me 340 final project detailed design report
TRANSCRIPT
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Detailed Design
Faucet-Powered Generator
Seth Forney
Tim Heindl
Aaron Weiss
Fikremariam Yami
April 16, 2010
Team I
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Executive Summary
This report contains a design proposal for a water powered generator designed to attach the
customer's sink faucet. This product will use sink flow to spin a small water pinwheel which
will generate electricity through the attached electrical generator. The electricity generated could
be used for a number of different applications, such as charging an electric razor or toothbrush,
recharging batteries, or providing light to the bathroom. The high cost of electricity makes this
product useful and money-saving for the customer.
The design described in this proposal report is for an off-set Pelton style water pinwheel. This
product will be easy to manufacture, contain waterproof housing to operate reliably in a high-
water environment, and be inexpensive for both the manufacturer and the customer. As water
flows from the faucet head through the device, the kinetic energy of the flow is transferred as the
flow spins the water pinwheel. This torque is translated through a shaft which is connected to an
electrical generator. After performing a conservation of momentum calculation and comparing
the results to the theoretical power produced via flow calculations, it was determined that the
output voltage of the system would be 4.4 Volts. This exceeds the minimum design requirement
of 1.5 Volts. Additionally, after performing an economic analysis of the design project, it was
determined that the NPV value of the project was $686,291.07.
This product utilizes energy from the water flow which normally goes to waste. In the long
term, this product will pay for itself with the electricity it produces, making it a great buy for any
customer.
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Table of Contents
Executive Summary ....................................................................... Error! Bookmark not defined.
1. Introduction ................................................................................................................................. 4
1.1 Problem Statement ................................................................................................................ 4
1.2 Background Information ....................................................................................................... 4
1.3 Project Planning....................................................................................................................4
2. Customer Needs and Engineering Specifications ....................................................................... 5
2.1 Customer Needs Assesment .................................................................................................. 5
2.2 Engineering Specifications .................................................................................................... 6
3. Concept Development
3.1 External Search ..................................................................................................................... 8
3.2 Black box Model..................................................................................................................9
3.3 Concept Generation...............................................................................................................9
3.4 Concept Selection................................................................................................................10
4. Detailed Design ......................................................................................................................... 12
4.1 Description of Chosen Design............................................................................................. 12
4.2 Analysis Calculations .......................................................................................................... 13
4.3 Test Procedure ..................................................................................................................... 17
5. Mass Production........................................................................................................................ 18
5.1 Material Selection and Fabrication Process ........................................................................ 18
5.2 Bill of Materials for Mass Production ................................................................................. 19
5.3 Economic Analysis for Full Scale ....................................................................................... 19
6. Conclusions ............................................................................................................................... 19
7. Supporting Materials ................................................................................................................. 19
7.1 References ........................................................................................................................... 19
Appendix A - Project Management .............................................................................................. 21
Appendix B - External Search Results.......................................................................................... 23
Appendix C - Blackbox Decomposition ....................................................................................... 27
Appendix D - Scoping Calculations ............................................................................................. 28
Appendix E - Bill of Materials for Mass Production .................................................................... 36
Appendix F - Full Scale Economic Analysis ................................................................................ 38
Appendix G - Dimensioned Drawings of Final Design ................................................................ 40
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1. Introduction
1.1 Problem Statement
The assigned task is to design and produce a product which will utilize the flow energy of a
customer's faucet by producing electricity through the use of an electrical generator.
Additionally, the team will propose an accessory for the product which will make use of this
electricity. In order to create such a product, the needs of the customer are of critical importance.
The goal of the design project is to create a high performance and efficient product which is
attractive and relatively inexpensive (retails under $50 dollars). Additionally, the product must
attach securely to a faucet with 3/8-18 NPS internal pipe thread and contain identical threading at
the termination point of the flow. The total length of the device should be less than 4" and be
self contained. Finally, the device must be reliable in the wet environment and end in vertical
downward discharge of water.
1.2 Background Information
The team working on this project is a group of four junior level mechanical engineers. The team
has experience with Solidworks for generating solid models for the design. Additionally, the
team working on this project has experience with the design process, background in reverse
engineering, and Learning Factor certification for prototype creation.
1.3 Project Planning
First, the team developed a list of customer needs which would be the basis for the proposed
design. After analyzing these needs, a series of engineering specifications were created in order
to explicitly state what our team's design had to accomplish. In addition to creating customer
needs and engineering specifications, the team dissected the problem using the black box method
and performed external research and patent searches. While using the patents as ideas during
concept generation, the team also explored different types of water turbines in order to get a
better understanding of which type of pinwheel would work best for this relatively low-flow
setting.
A series of scoping calculations were performed to determine the volumetric flow rate of the sink
and pressure of the flow. Using this data, it was possible to determine the optimal flow rate to
produce the most power at the generator. Finally, several concepts were generated and scored
based on the customer needs we had established. Using this selection process, the team decided
to proceed with the off-set pelton style water pinwheel. Included in this report are all of the
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above mentioned features leading to this decision, a Solidworks model of the concept, and a bill
of materials for the proposed design.
2. Customer Needs and Specifications
2.1 Customer Needs Assessment
The team began by generating a list of customer needs based on those given in the problem
description. After each customer need was clearly identified, the team proceeded to use the AHP
method in order to properly weight each need (Table 1). First, the customer needs were placed
into a screening matrix to compare the importance of each customer need. This matrix displayed
whether any given customer need was more important, less important, or of equal importance to
any other category. The customer needs, in order of importance were: performance, cost, ease of
use/safety, durability, appearance, and environmental effects. Safety was grouped with ease of
use for multiple reasons. Firstly, grouping safety with ease of use keeps the number of needs to a
manageable six. Also, the safety of all of the designs was determined to be about equal, so it
would not affect the outcome of the selection process.
Table 1: AHP Ranking of Needs
Customer Need Key
1 High performance
2 Low cost
3 Appearance
4 Ease of use/Safety
5 Durability
6 Environmentally friendly
The resulting matrix was used as a basis to develop the weighted comparison matrix (Table 2).
In this matrix, the weighted number of each customer need was the numerator over the weighted
number of its competing need. This pattern was repeated for each cell of the matrix until a net
score could be tallied. The net score was used to figure out the overall weighted percent to be
used for future matrices during concept selection.
1 2 3 4 5 6 Net Score Rank Weight
1 X 1 1 1 1 1 5 1 6
2 -1 X 1 0 1 1 2 2 4
3 -1 -1 X -1 0 1 -2 5 3
4 -1 0 1 X 1 1 2 2 4
5 -1 -1 0 -1 X 1 -2 4 3
6 -1 -1 -1 -1 -1 X -6 6 1
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Table 2: Weighting of Customer Needs
1 2 3 4 5 6 Net Score Weight
1 X 6/4 6/3 6/4 6/3 6/1 13 30%
2 4/6 X 4/3 4/4 4/3 4/1 8.33 20%
3 3/6 3/4 X 3/4 3/3 3/1 6 14%
4 4/6 4/4 4/3 X 4/3 4/1 8.33 20%
5 3/6 3/4 3/3 3/4 X 3/1 6 14%
6 1/6 1/4 1/3 1/4 1/3 X 1.33 2%
2.2 Engineering Specifications
Following the customer needs assessment, all data collected was used in the various tables
created for engineering specifications. A list of metrics was established to show: the calculated
importance, units, and ideal value of each metric (Table 3). The ideal values were created by
either referring to the problem constraints or estimating them based on knowledge and past
experience. These specifications will later become more accurate after more hand calculations
and testing is carried out.
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Table 3: List of Engineering Specifications
Metric Importance Units Ideal Value
Power Generation 6 Watts > 25 Watts
Efficiency 6 Percent 90%
$50 Retail Cost 4 Dollars < $50
Time to attach 3 Seconds < 30 seconds
Vertical discharge 6 Degrees 90 degrees
Length < 4" 6 Inches < 4 inches
See internal workings of product 4 Binary Yes
Produce minimum of 1.5V 6 Volts >= 1.5 volts
Load of 10 Ohm 6 Ohms 10 ohms
One Assembly/Component 6 Binary 1 component
Lifetime to Failure 3 Number > 5 yrs of avg. use
Positive Voltage Output 6 ± +
Components nontoxic 1 Binary Yes
3/8-18 NPS Internal Pipe Thread 6 Binary Yes
Watertight 6 Binary Yes
A QFD (Table 4) was created to clearly illustrate how each specification relates to the customer
needs. Although, the exact power generation and efficiency have not yet been computed, it is
known that the target cost of the final product is $50 or less. The task's progress can be found by
referring to the team’s Gantt chart, which is frequently updated.
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Table 4: QFD Matrix
Po
wer
Gen
erat
ion
Eff
icie
ncy
$5
0 R
etai
l C
ost
Tim
e to
att
ach
ver
tica
l dis
char
ge
Len
gth
< 4
"
See
inte
rnal
wo
rkin
gs
of
pro
du
ct
Pro
du
ce m
inim
um
of
1.5
V
On
e A
ssem
bly
/Com
po
nen
t
Lif
etim
e to
Fai
lure
Po
siti
ve
Vo
ltag
e O
utp
ut
Co
mp
onen
ts n
ot
toxic
3/8
-18
NP
S I
nte
rnal
Pip
e T
hre
ad
Wat
erti
ght
High Performance X X X X
Low Cost X
Attractive
Appearance X
Easy to Attach X X X
Doesn't hinder
faucet function X X
Self Contained
Device X
Function Reliably
and Safely X X
Ease of
Maintenance X
Environmentally
Friendly X
3. Concept Development
3.1 External Search
The team performed an external search to determine what similar products have been patented or
are on the market. The first, “Self-Powered Miniature Liquid Treatment System[1],” presents a
system which can be attached to a faucet and use that flow to turn a Pelton turbine. The power
created by this turbine powers an ultraviolet light used to treat the water. The second, “Water
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Faucet Generated Emergency Lighting System[2],” attaches to a faucet and uses a diverter in the
attachment to direct water over a turbine. This power is then used to power a light to be used in
emergencies. The third, “Water Powered Rotating Shower Brush[3],” uses water pressure to turn
a system of gears, which are used to rotate a shower brush. Finally, the fourth, “Small Power
Generating Device and Water Faucet Device[4],” has a radial flow turbine which is powered by
running water and can be used to produce power. The patent does not explicitly suggest a use for
this power. A summary of these results can be found in Appendix B. One product specifically on
the market is Sylvania’s Ecolight shower light[5]. The Ecolight uses an axial reaction turbine to
generate power from the flow of a shower head. This power is used to power a light to be used in
the shower. The Ecolight has relatively mixed reviews, but as it is one of the few products that is
similar to this project, it can be considered the benchmark for this type of product.
3.2 Black Box Model
The team evaluated the problem as a whole through the black box modeling technique. A black
box model of the problem can be found in Appendix C.
3.3 Concept Generation
The team brainstormed and arrived at three possible concepts.
Concept A
Concept A (Figure 1) is an impulse turbine in which a Pelton-style pinwheel is placed in the
pipe. The water is then throttled by a diverter such that it only hits one side of the wheel. The
motor is placed outside of the pipe with the shaft doing through the wall of the pipe.
Concept B
Concept B (Figure 2) is similar to Concept A in that it is an impulse turbine with a Pelton-style
pinwheel. It differs from concept A in that the motor and wheel are offset from the stream, which
travels through a nozzle to increase its velocity. The generator is again placed outside of the pipe
in its own housing.
Concept C
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Concept C (Figure 3) uses a radial flow turbine. The water is allowed to flow over the turbine
freely. However, since the motor must be placed outside of the flow in order to both shield it and
prevent the restriction of the flow, it is placed in its own housing to the side of the pipe with
gears used to turn the motor’s shaft.
Figure 1: Concept A Figure 2: Concept B Figure 3: Concept C
3.4 Concept Selection
These three concepts were then put into a concept scoring matrix (Table 5) for final selection.
The selection criteria are found in the left column of the matrix. The next column contains their
respective weights (see prior customer needs assessment for determination of weights). The team
rated each concept by each criterion on a 1-5 scale. Each rating was then multiplied by the
weight in order to get a weighted score. Finally, these weighted scores were summed to get a
score for each concept.
The most obvious deciding factor was performance. Concept B was determined to have the most
potential for high performance. The team’s research indicated that a Pelton-style impulse turbine
would be best suited for this circumstance, in which the flow has relatively high head and can be
throttled in order to increase the flow’s velocity[6]. Thus, concepts A and B received higher
scores. Also, it was assumed that water fed through a nozzle would have a more accurate flow
than one simply throttled to the side, thus increasing the turbine’s performance. Thus, Concept B
proved to be ranked the highest. Based on these scores, the team decided to go through with
Concept B.
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Table 5: Concept Scoring Matrix
Criteria Weight Concept A Concept B Concept C
Performance 30% 3 0.9 5 1.5 2 0.6
Cost 20% 5 1 3 0.6 1 0.2
Appearance 14% 4 0.56 3 0.42 4 0.56
Ease of Use/Safety 20% 3 0.6 3 0.6 3 0.6
Durability 14% 3 0.42 4 0.56 1 0.14
Environmentally Friendly 2% 3 0.06 3 0.06 3 0.06
Total 3.54 3.74 2.16
Rank 2 1 3
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4. Detailed Design
4.1 Description of the Chosen Design
As stated previously, the team chose the offset Pelton pinwheel design (Figure 4). In this design,
the motor and turbine are offset from the flow, which travels through a nozzle in order to
increase its velocity. The offset pinwheel design best fits the specifications that were set to
satisfy the primary purpose of the product. It has the highest expected performance rate of the
systems taken into consideration because it uses an impact turbine instead of a reactive turbine.
The disadvantage found in a reactive turbine is that there are two opposite forces applied to the
turbine; while this may be used for other purposes, it is not as efficient as the impact turbine
model for our product. Elevated performance in impact turbine is achieved through high pressure
gradient created at a nozzle. As the pressure changes, the kinetic energy of the water is increased
and the turbine is solely derived by the impact force collision at the blade of the turbine. In
addition, the offset pinwheel is designed for easy access for maintenance or repair. As it has few
parts and is relatively simple, product failure by fatigue can be prevented, giving this design a
greater life expectancy as well. Figure 5 shows an exploded view of the design, and detailed
drawings can be found in Appendix G. For the prototype, the turbine blade was rapid
prototyped, and its volume is 0.48 cubic inches.
Inlet Nozzle Turbine
(Within
Housing)
Motor Casing
(Motor inside)
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Figure 4: SolidWorks Model of Final Design Concept
Figure 5: Exploded View of the Chosen Design
4.2 Analysis Calculations
Pelton turbines work most effectively for high velocity flows. Thus, the team did an assessment
of flow rate as it relates to pressure drop in the sink that will be used for testing. A pressure
measuring device was attached to the end of the test faucet and both of the faucet’s valves were
opened fully. The throttle on the pressure device was turned to a predetermined value, and then a
volume of liquid was obtained while being timed. Then, the volume of the liquid was measured
and the volume flow rate was calculated A summary of these results can be found in Appendix
D.1.
Using these results, the team calculated the ideal nozzle diameter to maximize the power of the
flow. These results can be found in Appendix D.2.
Motor Calculations[10]
The following motor performance calculations were performed in order to determine the overall
efficiency of the motor. These tabulated values can be found in Appendix D.3. This was done by
Housing
Outlet
Turbine Nozzle
Motor Motor Casing
Outlet
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comparing the input power from the drill to the output power from the electric motor. In order to
arrive at these values, a series of formulas were used to evaluate the motor properties.
In order to determine the torque constants Ke and Kt, the following formula was used at no load
and stall conditions:
𝑇 = 𝑇𝑙𝑜𝑎𝑑 + 𝑇𝑙𝑜𝑠𝑠 =𝐾𝑡
𝑅𝑎
𝑉 − 𝐾𝑒𝜔 = 𝐾𝑡𝐼𝑎
After determining the constants, it was possible to determine the constant torque loss of
operating the motor. Following these calculations, the armature resistance was determined
through the following equation:
𝑉 = 𝑅𝑎𝐼𝑎 + 𝐾𝑒𝜔
Once this armature resistance was known, using the input voltage and currents, it was possible to
determine the input and output power, and thus the efficiency of the motor. All of the above
calculations are expressed in the data tables and graph below (Figure 6).
Figure 6: Motor Performance Curve
Generator Calculations
0
0.5
1
1.5
2
2.5
3
3.5
0
2
4
6
8
10
12
14
16
18
20
0 1000 2000 3000 4000 5000 6000
Applied Torque
Power In
Current
Power Out
Efficiency
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The generator performance calculations were performed very similarly to the motor calculations.
These tabulated values can also be found in Appendix D.3. First, the input torque was calculated
using the constant torque loss expression using the following equation:
𝑇𝑖𝑛𝑝𝑢𝑡 − 𝑇𝑙𝑜𝑠𝑠 = 𝐾𝑇𝐼𝑎
Once this input torque was calculated, using the known armature and load resistances, it was
possible to determine the armature current of the generator:
𝐼𝑎 =𝐾𝐸𝜔
𝑅𝑎 + 𝑅𝑙
Using this data, it was simple to calculate the input and output power of the generator. Using
these values, the same efficiency formula for the motor could be applied to calculate the
generator efficiency:
𝜂 =𝑃𝑜𝑢𝑡
𝑃𝑖𝑛
These calculations are expressed in the graph below (Figure 7)
Figure 7: Generator Performance Curve
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0
2
4
6
8
10
12
14
0 1000 2000 3000 4000 5000
Applied Torque
Power In
Power Out
Current
Efficiency
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In order to get an idea of voltage output from the generator, the team used an electric hand drill
to turn the motor shaft at various speeds and recorded the voltage output of the generator. A
summary of these results can be found in Appendix D.3.
Turbine Flow Analysis
In order to analyze the performance of the turbine, angular momentum calculations were
performed. For a turbine,
𝑊𝑑𝑜𝑡 ,𝑠𝑎𝑓𝑡 = 𝜔𝑇𝑠𝑎𝑓𝑡 = 𝜌𝜔𝑉𝑑𝑜𝑡 (𝑟2𝑉2,𝑡 − 𝑟1𝑉1,𝑡) [9]
Using this relationship, power and efficiency (assuming the input power is the maximum power
of the flow as determined in the initial flow analysis) were plotted against rpm (Figure 8 and 9).
For this analysis, in order to achieve a conservative estimate, it was assumed that when the flow
hits the turbine, it will be scattered exactly outward. The numerical results of this analysis can be
found in Appendix D.4
Figure 8: Theoretical Power delivered to generator vs RPM of Turbine
Figure 9: Torque Delivered to Generator vs RPM of Turbine
0
10
20
30
40
50
0 1000 2000 3000 4000
Po
we
r (W
atts
)
RPM
Power vs RPM
0
10
20
30
40
50
60
70
0 2000 4000 6000
Torque Delivered vs RPM
Torque Delivered vs RPM
RPM
mN-m
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0
10
20
30
40
50
60
70
0 1000 2000 3000 4000 5000 6000
mN
-m
RPM
Turbine and Generator Torque at Operating Power
Generator Input Torque
Out of Turbine Torque
Predicting Output Voltage
In order to determine the output voltage of the system, an operating turbine efficiency was
needed. Most products on the market operate at less than 5% efficiency. Therefore, the team
assumed that our design turbine had a 5% design efficiency. Therefore, using this assumed
efficiency and the theoretical power from the flow calculations, it was possible to determine the
out of turbine torque as a function of pinwheel RPM. Additionally, we plotted the generator
output torque. Together, the intersection point of these two curves represents the operating
conditions of the system at maximum power output. Figure 10 below shows this intersection
point which represents operating conditions at approximately 4300 RPM. Using these operating
conditions, it was possible to determine the output voltage of the system:
𝑃 =𝑉2
𝑅; 𝑉 = 𝑃𝑅 = 1.95 𝑊𝑎𝑡𝑡𝑠 ∗ (10 𝑂𝑚𝑠) = 𝟒. 𝟒 𝑽𝒐𝒍𝒕𝒔
Note that this final determined output voltage exceeds the design requirement of at least 1.5
Volts.
4.3 Test Procedure
The designed prototype will be brought to the required testing area (314 Reber building) for
experimentation and observation. The prototype set for use is one which was fully dimensioned
on SolidWorks. The faucet-powered generator also will include detailed drawings for each
component of the assembly to ensure proper installation. The sink has a 3/18-18 NPS internal
pipe thread that will be connected to the inlet of the generator. After the assembly is securely
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fastened, the sink will be turned on, starting at a low volume flow rate. The valves of the sink
will then be opened until both the hot and cold valves are fully open.
Ideally, the combination of volume flow rate and pressure drop will create the perfect conditions
for producing maximum power and efficiency with the water turbine. By examining outlet
velocity and generator output, the team can determine the overall power and efficiency of the
generator as compared to the preliminary calculations. Although a perfect match between
theoretical and actual values cannot be expected, the results of this experiment should be close to
the predicted performance.
5. Mass Production
5.1 Material Selection and Fabrication Process for Mass Production
Table 6 below displays information for the project prototype for each component, quantity of
that component, material, and associated manufacturing process. Costs are not included in this
prototype analysis; however, for the mass production table seen below, cost of components and
manufacturing are estimated.
Table 6: Material and Fabrication Process for Prototype System
Table 7 below displays information for the actual design including each component, the quantity
of that component, the material, manufacturing process required for its production, and the total
cost. These materials have been selected for the mass production of at least 100,000 units.
Component Quantity Material Manufacturing Process
Generator 1 Pre-fabricated (composite) Pre-fabricated
Shaft 1 Plain Carbon Steel Drawn and Cut
Water Seals 3 plastic Shaped and Compression fit
Pinwheel 1 Pre-fabricated Rapid Prototyping
Generator Housing 1 Plexiglass Cut to shape and glued
Flow Guide
Housing 1 Plexiglass Cut to shape and glued
Nozzle 1 6061 Aluminum Cut, Shaped, & MIG Welded
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Table 7: Material, Fabrication, and Cost Per Unit for Mass Production
5.2 Bill of Materials for Mass Production
A full bill of materials for mass production can be found in Appendix E.
5.3 Economic Analysis for Full Scale
A full economic analysis for full scale manufacturing can be found in Appendix F.
6. Conclusions
Overall, the team has made excellent progress in the design and development process for
creating this faucet-attached water powered generator. This product will satisfy all the customer
needs developed in our analysis while providing an excellent profit margin for the manufacturing
company. The design meets all project requirements including a produced output voltage of 4.4
Volts, which exceeds the design criteria of 1.5 Volts. Additionally, the economic analysis
showed a net present value of $686,291.07 for the project. This product will save the customer
money through the utilization of wasted flow energy to produce electricity for battery charging.
The team intends to move forward with the design process with this design proposal successfully
completed. A more detailed design analysis will now be performed, along with a supplementary
economic analysis for the product.
7. Supporting Materials
7.1 References
[1] Baarman, David W., and Thomas Leppien. Self-powered Miniature Liquid Treatment
System. Access Business Group International, assignee. Patent 6927501. 9 Aug. 2005. Print.
Component Quantity Material Manufacturing Process Cost
Generator 1 Pre-fabricated (composite) Pre-fabricated $5.00
Shaft 1 Plain Carbon Steel Drawn and Cut $0.75
Water Seals 3 plastic Cut to shape $2.50
Pinwheel 1 Pre-fabricated (aluminum) Rapid Prototyping $14.99
Generator Housing 1 6061 Aluminum Drawn and Cut $4.00
Flow Guide
Housing 1 6061 Aluminum Drawn and Cut $4.00
Nozzle 1 6061 Aluminum
Cut, Shaped, & MIG
Welded $3.50
Total Material Cost: $34.74
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[2] Spiller, Andrew. Water Faucet Generated Emergency Lighting System. Patent 6036333. 14
Mar. 2000. Print.
[3] Terry, Robert L., and Daniel V. Sallis. Water Powered Rotating Shower Brush. Synergetic
Industries, Inc., assignee. Patent 4841590. 27 June 1989. Print.
[4] Yukinobu Yumita, Nagano. Small Power Generating Device and Water Faucet Device.
Kabushiki Kaisha Sankyo Seiki Seisakusho, Nagano; Toto Ltd., Fukuoka, assignee. Patent
6876100. 5 Apr. 2005. Print.
[5]“Sylvania Ecolight Water Powered LED Shower Light.” Sylvania, 2008.
<http://www.sylvania.com/AboutUs/Pressxpress/Tradeshowevents/Greenbuild2008/PressKit/Ec
oLightShowerLight.htm>
[6] Naveenagrawal. "Hydraulic Turbines: Definition and Basics." Hydraulic Turbines: Definition
and Basics. Haresh Khemani, 22 Nov. 2009. Web. 24 Mar. 2010.
<http://www.brighthub.com/engineering/mechanical/articles/26551.aspx>.
[7] "Stainless Steel Cylinder with Gecko." Stainless Steel Cylinder with Gecko. Memorial
Gallery, 2005. Web. 31 Mar. 2010. <http://www.funeral-urn.com/stainless-steel-cylinder-with-
gecko.aspx>.
[8] Ulrich, Karl T., and Steven D. Eppinger. Product Design and Development. 4th ed. New
York: McGraw-Hill Higher Education, 2007. Print.
[9] Cengel, Yunus A. and John. M. Cimbala. Fluid Mechanics: Fundamentals and Applications.
2nd ed. New York: McGraw-Hill, 2010. Print.
[10] Kenjo, T. and S. Nagamori. "Permanent Magnet and Brushless DC Motors". Oxford.
Clarendon Press. 1985
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Appendix A: Project Management
Team roles
Program Manager (Tim Heindl) – Responsible for completing the project on schedule,
continuously monitors and updates the Gantt chart. With Fi, performed motor and
generator calculations and with Seth compiled report
Financial Officer (Aaron Weiss)– Responsible for tracking all expenditures, provides BOM
and economic analyses. Aided with SolidWorks and performed turbine flow calculations
with Seth
Record Keeper (Seth Forney) - Responsible for maintaining project records and
documentation, is the primary point of contact for all communications with the instructor.
Created SolidWorks Models, aided in turbine flow calculations, and compiled report
Safety Officer (Fikremariam Yami) - Responsible for the safety of the project. Performed
motor and generator calculations and drew sketches for concept selection.
Gantt Chart
The current Gantt chart illustrates all progress from the start of the project up to the most
recent team meeting on April 15, 2010. According to this chart, the team is currently on-task and
has made tremendous progress with the pending design.
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Appendix B: External Search Results
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Appendix C: Black Box Decomposition
Input Output
Energy (Mechanical) Energy (Electrical)
Open flow (activation of process) Power generation
Raw material Product component
The overall function of the new micro-hydropower system in product development.
Energy
Open faucet
Raw material
Illustration of the subfunctions of the micro-hydropower system intended to be produced.
Faucet head electric
generator
Gather kinetic
energy from
the fluid flow
Convert into
electrical energy
Power household
appliance
Initiate
pressure
gradient in the
flow
Draw flow of
water into the
system
Construct
fixed, self-
contained
components
entire system
Drive a generator
using a shaft
Page | 28
Appendix D: Scoping Calculations
D.1. Faucet Test
Flow rate = liters of water / amount of time needed
Power generated = flow rate * pressure drop
Power (Watts) and Pressure Drop (m^3/s) vs Flow Rate (m^3/s)
D.2. Nozzle Calculations
First, we begin with the conservation of mass relationship, since we assume no water leaks from the
system when the pinwheel is connected to the faucet:
0
10
20
30
40
50
60
70
80
90
0
50000
100000
150000
200000
250000
300000
350000
400000
0 0.0002 0.0004 0.0006 0.0008
Po
we
r (W
atts
)
Pre
ssu
re D
rop
(P
a)
Volume Flow Rate (m^3/s)pressure drop
Power
Pressure
Drop Pressure Drop (Pascals)
Volume
(L) Time (s)
Flow Rate
(L/s)
Flow Rate
(m^3/s)
Power
(Watts)
0 0 1.7 2.94 0.578231293 0.000578231 0
0 0 3.56 6.16 0.577922078 0.000577922 0
53 365422.1364 0
0 0 0
50 344737.8645 0.85 8.56 0.099299065 9.92991E-05 34.23214776
40 275790.2916 1.89 6.66 0.283783784 0.000283784 78.26481248
30 206842.7187 2.05 5.53 0.370705244 0.000370705 76.67768053
20 137895.1458 2.6 5.69 0.456942004 0.000456942 63.0100842
10 68947.5729 2.44 4.6 0.530434783 0.000530435 36.57219084
Page | 29
ṁ𝑖𝑛 𝑘𝑔
𝑠 = ṁ𝑜𝑢𝑡
𝑘𝑔
𝑠
Letting 1 subscripts represent flow into the system and 2 represent flow leaving the system, breaking
down this equation into its components gives:
𝜌1𝑉1𝐴1 = 𝜌2𝑉2𝐴2
Assuming the flow of water is incompressible, it is possible to state that ρ1 = ρ2 and thus the equation
simplifies:
𝑉1𝐴1 𝑚3
𝑠 = 𝑉2𝐴2
𝑚3
𝑠
Using the appropriate control volume for the system, we represent state 1 as the open flow conditions and
state 2 as the constricted nozzle flow at which maximum power exists. Therefore, we can solve for the
velocity and area at state 1 as follows:
Ṿ𝑉𝑜𝑙𝑢𝑚𝑒 𝐹𝑙𝑜𝑤 𝑅𝑎𝑡𝑒 𝑚3
𝑠 = 𝑉 ∗ 𝐴
Note: the measured open radius of the faucet is .337 in = .0085598 m
Ṿ𝑚𝑎𝑥𝑃 = . 000283784𝑚3
𝑠 = 𝑉1 𝜋 . 0085598 𝑚 2
𝑉1 𝑜𝑝𝑒𝑛 𝑓𝑙𝑜𝑤 = 𝟏. 𝟐𝟑𝟐𝟖𝟓𝒎
𝒔
In order to calculate the required radius of the nozzle in order to produce the desired power, use the
Bernoulli Energy Equation to calculate for V2 and then back calculate using the above relationship to
solve for A2:
1
2𝜌𝑉2 + 𝜌𝑔𝑧 + 𝑃 = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
1
2𝜌1𝑉1
2 + 𝜌1𝑔𝑧1 + 𝑃1 =1
2𝜌2𝑉2
2 + 𝜌1𝑔𝑧2 + 𝑃2
Continue to apply the incompressible assumption to set ρ1 = ρ2 and assume that the potential drop over the
height of the nozzle is negligible to cancel the potential energy terms. This leaves the remaining terms in
the energy equation:
1
2𝑉1
2 +𝑃1
𝜌=
1
2𝑉2
2 +𝑃2
𝜌 →
1
2 𝑉1
2 − 𝑉22 =
𝑃2 − 𝑃1
𝜌
Using 1000 kg/m3 as the value for the density of water, and 2.73e5 Pa as the delta P across the nozzle as
the flow is constricted, it is possible to solve for the speed of the water through the nozzle:
Page | 30
1
2 1.21
𝑚
𝑠
2
− 𝑉22 =
−2.73 𝑥 105 𝑘𝑔 𝑚𝑠2 𝑚2
1000𝑘𝑔𝑚3
𝑉2 𝑚
𝑠 = 𝟐𝟑. 𝟑𝟗𝟕𝟗
𝒎
𝒔
Using this value for exit velocity from the nozzle, it is possible to back calculate for the radius of the
nozzle as follows:
𝑉𝑑𝑜𝑡 𝑛𝑜𝑧𝑧𝑙𝑒= . 000283784
𝑚3
𝑠 = 23.3979
𝑚
𝑠 𝜋 𝑟𝑛𝑜𝑧𝑧𝑙𝑒
2
𝑟𝑛𝑜𝑧𝑧𝑙𝑒 = .0019651 𝑚𝑒𝑡𝑒𝑟𝑠
Converting this nozzle radius to inches gives:
𝑟𝑛𝑜𝑧𝑧𝑙𝑒 = . 𝟎𝟕𝟕𝟑𝟔𝟓𝟒 𝒊𝒏𝒄𝒉𝒆𝒔
D.3. Motor/Generator Data
Motor Data
Kt = 0.017698259
Td = In* Kt 0.000460155
Ke = 0.017698259
In = 0.026
Ra = Va/Is 11.32075472
Is = 1.06
Va = 12
Exp Drill Voltage rpm ω(rad/sec) Vb (Volts) I (Amps) Ta (N-m) P_in (W) P_out (W)
0.13 130 13.61356817 0.240936455 1.03871728 0.017923333 12.464607 0.244000512
0.235 250 26.17993878 0.463339337 1.019071692 0.01757564 12.22886 0.460129179
0.265 290 30.36872898 0.537473631 1.012523163 0.017459742 12.150278 0.530230186
0.37 400 41.88790205 0.741342939 0.994514707 0.017141024 11.934176 0.71800154
0.447 475 49.74188368 0.880344741 0.982236215 0.016923716 11.786835 0.841817522
0.53 590 61.78465552 1.093480836 0.963409193 0.016590511 11.56091 1.025038988
0.597 640 67.02064328 1.186148703 0.955223531 0.016445639 11.462682 1.102197286
0.669 715 74.87462491 1.325150504 0.942945039 0.016228331 11.31534 1.21509018
0.701 750 78.53981634 1.390018011 0.937215076 0.01612692 11.246581 1.266605367
Page | 31
0.773 840 87.9645943 1.556820173 0.922480885 0.015866151 11.069771 1.395659526
0.811 885 92.67698328 1.640221253 0.915113789 0.015735766 10.981365 1.458343334
0.886 960 100.5309649 1.779223055 0.902835297 0.015518458 10.834024 1.560085575
0.937 1010 105.7669527 1.871890922 0.894649635 0.015373586 10.735796 1.626017367
1.011 1100 115.1917306 2.038693083 0.879915444 0.015112817 10.558985 1.74087151
1.221 1360 142.418867 2.520565994 0.837350004 0.014359483 10.0482 2.045061229
1.435 1600 167.5516082 2.965371758 0.798058828 0.013664097 9.5767059 2.289441444
1.592 1800 188.4955592 3.336043227 0.765316182 0.013084609 9.1837942 2.46639074
1.78 2000 209.4395102 3.706714697 0.732573535 0.012505121 8.7908824 2.619066507
2.145 2500 261.7993878 4.633393371 0.650716919 0.011056402 7.808603 2.894559231
2700 282.7433388 5.004064841 0.617974272 0.010476914 7.4156913 2.962277643
2800 293.2153143 5.189400576 0.601602949 0.01018717 7.2192354 2.987034276
2900 303.6872898 5.374736311 0.585231626 0.009897426 7.0227795 3.005722526
3000 314.1592654 5.560072046 0.568860303 0.009607682 6.8263236 3.018342393
3200 335.1032164 5.930743515 0.536117656 0.009028194 6.4334119 3.025376981
3400 356.0471674 6.301414985 0.50337501 0.008448707 6.0405001 3.008138039
3600 376.9911184 6.672086455 0.470632363 0.007869219 5.6475884 2.966625568
3800 397.9350695 7.042757924 0.437889717 0.007289731 5.2546766 2.900839566
4000 418.8790205 7.413429394 0.40514707 0.006710243 4.8617648 2.810780035
4200 439.8229715 7.784100864 0.372404424 0.006130755 4.4688531 2.696446974
4400 460.7669225 8.154772334 0.339661777 0.005551267 4.0759413 2.557840383
4600 481.7108736 8.525443803 0.306919131 0.00497178 3.6830296 2.394960262
4800 502.6548246 8.896115273 0.274176484 0.004392292 3.2901178 2.207806612
5000 523.5987756 9.266786743 0.241433838 0.003812804 2.8972061 1.996379431
5200 544.5427266 9.637458212 0.208691191 0.003233316 2.5042943 1.760678721
5400 565.4866776 10.00812968 0.175948545 0.002653828 2.1113825 1.500704482
5600 586.4306287 10.37880115 0 -
0.000460155 0 0
rpm Ta+Td (Total Applied
Load, mN-m) Kt*I
eff (%)
130 18.38348745 0.018383 0.019575
250 18.03579474 0.018036 0.037626
290 17.91989717 0.01792 0.043639
400 17.60117886 0.017601 0.060163
475 17.38387092 0.017384 0.07142
590 17.05066542 0.017051 0.088664
640 16.90579346 0.016906 0.096155
715 16.68848552 0.016688 0.107384
750 16.58707515 0.016587 0.112621
840 16.32630562 0.016326 0.126078
Page | 32
885 16.19592086 0.016196 0.132802
960 15.97861292 0.015979 0.143999
1010 15.83374096 0.015834 0.151458
1100 15.57297143 0.015573 0.164871
1360 14.81963724 0.01482 0.203525
1600 14.12425184 0.014124 0.239064
1800 13.544764 0.013545 0.268559
2000 12.96527616 0.012965 0.29793
2500 11.51655657 0.011517 0.370688
2700 10.93706873 0.010937 0.399461
2800 10.64732481 0.010647 0.41376
2900 10.35758089 0.010358 0.427996
3000 10.06783697 0.010068 0.442162
3200 9.488349133 0.009488 0.47026
3400 8.908861295 0.008909 0.497995
3600 8.329373457 0.008329 0.525291
3800 7.749885619 0.00775 0.552049
4000 7.170397781 0.00717 0.57814
4200 6.590909943 0.006591 0.603387
4400 6.011422105 0.006011 0.627546
4600 5.431934267 0.005432 0.650269
4800 4.85244643 0.004852 0.671042
5000 4.272958592 0.004273 0.689071
5200 3.693470754 0.003693 0.703064
5400 3.113982916 0.003114 0.710769
5600 0 0 0
Generator Data
rpm ω(rad/sec) Vb (Volts) I (Amps) Ta (N-m) P_in (W) P_out (W)
0 0 0 0 0 0
130 13.61356817 0.284563871 0.013346801 -0.00022394 -0.003049 0.001781371
250 26.17993878 0.547238213 0.025666925 -5.89485E-06 -0.000154 0.00658791
290 30.36872898 0.634796327 0.029773633 6.67867E-05 0.0020282 0.008864692
400 41.88790205 0.875581141 0.04106708 0.000266661 0.0111699 0.016865051
475 49.74188368 1.039752605 0.048767158 0.000402939 0.0200429 0.023782357
590 61.78465552 1.291482183 0.060573943 0.000611899 0.0378059 0.036692026
640 67.02064328 1.400929826 0.065707328 0.000702751 0.0470988 0.04317453
715 74.87462491 1.56510129 0.073407406 0.000839029 0.0628219 0.053886472
750 78.53981634 1.641714639 0.077000775 0.000902625 0.070892 0.059291194
Page | 33
840 87.9645943 1.838720396 0.086240868 0.001066158 0.0937842 0.074374873
885 92.67698328 1.937223274 0.090860915 0.001147925 0.1063863 0.082557058
960 100.5309649 2.101394738 0.098560992 0.001284203 0.1291022 0.097142692
1010 105.7669527 2.210842381 0.103694377 0.001375055 0.1454354 0.107525239
1100 115.1917306 2.407848138 0.11293447 0.001538589 0.1772327 0.127541946
1360 142.418867 2.976975879 0.139628072 0.002011019 0.2864071 0.194959986
1600 167.5516082 3.502324564 0.16426832 0.002447109 0.410017 0.26984081
1800 188.4955592 3.940115134 0.18480186 0.002810516 0.5297699 0.341517276
2000 209.4395102 4.377905705 0.2053354 0.003173924 0.6647452 0.421626266
2500 261.7993878 5.472382131 0.25666925 0.004082444 1.0687814 0.658791041
2700 282.7433388 5.910172702 0.27720279 0.004445852 1.2570351 0.76841387
2800 293.2153143 6.129067987 0.28746956 0.004627556 1.3568703 0.826387482
2900 303.6872898 6.347963272 0.29773633 0.00480926 1.4605111 0.886469225
3000 314.1592654 6.566858557 0.3080031 0.004990964 1.5679576 0.948659099
3200 335.1032164 7.004649128 0.328536641 0.005354372 1.7942672 1.079363242
3400 356.0471674 7.442439698 0.349070181 0.00571778 2.0357993 1.218499909
3600 376.9911184 7.880230269 0.369603721 0.006081188 2.2925537 1.366069103
3800 397.9350695 8.318020839 0.390137261 0.006444596 2.5645306 1.522070821
4000 418.8790205 8.75581141 0.410670801 0.006808003 2.8517298 1.686505065
4200 439.8229715 9.19360198 0.431204341 0.007171411 3.1541515 1.859371834
4400 460.7669225 9.631392551 0.451737881 0.007534819 3.4717955 2.040671129
4600 481.7108736 10.06918312 0.472271421 0.007898227 3.8046619 2.230402948
4800 502.6548246 10.50697369 0.492804961 0.008261635 4.1527507 2.428567294
5000 523.5987756 10.94476426 0.513338501 0.008625043 4.516062 2.635164164
5200 544.5427266 11.38255483 0.533872041 0.008988451 4.8945956 2.85019356
5400 565.4866776 11.8203454 0.554405581 0.009351859 5.2883516 3.073655481
5600 586.4306287 12.25813597 0.574939121 0.009715267 5.69733 3.305549927
rpm T_input (mN-m) Kt*I
eff (%)
0 0.460155 0.00046 0
130 0.696369875 0.000236 -0.58432
250 0.914414621 0.000454 -42.6881
290 0.987096203 0.000527 4.370658
400 1.186970553 0.000727 1.509869
475 1.323248519 0.000863 1.18657
590 1.532208068 0.001072 0.970536
640 1.623060045 0.001163 0.91668
715 1.759338011 0.001299 0.857765
750 1.822934395 0.001363 0.836359
840 1.986467955 0.001526 0.793043
Page | 34
885 2.068234734 0.001608 0.776012
960 2.2045127 0.001744 0.752448
1010 2.295364678 0.001835 0.739333
1100 2.458898237 0.001999 0.71963
1360 2.93132852 0.002471 0.680709
1600 3.367418011 0.002907 0.658121
1800 3.730825921 0.003271 0.644652
2000 4.094233831 0.003634 0.634268
2500 5.002753605 0.004543 0.616395
2700 5.366161515 0.004906 0.611291
2800 5.547865469 0.005088 0.609039
2900 5.729569424 0.005269 0.606958
3000 5.911273379 0.005451 0.605029
3200 6.274681289 0.005815 0.601562
3400 6.638089198 0.006178 0.598536
3600 7.001497108 0.006541 0.595872
3800 7.364905018 0.006905 0.593509
4000 7.728312927 0.007268 0.591397
4200 8.091720837 0.007632 0.5895
4400 8.455128747 0.007995 0.587786
4600 8.818536657 0.008358 0.586229
4800 9.181944566 0.008722 0.584809
5000 9.545352476 0.009085 0.583509
5200 9.908760386 0.009449 0.582314
5400 10.2721683 0.009812 0.581212
5600 10.6355762 0.010175 0.580193
D.4. Turbine Flow Analysis
rpm w abs(Power) efficiency Torque
r1 0.01905 m 0 0 0 0 0
r2 0.01905 m 100 10.47198 1.321070184 0.016879491 0.372423
v1 23.4 m/s 200 20.94395 2.642140369 0.033758982 0.186211
v2 0 m/s 300 31.41593 3.963210553 0.050638472 0.124141
400 41.8879 5.284280737 0.067517963 0.093106
vdot 0.000283 m^3/s 500 52.35988 6.605350921 0.084397454 0.074485
p 1000 kg/m^3 600 62.83185 7.926421106 0.101276945 0.06207
700 73.30383 9.24749129 0.118156436 0.053203
800 83.7758 10.56856147 0.135035927 0.046553
max power 78.26481 watts 900 94.24778 11.88963166 0.151915417 0.04138
Page | 35
Assumed Efficiency 0.05 1000 104.7198 13.21070184 0.168794908 0.037242
Actual Power 3.913241 1100 115.1917 14.53177203 0.185674399 0.033857
1200 125.6637 15.85284221 0.20255389 0.031035
1300 136.1357 17.1739124 0.219433381 0.028648
1400 146.6077 18.49498258 0.236312872 0.026602
1500 157.0796 19.81605276 0.253192362 0.024828
1600 167.5516 21.13712295 0.270071853 0.023276
1700 178.0236 22.45819313 0.286951344 0.021907
1800 188.4956 23.77926332 0.303830835 0.02069
1900 198.9675 25.1003335 0.320710326 0.019601
2000 209.4395 26.42140369 0.337589817 0.018621
2100 219.9115 27.74247387 0.354469307 0.017734
2200 230.3835 29.06354405 0.371348798 0.016928
2300 240.8554 30.38461424 0.388228289 0.016192
2400 251.3274 31.70568442 0.40510778 0.015518
2500 261.7994 33.02675461 0.421987271 0.014897
2600 272.2714 34.34782479 0.438866761 0.014324
2700 282.7433 35.66889498 0.455746252 0.013793
2800 293.2153 36.98996516 0.472625743 0.013301
2900 303.6873 38.31103534 0.489505234 0.012842
3000 314.1593 39.63210553 0.506384725 0.012414
Page | 36
Appendix E: Bill of Materials for Mass Production
The offset pinwheel design contains the following parts in assembly:
Generator – for electrical generation
Cost = $5.00
This cost estimate was made based on similar generator models found online. Assuming the
Mechanical Engineering department purchases the generators in bulk, a similar price would be
provided on a large manufacturing scale.
Shaft – to translate the torque generated by the water flow
Cost = $0.75
This component will be made of plain carbon steel in order to survive the torque applied by the
pinwheel. Additionally, this cost estimate was made using the current prices of steel rods. The
small dimensions of the shaft (less than a half inch diameter), reduce the price of the component.
Water seals (3) – to prevent leakage and keep the motor assembly dry
Cost = $2.50
These components will be made of plastic and will prevent water from entering the motor area.
These water seals will surround the shaft and be tight against the housing to maintain protection
against leakage. The cost estimate was based on current water seal prices scaled down to the
small dimensions required for this project.
Pinwheel – the powerhouse of the product, a Pelton style turbine
Cost = $14.99
The pinwheel is the most critical piece for the project. Care must be taken during manufacturing
to produce the most efficient design that will utilize power from the water flow most effectively.
Since this portion of the product will be made in the rapid prototyping machine, it is difficult to
estimate the actual manufacturing cost. Using web resources, the team discovered prices of
similar water pinwheels and assumed that the cost would be similar for a smaller design due to
difficulties in manufacturing.
Pinwheel/Generator housing – Metal housing to protect and hold the pinwheel, seals,
shaft, and generator components in place
Cost = $4.00
This piece will be made of 6061 Aluminum for its light weight and strong properties and will be
rectangular in shape. Using current prices for this alloyed aluminum at the specified dimensions
(around 1.25 inches in outer diameter), the team was able to estimate a price.
Page | 37
Flow guide housing – Metal housing to guide the flow to the pinwheel. A threaded
portion of this component connects to the sink faucet.
Cost = $4.00
This piece will be nearly identical to the Pinwheel/Generator housing. It will be made of the
same material, be the same rectangular shape, and have nearly identical dimensions. Therefore,
we applied the same cost estimate to this portion of the design.
Nozzle – To direct the flow to the turbine and increase the kinetic energy of the flow
Cost = $3.50
The nozzle will be an integral part of the product design. It is used to increase the kinetic energy
of the water flow to spin the pinwheel at a higher angular velocity to increase the power
produced. This will be the same material as the 6061 Aluminum housing and will be connected
to the housing with a simple butt weld. Additionally, the top of the nozzle will be threaded in
order to easily connect to the customer’s faucet.
Using the above cost estimates, the overall price for all the components will be $34.74.
However, this price does not take into account manufacturing costs associated with making a
single unit. Although overhead to operate the business does not need to be considered, we
assumed around a 15% manufacturing cost when producing each unit. This brings the new total
cost to $39.95 per unit. Note that this cost estimate does not include marketing costs for
spreading word about the product or labor costs during production.
Finally, using the above total unit cost estimate, it was possible to determine the cost of
producing 100,000 units. In order to produce this volume, it would cost roughly $3.9 million
dollars. Although this cost may seem high, the proposed retail price for the final product is
$50.00 a unit. This would yield around $5 million dollars in gross sales and nearly $1.1 million
dollars in company profit (not accounting for marketing and labor costs).
Page | 38
Appendix F: Economic Analysis for Full Scale
Economic Analysis:
Net Present Value (NPV) is an important economic gauge often applied during project design. It
represents the present worth of the total costs and profits over the period of the project at an assumed
interest rate. The following equation quantitatively expressed NPV:
𝑁𝑃𝑉 = 𝑝𝑒𝑟𝑖𝑜𝑑 𝑐𝑎𝑠 𝑓𝑙𝑜𝑤
1 + 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑟𝑎𝑡𝑒 𝑝𝑒𝑟𝑖𝑜𝑑𝑝𝑒𝑟𝑖𝑜𝑑𝑠
𝑁𝑃𝑉 = 𝐶𝑖
1 + 𝑟 𝑖
𝑁
𝑖=1
For calculating NPV, the following assumptions were made:
Interest Rate on costs = 10%
Cost of student labor = $20/hr
Cost of machining labor = $60/hr
Tooling cost per unit = $0.10/unit
Ramp-up cost per unit = $0.10/unit
Marketing and Support Costs = $100/hr for 10 total hours (commercials, paid marketers, etc.)
Manufacturing time = 5 minutes/unit, at machining labor price and $5.00 variable cost per unit
Sales Volume = 100,000 units per year in a 4 year period
The table below displays the above listed costs and their summation excluding the cost of materials for
the project.
Time (hr) Cost/Time
($/hr) Total Time
Cost ($) Variable
Cost/Unit ($/u) Variable Cost Total Total Cost
Development Cost 147.5 20 2950 0 0 2950
Testing Cost 2 20 40 0 0 40
Tooling Investment 0.25 60 15 0.1 40000 40015
Ramp-up Cost 40 20 800 0.1 40000 40800
Marketing and Support Cost 10 100 1000 0 0 1000
Manufacturing Costs 0.0833333 60 4.999998 5 2000000 2000000
Total Costs (excluding materials) 2084805
The table below shows a summary of the above results, includes the retail price, sales volume, and
material cost. Using all of this data, the table calculates the cash flow in a given period (1 year) and the
final Net Present Value for the entire project.
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Sales Volume (# of units/year) 100,000 units
Retail Price ($/unit) $50/unit
Revenue ($) 20,000,000
Material Costs 13,896,000
Total Costs 2,084,805
Interest Rate (%) 0.1
Cash Flow (per period) 1,004,798.75
NPV 686,291.0662
Included below is the sample calculation for net present value for the project using 4 periods (1 year each)
and the calculated cash flow per period:
𝑁𝑃𝑉 = 𝐶𝑖
1 + 𝑟 𝑖
𝑁
𝑖=1
=$1,004,798.75
1 + .10 4= $𝟔𝟖𝟔, 𝟐𝟗𝟏. 𝟎𝟕
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Appendix G: Dimensioned Drawings of Final Design
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