equation 2 could be used; derived from Bernoulli’s equation,
to calculate the major head loss due to friction, 𝐻𝑓 . After finding what the major head loss in the
system is equal to, the group can use the known equation for the major head loss (Equation 4)
equation and solve for the friction factor using Equation 5. Lastly the Reynolds number was
calculated using the velocity of the fluid, diameter of the pipe and the kinematic viscosity as
seen in Equation 3. The kinematic viscosity of .000001 m^2/s was also used. The values from
Equations 2, 3 & 5 were recalculated for each data point in the series.
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The accuracy of the data that was collected was relatively high all the way up to the point where
the Reynold’s number went above 2000 which is what should be expected. The red line on the
graph represents 64/Re which is where the data should fall from a theoretical standpoint. This
would have been more apparent if more data points were found in the Reynold’s number range
of 1000 to 2000. Reason being why there were not more data points in this range is because the
flow rate jumped up quickly and left the theoretical model of laminar flow. Using the one half
turn of the needle valve may have left out some other data points that could have been
collected “between” those turns. This will be explained more in the conclusion section.
At a Reynold’s number value of around 2000, the data started deviating but uniformly from the
theoretical laminar flow line (red line) through the transitional stage and approaching fully
turbulent flow. The data was very uniform in this transitional stage in comparison to the other
group’s. The other group’s data seems much more sporadic and does not seem to conform to
any sort of curved line in the manner that our data does. This could be in part from the ways the
time for finding volumetric flow rate was done with that particular group.
Conclusions:
Once all of the data and the calculations had been completed, the group came to a few
conclusions. When looking upon the data in the graphs and plots of Table 1 and Figure 4, one
can see where these conclusions are coming from. From Figure 4, it can be seen that the first
couple of points, which came from Part A in the procedure, lie directly on the Theoretical model
of laminar flow (Red line). Only three points exactly lie on this line and the fourth data point is
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where the group’s data deviate from this theoretical model. At about 2000 Reynolds number
the data starts trending away and into the transitional stage.
Looking off of a published Moody Diagram and comparing to what the group has, you can
classify what the data points represent. From the point at which the data starts to deviate it is
approaching wholly turbulent flow, but never crosses into it. Instead the flow stays in the
transitional stage for the entirety of the data series. When looking closely it can be seen at the
very end of our data series where it wants to start flattening out. If the data would flatten out
completely then it would be classified as wholly (or fully) turbulent.
Previously in this report it was stated that the assumed values of the flow characteristics were;
Laminar flow (<2000-2300), Transitional (2300-4000) and turbulent (>4000). So it would appear
that all of the values would appear to be turbulent if the Reynolds number associated with them
would be greater than 4000. That is partially true, but those flows are not fully developed
turbulent flows. Most of the time a liquid would conform to be fully turbulent when they
approach and exceed 4000 Reynolds number. The group knows that this data is not fully
turbulent due to the nature of the graph and it not becoming completely flat at the end of the
data series.
Laid out in the Procedure Steps, the group talked about how to adjust the needle value in such a
manner to achieve more accurate results. Figure 4 best represents this accuracy. In the results
section, it was briefly talked about how another group’s data followed the same general curve
from laminar through transitional and approached turbulent but not in the smooth manner ours
did. The group believes that this is due in part to our more accurate method of finding
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volumetric flow rate but also adjusting the needle valve in a consistent method every time. This
lead to our data being more equally spread out and not as sporadic.
Answers to Initially Stated Questions:
This whole experiment really revolved around one main question that needed answering, "At
which Reynolds number will the flow through the pipe start to deviate from the laminar flow
model?" From our data it is safe to say that Equation 6 holds true for values up to a Reynold’s
number of 2000. After that, flow starts transitioning into fully turbulent and conforms to a new
function line, but in a uniform manner—first curving up, and then curving back down. The model
shows that the data points do not curve all the way back down until they are flat, which would
indicate that they were wholly turbulent. So to answer the question stated, the group found at a
Reynolds number of 2000, the flow started to deviate from the laminar flow model.
Recommendations:
If this lab were to be run again there is only one real recommendation the group would offer.
That is to take many more data points which would leave for a more detailed model. Although
the group feels that our model is very detailed and explains what is going on, more data points
especially in the Reynolds number range, would further confirm how well our experiment
showed how our data fit the laminar flow model. If it were possible to run a higher flow rate
through the pipe (the group ran the flow rate as high as possible for the bench) it is suggested to
plot more points with Reynolds number >8500 to show how the data starts to flatten out and
become turbulent.
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The group also highly recommends using the method turning the needle valve with a repetitive
turn each and every time. The only change might possibly be to instead of a half turn, make it a
quarter of a turn, especially for lower flow rates. Overall the group feels that the data, plots and
calculations provided give a well explained write up of the characteristics of laminar flow.
References
"Moody Diagram." Diagram-me. 21 Nov. 2013. 15 Dec. 2013.
<http://diagramme.info/moody-diagram/>.
MorMoran, Michael J. Introduction to thermal systems engineering:
thermodynamics, fluid mechanics, and heat transfer. New York: Wiley,
2003
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