Performance Testing with American Society for Testing and Materials
Procedure
Justin Showghi
Department of Mechanical Engineering
Clemson University
“I certify that all the writing presented here is my own and not acquired from
external sources (including the student lab manual). I have cited sources
appropriately and paraphrased correctly. I have not shared my writing with other
students, nor have I acquired any written portion of this document from past or
present students.”
1. Introduction
When designing vacuums, engineers take into account flow rate, suction, and
efficiency to determine how well a vacuum will perform a specific task. These
characteristics of flow rate, suction, and efficiency are the foundation for
determining overall performance in a vacuum. In order to compare the overall
performance of similar household vacuums, the American Society for Testing and
Materials standardized test procedure was applied. The vacuum cleaners under
comparison were two vacuums from two separate companies. One vacuum was
made by Hoover and the other vacuum was made by Eureka. Two vacuums were
tested in this experiment so comparisons could be made as to what characteristics
are important when designing a vacuum to perform a specific task. Tests and
experiments were conducted to compare overall performance by examining
efficiency, pressure, and flow rate. These results enabled conclusions to be drawn
as to why each vacuum cleaner was designed a certain way. An uncertainty
propagation was conducted to determine the total uncertainty in output power of
the Eureka and Hoover vacuums. This information was accounted for when
analyzing and comparing overall performance of each vacuum [1].
2. Following American Sociecty for Testing and Materials Standards
When conducting this experiment, the method set forth by the American Society
for Testing and Materials (ASTM) was used because when similar machines are
being compared, using one precise procedure eliminates any discrepancies when
looking at physical properties. “It is common for a physical property to be strongly
affected by the precise method of testing or measuring that property”, thus one
method makes a level foundation for comparing physical properties [1]. ASTM
standards were used because it is an international standards organization and a
“respected standards organization” [1]. Because ASTM standards are so widely
used and agreed upon, engineers and manufacturers can use results and data from
experiments conducted by other engineers and manufacturers. For this experiment,
one group tested the Hoover vacuum and another group tested the Eureka vacuum
and then both groups exchanged data. It was acceptable to have two groups run
tests on separate vacuums and then exchange data because ASTM standards were
used. If one group did tests on both vacuums, nearly identical results would be
attained because if ASTM standards were followed, the procedure would have to
have been exactly the same for both groups.
3. Vacuum Operation
A vacuum is able to pick up particles due to a process called pneumatic
transport. Pneumatic transport is the process where “particles are suspended in a
high velocity air stream for the purpose of relocating [the air particles]” [1]. The
blower within a vacuum creates a pressure gradient and the pressure gradient
causes air to move. This movement of air causes particles to be pulled into the air
stream if the drag force is strong enough to overcome the force of gravity and static
friction acting upon the particle. The drag force will have the particle enter the air
stream and once the particle has moved through the vacuum, the particle will be
“arrested by the bag or filter inside the vacuum cleaner” [1].
4. Experiment Setup
Besides the Hoover and Eureka vacuums, the main instruments and devices used
for the experiment from which data was gathered were a wattmeter, plenum, and
manometer. A wattmeter is an electronic device that measures the amount of
power (in watts) running through it. For example, the vacuum was plugged into the
wattmeter and the wattmeter was plugged into the power outlet. At any given time,
the wattmeter would give a reading for how much power the vacuum was absorbing
from the power outlet.
A plenum is a six sided plexi-glass cube. For the purposes of this experiment, the
plenum acted as an extension of the vacuum hose. On the top face of the plenum,
there was a hole in which air could flow through. The different sized orifice plates
were placed over this cut out. An orifice plate is a thin metal plate that has a circular
cut centered on the plate. Different sized orifice plates were placed over the hole in
the plenum. Each orifice plate symbolized a change in diameter of the vacuum hose.
The plenum acted as an extension of the vacuum hose while the orifice plates acted
as different diameters of the vacuum hose. During this set of tests, each orifice plate
was slid under two mounts over the hole in the plenum so that the only flowing air
was through the hole in the orifice plate.
The final device used was a manometer. A manometer is a tall, thin tube that
measures pressure through a height change of water in the tube. The height of the
liquid in the manometer is described as pressure head. The liquid in the manometer
used for this experiment was water. The vacuum, wattmeter, manometer, and
plenum were set up for the experiment as seen below.
Fig. 1. Setup for performance testing of vacuum cleaners.
For purposes of this experiment, the vacuum was raised and placed on a stool so
that the vacuum hose was as straight as possible. The vacuum hose needed to be
straight so that head loss, or loss or pressure, was uniform throughout the
experiment except for the changing orifice plates. [1].
In accordance with ASTM standards, the vacuum ran for two minutes to warm
up unattached to the plenum. After the vacuum ran for two minutes, an orifice plate
was slid over the cut out on the top face of the plenum, and after 10 seconds, the
pressure change on the manometer and the power reading on the wattmeter were
recorded. After recording the data, the orifice plate was removed and the vacuum
was left running for one minute while attached to the plenum. After one minute, the
next orifice plate was situated and the same steps were repeated. This series of
steps was repeated seven times for each of the seven orifice plates. [1].
5. Head Losses, System Curves, and Operating Points
Every time a different orifice plate was put on top of the plenum and data was
gathered, a new system curve was represented. “A system curve…tells how much
head (pressure difference) is required in order to maintain a given flow rate” [1].
With each new orifice plate, the head loss was changed. Head loss, hL, refers to the
loss of pressure and is given by the equation
𝑙 8𝑄 2
ℎ𝐿 = 𝑓 𝐷5 𝜋2 𝑔
(1)
where f is the friction factor, l is the length of the pipe, D is the diameter of the pipe,
Q is the flow rate through the pipe, and g is gravitational acceleration. Because
diameter is raised to the fifth power, which is the highest order in Eq. 1, exchanging
orifice plates and changing the hypothetical diameter of the vacuum hose yielded
the most sensitive changes in head loss. The plenum helped keep tube length
constant because the focus of head loss was in terms of tube diameter change. Any
additional length in piping would have “altered performance of that system by
introducing losses” [1].
The purpose of analyzing head losses and the seven different system curves as
determined by each orifice plate was to determine a pump curve. A pump curve
“illustrates the performance of the pump itself” [1]. A change of the diameter in the
orifice plate changed the amount of head loss, making a new system curve. The
intersection of the pump curve and each system curve was an operating point. The
operating point of the system is “the point at which the head produced by the pump
is equivalent to the losses in the pipes” [1].
6. Pump Curve and Efficiency Curve
After the physical tests were run, data on pressure head and input power had
been gathered for each orifice plate used on both the Hoover and Eureka vacuums.
Pressure change, pabs, was calculated from pressure head using the following
equation:
𝑝𝑎𝑏𝑠 = 𝑝0 + 𝛾ℎ
(2)
The height of the liquid, or head, is described as the variable h, while 𝛾 is the specific
weight of the liquid and p0 is the reference pressure.
The flow rate, Q, in this experiment was “the volumetric flow rate through an
orifice [plate]” [1]. It was not something measured, but rather calculated using the
equation below.
2∆𝑃
𝑄 = 𝐾1 𝐴0 √
𝜌
(3)
In Eq. 3, K1 is a “dimensionless flow coefficient” obtained from any thermodynamics
book, A0 is the “cross sectional area of the orifice plate, 𝜌 is the fluid density”, and P
is the pressure as calculated from Eq. 2 [1]. After calculating pressure and flow rate
from each orifice plate for each vacuum, the pump curves for each vacuum were
generated, and are seen below in Fig. 2. A pump curve is the graphical relationship
of “the amount of pressure difference (or head)” the vacuum generates “at a given
flow rate” [1].
18
Change in Pressure (in thousands of
Pascals)
16
14
12
10
Eureka
8
Hoover
6
4
2
0
0
0.005
0.01
0.015
0.02
Volumetric Flow Rate (Q)
0.025
0.03
Fig. 2. Pump curves for Eureka and Hoover vacuums.
The importance of the pump curves is that they determine pressure at a given flow
rate. This presence of this relationship is key when evaluating overall performance.
From the two curves in Fig. 2, the fluid power, pfluid, of each vacuum was calculated
using the equation below.
𝑝𝑓𝑙𝑢𝑖𝑑 = ∆𝑃𝑄
(4)
With the fluid power calculated and the input power, pinput, gathered from the
experiment, the efficiency, 𝜂, for each orifice plate on each vacuum was calculated
using the equation below.
𝑝
𝜂 = 𝑝𝑓𝑙𝑢𝑖𝑑 × 100
𝑓𝑙𝑢𝑖𝑑
(5)
After the efficiencies were determined, the efficiency versus flow rate plot was
generated, as seen below in Fig. 3.
Effieciency (percentage)
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
Eureka
Hoover
0
0.005
0.01
0.015
0.02
Volumetric Flow Rate (Q)
0.025
0.03
Fig. 3. Efficiency vs. flow rate plot for Eureka and Hoover vacuums.
The importance of the efficiency curves as seen in Fig.3 was that a relationship was
determined between flow rate and the efficiency of the vacuum. With this
relationship, a better comparison between the two household vacuums was capable
of being made.
7. Best Efficiency Point
As seen in Fig. 3, the maximum efficiency is higher for the Hoover vacuum than
the Eureka vacuum. The maximum efficiency for each vacuum occurred at the best
efficiency point (BEP). By determining the efficiency, flow rate, and pressure of each
vacuum at the BEP, conclusions could be drawn as to the reasons why engineers for
each company designed their vacuum a certain way. After the data in Fig. 3 was
carefully analyzed, the following information at the BEP for each vacuum was
determined.
Table 1
Physical characteristics of Hoover and Eureka vacuums at BEP.
(m3/s)
Flow rate
Pressure (Pa)
Efficiency (percent)
Hoover
0.01279
11561
12.88
Eureka
0.01289
9717
9.65
The maximum efficiencies and flow rates at those respective points were
determined by examining a magnified view of Fig. 3 on an Excel chart. To find
pressure at the BEP, the flow rates were taken and examined on a magnified view of
Fig. 2.
8. Operating Point
Each vacuum had a certain size diameter for the vacuum hose. Each diameter
corresponds to a specific flow rate, and therefor a specific pressure. The point
corresponding to that specific flow rate and specific pressure on each vacuum’s
respective pump curve is the operating point for each vacuum. The purpose of
finding the operating point for each vacuum was to better compare overall
performance and understand the design behind each vacuum cleaner. For example,
the diameter of the vacuum hose on the Hoover vacuum was 26.85 mm so the
operating point would be the point at which the flow rate, pressure, and efficiency
are analyzed at a vacuum hose diameter of 26.85 mm on the Hoover vacuum pump
curve and efficiency curve. The diameters of the vacuum hoses on the Eureka and
Hoover vacuums were determined by measuring the inside diameter of the vacuum
hose with a dial caliper. After the diameters had been recorded, the process of
interpolation was used to determine flow rates correlating to each measured
diameter. Once flow rates for each vacuum’s operating points were gathered, those
flow rates were analyzed on Fig. 2 and Fig. 3 to gain corresponding pressures and
efficiencies. The pressures and efficiencies were obtained using the trend line
feature in Excel. The following data was gathered for each of the vacuum’s
operating point [1].
Table 2
Physical Characteristics of Hoover and Eureka vacuums at respective operating points.
Diameter (mm)
Flow Rate (m3/s)
Pressure (Pa)
Efficiency (percent)
Hoover
26.85
0.020346
2233.256
3.8947
Eureka
37.084
0.02567
916.7869
1.9077
9. Error Propagation and Total Uncertainties in Output Power
In many cases where products are being engineered, and for the purposes of this
laboratory experiment, the value of a certain parameter is “calculated from several
different measurements” [1]. Since each measurement presents its own level of
uncertainty, uncertainties can quickly add up for a calculation of a single value.
Uncertainties were calculated because the true value of a parameter is almost never
known. By finding these uncertainties, a range around the measured value was
obtained and that range will, with a certain confidence, contain the true value. To
account for the total uncertainty in output power of this experiment, an error
propagation was used. Error propagation accounted for the uncertainty in each
measurement used to calculate the value of a parameter. An example of an error
propagation and how uncertainty creates a range in which the true value should lie
is seen below in Fig. 4.
Fig. 4. Example of error propagation [2].
The black dot represents the data point gathered from an experiment. The
uniformly broken lines acts as the uncertainty range for that data point. According
to error propagation, the data point could be at any point along its derivative line
within the specified range [1].
For this experiment, an error propagation was used to find the uncertainties in
fluid power, pfluid. Error propagation, Θ𝑖 , for a single variable is given as the partial
derivative of the parameter in terms of the variable with uncertainty. The equation
for error propagation of a function 𝑦 = 𝑓(𝑤) is
𝜕𝑦
Θ𝑖 = (𝜕𝑤 )𝑤=𝑤𝑖
𝑖
(6)
Thus, the combinations of all uncertainties used to calculated a single parameter, uY,
is expressed as
2
u𝑌 = ±√∑𝑀
𝑖=1(Θ𝑖 𝑢𝑤𝑖 )
(7)
where uwi is the zero order uncertainty of the instrument used to measure the given
variable of uncertainty. For example, a dial caliper was used to determine the
diameter of the vacuum hose. The zero order uncertainty of the dial caliper is
0.00001m, thus uwi would be 0.0001m.
The general equation of fluid power is
𝑝𝑓𝑙𝑢𝑖𝑑 = ∆𝑃𝑄
(8)
where P is pressure and Q is flow rate. When Eq. 3 is substituted for Q, the
expanded form of fluid power becomes
𝑝𝑓𝑙𝑢𝑖𝑑 = ∆𝑃𝐾1 𝐴0 √
2∆𝑃
(9)
𝜌
When A0 is substituted with it’s most basic form of
𝜋
𝐴0 = 4 𝐷0 2
(10)
fluid power now becomes
𝜋
2∆𝑃
𝑝𝑓𝑙𝑢𝑖𝑑 = ∆𝑃𝐾1 4 𝐷0 2 √
(11)
𝜌
where D0 is defined as diameter. For the purposes of this experiment, D0 was the
diameters of the multiple orifice plates. From Eq. 11, the only variables containing
uncertainty are diameter and pressure because those were the only two parameters
measured and recorded to calculate fluid power [1].
To perform an error propagation, the partial derivative of fluid power was taken
in terms of both diameter and pressure and thus yielded
𝑈𝑝𝑓𝑙𝑢𝑖𝑑 = ± √(
𝜕𝑝𝑓𝑙𝑢𝑖𝑑
𝜕𝐷0
𝑈𝐷0 )2 + (
𝜕𝑝𝑓𝑙𝑢𝑖𝑑
𝜕∆𝑃
𝑈∆𝑃 )2
(12)
Calculation showed that 𝑈𝐷0 was equal to 0.0001m and 𝑈∆𝑃 was equal to 12.45 Pa.
Because 𝑈∆𝑃 had a magnitude 6 orders larger than 𝑈𝐷0 , the first team under the
square root in Eq.12 was assumed to be negligible. That determination condensed
Eq. 12 into
𝑈𝑝𝑓𝑙𝑢𝑖𝑑 = ± √(
𝜕𝑝𝑓𝑙𝑢𝑖𝑑
𝜕∆𝑃
(13)
𝑈∆𝑃 )2
After calculations, the total uncertainties for each vacuum were calculated. The
error propagation did not give just one value for each vacuum. Instead, the error
propagation yielded an uncertainty range for each orifice plate. So for each vacuum,
there was a column of 7 uncertainty ranges. Once total uncertainties had been
calculated, the equation below was used to calculate percent uncertainty.
𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 =
𝑈𝑝𝑓𝑙𝑢𝑖𝑑
𝑝𝑓𝑙𝑢𝑖𝑑
× 100
The values for largest percent uncertainty for each vacuum are seen below.
(14)
Table 3
Highest percent uncertainty and respective flow rates and pressure for Hoover and Eureka vacuums.
Largest Percent Uncertainty
Flow Rate at Highest Uncertainty (m3/s)
Pressure at Highest Uncertainty (Pa)
Hoover
12.3631
0.0194
149.5047
Eureka
9.27234
0.0224
199.3396
The largest percent uncertainty occurred with the largest diameter orifice plates for
both the Hoover and Eureka vacuums. These percent uncertainties and their
respective flow rates and pressure helped in comparing overall vacuum
performance and drawing conclusion about each vacuum cleaners’ design [1].
10. Data Analysis
The pump curves as seen in Fig. 2 act similar to a conservation of energy curve,
where pressure on the y-axis is potential energy and flow rate on the x-axis is
kinetic energy. As one of those parameters increases, the other must decrease. On
an ideal curve, the y-intercept of the curve is where pressure is highest and flow rate
is zero. The same holds true for the x-intercept on an ideal curve. The flow rate
reaches its highest value when pressure is zero. The basic relationship is that when
pressure increases, flow rate decreases, and when flow rate increases, pressure
must decrease. That increase-decrease relationship is because the relationship
between pressure and flow rate act according to the conservation of energy
principle.
As shown in Fig. 2, there was a discrepancy to this trend. The final data point on
both the Hoover and Eureka pump curves hooks inward. After performing the error
propagation and determining all the uncertainties, it was determined that the last
data point, which corresponded to the largest diameter orifice plate, carried the
largest percent uncertainty, thus skewing the curve. Part of the uncertainty range
for the data point with the largest uncertainty fell into an area which would have
satisfied the trend determined between flow rate and pressure.
The error propagation and large uncertainty also explained the inward hooking
on the efficiency curve. One of the variables used to calculate efficiency was flow
rate. It makes sense that if there was a discrepancy in the trend of flow rate and
pressure, there would also be a discrepancy in efficiency. The uncertainty range
explains why there is a tail on both the pressure and efficiency curves. The
assumption was made that at the final data point that hooks inward for both
vacuums on both curves, overall performance of flow rate, pressure, and efficiency
were not accurately portrayed because of the calculated uncertainties.
After all raw data had been gathered from the experiment, pressure was found
to be inversely proportionate to the diameter in the orifice plate. As the diameter of
the orifice plates increased, the pressure began to decrease. Each individual orifice
plate represented a change in head losses and consequently, a new system curve.
Each of the seven system curves intersected the pump curve and each point of
intersection is known as an operating point. The operating will remain the same for
any given system “unless a pump having a different performance is installed or the
system curve is altered by adding/removing a section of pipe thus changing the
magnitude of the losses” [1].
Since pressure is force divided by area, it is mathematically proven the pressure
decreases as area (which is calculated from diameter) increases over a constant
force. Since it was already determined that flow rate and pressure are inversely
proportional, flow rate and diameter of the orifice plate were directly proportional.
As the diameters in the orifice plates were increasing, the flow rate was also
increasing [1].
As pressure generated by the vacuum deceases, the size of particles capable of
being sucked up decreases. Since the blower inside the vacuum creates a pressure
gradient consequently making a drag force with air flow, the size of particles being
sucked up decreases because the drag force decreases. That drag force has to
overcome the effects of gravity and static friction on the particle. As particles
become smaller, the effects of gravity and static friction also decrease[1].
11. Vacuums Designed for a Task
A vacuum can not be said to be better than other vacuum. All vacuums are
designed for separate tasks and different environments. When looking at the BEP,
the Hoover vacuum had a higher percent efficiency than the Eureka vacuum. In no
way does that make the Hoover vacuum better. Because the flow rate, pressure,
efficiency, and hose tube diameter (or orifice plate diameter) are different for both
vacuums at the BEP and operating point, it is proven that vacuum cleaners are
designed for certain tasks with specific purposes and not necessarily for highest
efficiency.
Pressure is related to the size of particles that the vacuum will pick up and the
flow rate corresponds to the number of particles that the vacuum will pick up.
Pressure is related to the size of particles because pressure is defined in terms of
force. If pressure intake is large enough to overcome weight and static friction of
the particle, the particle will be sucked up into the hose [1].
At the BEP, the Hoover vacuum has a lower flow rate and higher pressure than
the Eureka vacuum. This means that at highest efficiency, the Hoover vacuum is
going to pick up a smaller number of larger objects compared to the Eureka vacuum.
Since the Eureka vacuum has a higher flow rate and lower pressure, the Eureka
vacuum will pick up a larger number of smaller objects compared to the Hoover
vacuum.
At the operating point for each vacuum, the Hoover vacuum again had a lower
flow rate and higher pressure than the Eureka vacuum. Thus, the Hoover vacuum
was picking up larger particles in smaller quantities compared to the Eureka, which
was picking up smaller particles in larger quantities. What these values for flow
rate, pressure, and efficiency suggest is that each vacuum was designed for a
different purpose. The engineers who made the Hoover vacuum intended the
vacuum to pick up small particles in large quantities, but not particles as small or in
quantities as large as the engineers who designed the Eureka vacuum. The
efficiency of a vacuum is not a key factor in vacuum cleaner design. At the BEP,
efficiencies were low for both vacuum cleaners. At each vacuum cleaner’s
respective operating point, the efficiencies were even lower. When engineers
designed these Hoover and Eureka vacuums, flow rate and pressure where the key
factors. The engineers had a specific task and purpose during the design of each
vacuum and flow rate and pressure helped them meet their goals. Efficiency did not
play as vital of a role as flow rate and pressure when those engineers were
attempting to meet the goals set during the design stage.
After error propagation determined uncertainties in the output power of each
vacuum. The uncertainties were highest with the largest diameter orifice plate. The
motors may not have been sensitive enough to sense much of a difference in the
range of the two largest orifice plates. This assumption to lack of sensitivity may
explain an input power drop in the Eureka vacuum. The orifice plate with the third
largest diameter had the largest input power for the Eureka vacuum, while the two
largest orifice plates recorded smaller input powers. Although the change in input
power for the last two orifice plates on the Eureka vacuum is much smaller than all
the other recorded input power changes, this input power could just be attributed to
the behavior of the motor. A reason for this motor behavior might be based off the
design of the filter, but since this theory was not tested, nothing related to this
behavior can be stated with confidence.
12. Conclusion
Overall performance is based on what type of task the vacuum is being designed
for. If a vacuum is designed to work at a construction site, pressure would be high
and flow rate would be low so that the vacuum could suck up large objects found at
a construction site. If engineers are designing a vacuum for home use, then the
engineers will ensure the vacuum has a lower pressure and higher flow rate, similar
to the Hoover and Eureka vacuums tested, so the vacuum could suck up small
objects and dust particles. Vacuum motors and filters are also designed to behave a
certain way depending on the desired pressure and flow rate intended for vacuum.
Not all vacuums are designed to perform at peak efficiency, either. Since vacuums
are designed to perform certain tasks and in certain environments, vacuums often
perform below their peak efficiency so that a desired flow rate and pressure are
met. An error propagation showed large uncertainties for some of the data gathered
while running tests in the experiment. These uncertainties related to output power
of each vacuum helped in the comparison of overall performance of the vacuums.
Flow rate and pressure depend on multiple factors including vacuum tube diameter,
or in other terms, the area in which particles and objects are sucked into the
vacuum. Flow rate and pressure also depend on hose length because a change in
length of the tube hose could introduce change in losses [1].
References
[1] Todd Schweisinger, Ph.D. and Tim Freeman. ME 222 Mechanical Engineering Lab
1 Student Manual. Clemson University. 2013.
[2] Richard S. Figliola and Donald E. Beasley. Theory and Design for Mechanical
Measurements. John Wiley & Sons, Inc., fifth edition, 2011.