Final_Report_Humpback_Hydro

ENGR 499 Final Design Report
Offshore Hydro Energy Storage System
Submitted By:
Group 8
Shariq Codabux
Mitchell Lamoureux
David Martens
Billy Su
Faculty Supervisor:
Joshua Brinkerhoff
In association with:
Humpback Hydro
April 10th, 2015

Humpback Hydro: Offshore Hydro Energy Storage System Group 8
Final Design Report ii
Executive Summary
This report discusses the final design of Humpback Hydro’s proposed Offshore Hydro Energy
Storage System. Humpback Hydro’s system uses traditional pumped storage hydro technology
and places it in an offshore environment to utilize the ocean as a reservoir. This is
advantageous for coastal regions where land is limited but access to ocean water is plentiful.
Humpback Hydro has proposed this Capstone project with UBC, to further develop their
patented design.
The scope of this project includes developing a proof of concept design and creating CAD
models of the Humpback Hydro System. The objectives of this project include creating a
computer program, calculating the efficiency of the system, designing the gravity dam, selecting
the power generator and transformer, and completing CAD modelling. The proof of concept
design must address a number of constraints, including a design flexible to different locations,
and a solution that is scalable for future upgrades. The report further addresses these
constraints and develops specifications to meet these requirements.
This report details the work completed throughout the project, which produced the following
outcomes:
• It was determined that a 10 MW facility with 3 hours of power delivery time can achieve
70.2% efficiency and would require 220,000 ݉ଷ
of concrete.
• A MATLAB Graphical User Interface was developed which enables the user to input
required power, storage time, and low demand duration to calculate efficiency,
concrete volume, flow rates, penstock sizes, and required head.
• A power transmission set was specified, including a TMEIC turbine generator and a HPS
dry-type medium three phase transformer with an efficiency of 99.48% at full load.
• A CAD model has been created using Autodesk Inventor along with a flow animation
which illustrates the operating principle of Humpback Hydro’ system.

Final Design Report iii
Table of Contents
Executive Summary..........................................................................................................................ii
1 Introduction............................................................................................................................. 1
1.1 Purpose......................................................................................................................... 1
1.2 Overview of Project Work ............................................................................................ 1
2 Background and Motivation.................................................................................................... 2
2.1 Background and Problem ............................................................................................. 2
2.2 Objectives ..................................................................................................................... 2
2.3 Deliverables .................................................................................................................. 3
3 Design Considerations ............................................................................................................. 4
3.1 Description of the Offshore Storage System and Constraints ..................................... 4
3.2 Project Specifications and Technical Scope.................................................................. 5
4 Design Description................................................................................................................... 6
4.1 Facility Design and CAD Model..................................................................................... 6
4.1.1 Design Alternative 1.................................................................................................. 6
4.1.2 Design Alternative 2.................................................................................................. 7
4.1.3 Final Design............................................................................................................... 8
4.1.4 Design Comparison ................................................................................................. 10
4.2 Dam Design................................................................................................................. 11
4.3 Hydraulic Components ............................................................................................... 12
4.3.1 Penstock and Piping................................................................................................ 12
4.3.2 Turbine Selection .................................................................................................... 12
4.3.3 Pumping selection................................................................................................... 13
4.4 Power Transmission Selection.................................................................................... 14
4.5 Graphical User Interface Design................................................................................. 15
5 Results and Verification......................................................................................................... 17
5.1 Hydraulic Calculations ................................................................................................ 17
5.2 Dam Design Calculations ............................................................................................ 19

Final Design Report iv
5.3 Finite Element Analysis............................................................................................... 22
6 Organizational Approach....................................................................................................... 25
6.1 Overview of Organizational Approach ....................................................................... 25
6.2 Project Schedule......................................................................................................... 25
6.3 Work Distribution ....................................................................................................... 25
7 Conclusion.............................................................................................................................. 27
8 References ............................................................................................................................. 28
Appendix A: MATLAB Code........................................................................................................... 29
Appendix B: Hydraulic Analysis of System.................................................................................... 48
Appendix C: Dam Design Procedure............................................................................................. 52
Appendix D: Dam Design Sample Calculations............................................................................. 55
Appendix E: Calculation for FEA Values........................................................................................ 58
Appendix F: Description of GUI Outputs....................................................................................... 59
Appendix G: Project Schedule Gantt Chart................................................................................... 60
Appendix H: Dimensioned Drawings ............................................................................................ 61

Final Design Report v
List of Figures
Figure 3.1 - Schematic of Humpback Hydro's Offshore Hydro Storage System............................. 4
Figure 4.1 - Design Alternative 1 based on Original Schematic...................................................... 7
Figure 4.2 - Design Alternative 2..................................................................................................... 8
Figure 4.3 - Final Design.................................................................................................................. 9
Figure 4.4 - Top of the structure showing the helipad and jib crane ........................................... 10
Figure 4.5 - Dam Dimensions for 10 MW system with a Head Ratio of 2.5 ................................. 11
Figure 4.6 - Penstock and Piping Components............................................................................. 12
Figure 4.7 - Series Pumping Arrangement.................................................................................... 13
Figure 4.8 - Screenshot of the Graphical User Interface .............................................................. 16
Figure 5.1 - Offshore Hydro Energy Storage System Hydraulic Schematic .................................. 17
Figure 5.2 - Efficiency vs. Lower Turbine Head for the 10 MW Facility....................................... 18
Figure 5.3 - Forces acting on a Gravity Dam................................................................................. 20
Figure 5.4 - Von Mises Stress in Structure of a 10 MW Facility.................................................... 22
Figure 5.5 - Minimum Safety Factor for a 10 MW Facility............................................................ 23
Figure 5.6 - Deflection in the Structure of a 10 MW Facility........................................................ 23
Figure B.0.1 - Upper Turbine Analysis Schematic......................................................................... 50
Figure C.0.1 - Dam Cross-Section with dimensions ...................................................................... 52
Figure C.0.2 - Forces Acting on a Gravity Dam ............................................................................. 53

Final Design Report vi
List of Tables
Table 3.1 - Project Specifications and Scope .................................................................................. 5
Table 4.1 - Comparison of Designs ............................................................................................... 10
Table 4.2 - TMEIC Turbine Generator Specifications (CORPORATION) ........................................ 14
Table 4.3 - HPS Three Phase Voltage Distribution Transformer (Systems, 2014)........................ 15
Table 5.1 - Results of Hydraulic Calculations for the 10 MW Facility........................................... 19
Table 5.2 - Dam Design Results for a 10 MW facility at Different Head Ratios............................ 21
Table 6.1 - List of Tasks with the person(s) responsible............................................................... 26

Final Design Report vii
List of Symbols & Subscripts
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Final Design Report 1
1 Introduction
The purpose and overview of project work are discussed in this section of the report.
1.1 Purpose
The purpose of this project is to evaluate the technical feasibility, complete CAD/CFD modelling,
and proof of concept design for Humpback Hydro’s patented offshore hydro energy storage
system.
Specifically the design addresses the limitations of traditional pumped storages hydro which
uses two reservoirs, one at low elevation, and one constructed at a high elevation. These
traditional pump storage stations require specific geography, either a natural lake, or a
substantial amount of land for a man-made reservoir, and each station requires a unique
design. Humpback Hydro has patented a design which places the platforms near the shore of an
ocean. This uses the ocean as the main reservoir, eliminating the need of an on shore reservoir.
This makes it possible to implement the system in numerous locations where an ocean or large
lake is available. This is advantageous for locations where there isn’t enough land to construct a
conventional pumped storage station. Section 3.1 will further detail how the system operates.
1.2 Overview of Project Work
The project work that will be described in this report includes four main objectives that were
previously defined. These objectives include the following:
• Estimating the system efficiency and determining the amount of concrete required for a
10 MW facility
• Selecting the power transmission equipment
• Developing a computer program to aid in sizing of the facilities
• Completing CAD modelling with flow animations to show the operating principles of the
invention

2 Background and Motivation
The background and problem, objectives, and deliverables are discussed in this report.
2.1 Background and Problem
Traditional pumped storage technology uses two reservoirs, one at low elevation, and one
constructed at a high elevation. These pump storage stations require specific geography, either
a natural lake, or a substantial amount of land for a man-made reservoir, and each station
requires a unique design. Humpback Hydro has patented a design which places the platforms
near the shore of an ocean. This uses the ocean as the main reservoir, eliminating the need of
an on-shore reservoir. This makes it possible to implement the system in numerous locations
where an ocean or large lake is available. This is advantageous for locations where there isn’t
enough land to construct a conventional pumped storage station. Section 3.1 will further detail
how the system operates.
2.2 Objectives
The main objectives of this project includes creating a computer program, calculating the
efficiency, designing the gravity dam, selecting the power generator and transformer, and
completing CAD and CFD Modelling.
For the computer program objective, the group will create a computer program to capture the
operating principles of the system. This will aid with the sizing of the turbomachinery,
determining the reservoir and penstock sizes, determining the amount of concrete, and
calculating the expected efficiency.
The power transmission equipment selection will include design considerations and possible
selection for generators, which work with the turbine and the power transformer.
The CAD modelling will include a 3D model of the hydro energy storage system, and create flow
simulations to show the operating principles of the system.

2.3 Deliverables
The project deliverables include a CAD Model, a report, and a computer program.
The CAD Model will include the layout of the turbines, penstocks, pumps, and piping. A focus
will be given on making the model aesthetically pleasing for Humpback Hydro to showcase.
The report will include estimates on system efficiencies sizes of reservoirs, required concrete
volume, penstocks, turbomachinery selections, and power transmission considerations. The
report will detail the design of a 10MW facility with 3 hours of power delivery.
The computer program will query the user for expected power output and storage time, and
will output penstock sizes, expected efficiency, amount of concrete, reservoir volumes, and
flow rates. This will be provided to Humpback Hydro to help size these facilities based on
different requirements.

3 Design Considerations
The description of the Offshore Storage System, constraints, and project specifications and
technical scope are discussed in this section of the report.
3.1 Description of the Offshore Storage System and Constraints
The objective of this project is to show the proof of concept design, technical feasibility and a
CAD Model of Humpback Hydro’s patented offshore hydro storage system. Figure 3.1 below
shows a schematic of Humpback Hydro’s pumped storage system. From 1-2 the water is
released from the ocean and run through the lower turbine to create power. From 2-3 the
water is pumped to the upper reservoir, where it stored until peak electricity demand. From 3-1
the water is released through the upper turbine during peak hours, to supplement the base
electricity load.
Figure 3.1 - Schematic of Humpback Hydro's Offshore Hydro Storage System Adapted from Unpublished
PowerPoint, Humpback Hydro Inc. (Humpback Hydro, 2014)
The system will be designed to have an economic life cycle cost. This includes a 65-80 year life
and low operations and maintenance costs. The design will be flexible to different locations and
depths. The system will operate in depths ranging from 15 to 70 meters. Additionally,

Humpback Hydro is interested in developing a solution that is scalable to larger storage
capacities.
3.2 Project Specifications and Technical Scope
Table 3.1 below summarizes the scope previously outlined in Section 2.1, along with relevant
specifications for each objective. There are four main objectives to the project which include:
calculating the system efficiency and total amount of concrete required, developing a computer
program, selecting power transmission equipment, and completing a CAD model with flow
animations. The objectives were developed by the group and the faculty sponsor in response to
the first meeting with Humpback Hydro. To verify these objectives, the project definition report
was supplied to Humpback Hydro to ensure they were satisfied with these objectives. Based off
the objectives, specifications were developed to address the constraints of the project as
discussed in the Table 3.1.
Table 3.1 - Project Specifications and Scope
Objective/Requirement Specifications
Calculate Expected Efficiency & Total Amount
of Concrete Required
Estimate expected efficiency of system based
off sketches provided by Humpback Hydro
Using a head range of 15-70 meters for the
lower turbine, calculate the system efficiency
for a 10 MW facility with 3 hours of power
delivery
Analyze the gravity dam design to estimate the
amount of concrete required for the structure
Dam must be stable enough to have a factor
of safety against sliding of 1.5 and withstand
compressive stresses with a safety factor of 3
Develop a Computer Program
Create a computer program to aid with sizing
turbomachinery, reservoir sizes, penstock
sizes, and concrete amount.
User will specify desired power output and
storage time and the program will output the
sizes of penstocks, reservoirs, flow rates,
pump head, and volume of concrete
Power Generator and Transformer Selection
Select generator to work with the turbine Specify a generator based on the turbine
RPM range of 100 to 200 RPM, 1-10 MW
power output, and determine rated voltage
and frequency

Select transformer for power
transmission/distribution
Specify a transformer based on the generator
power output (10 MW), and frequency (50 or
60 Hz)
CAD Modelling
Create a 3D CAD model of the Hydro system A 3D Model of the system will be developed
using Autodesk Inventor
Create a simulation to show the operation of
the system
Simulation of invention will be completed
using Autodesk Inventor to show operating
principles
4 Design Description
This section of the report details the design description of the offshore storage system for a 10
megawatt facility with 3 hours of power delivery.
4.1 Facility Design and CAD Model
A CAD model was created in order to understand the components and structure of the system.
It is used to illustrate the system’s size, amount of concrete used, and locations of components.
As explained above, the system consists of turbines, pumps, and reservoirs. This section of the
report will focus on the CAD model of the system.
4.1.1 Design Alternative 1
Using the schematic provided by Humpback Hydro (Figure 3.1), a facility was designed
and sized, to produce 10 MW of power for 3 hours of power delivery. With the layout
provided by Humpback Hydro, a design was developed as shown in Figure 4.1 below.

Figure 4.1 - Design Alternative 1 based on Original Schematic
In this particular design, there is a dual system with two upper turbines, two lower
turbines and two pumps. From the calculations, it was found that only one upper
turbine and one lower turbine was required in order to meet the system’s conditions. In
this design the pumps can either be used simultaneously or independently, based on the
rate at which the upper reservoir must be filled.
The upper turbine and lower turbine each require a head of 20 meters for maximum
efficiency. The drawback to this design, was that the upper penstock is about 200
meters in length from the intake to the turbine. Additionally, due to the large size of the
reservoirs the design would require a significant amount of concrete.
4.1.2 Design Alternative 2
Referring back to the design alternative one (Figure 4.1), it can be seen that it was not a
very economical or efficient arrangement for the offshore hydro energy storage system.
In order to improve the efficiency, it was found that placing the upper reservoir on top
of the lower reservoir would be a more effective design. Figure 4.2 below was another
design considered, which drastically reduced the amount of concrete used. This design

makes the penstock much shorter, thus reducing the friction loss. This design uses 20
meters of head for the lower and upper turbine. Figure 4.2 below shows the
components of the system including the upper turbines (red), lower turbines (green),
and pumping system (blue)
Figure 4.2 - Design Alternative 2
As mentioned previously, the pump system is able to replenish the upper reservoir in 6
hours. In order to attain this requirement, a design of two pumps in parallel was
selected to reach the high flow rate required.
4.1.3 Final Design
The final design is similar to Design 2 shown above (Figure 4.2), however, the final
design further reduced the amount of concrete, making it even more compact. It was
determined that one turbine for each the lower, and upper reservoir was sufficient and
that two pumps in series are required. This facility still meets the operational
requirements of 10 megawatts of power out, 3 hours of power delivery, and 6 hours to
replenish the upper reservoir. The hydraulic components, and dam design for this final
design are further discussed in Section 4.2, and 4.3 of the report. Figure 4.3 below

shows the final design. A drawing with the overall dimensions of this facility can be
found in Appendix H.
Figure 4.3 - Final Design
As the upper reservoir is placed on top of the lower reservoir, a structure to support the
upper reservoir is required. Four circular pillars, with a diameter of 5 meters are used in
this design to reduce the bending, and stress on the upper reservoir. A detailed finite
element stress analysis is discussed in Section 4.4.4.
As shown in Figure 4.4 below, cranes, an access shaft, and a helipad are included to the
final design of the system. The access shaft facilitates access to every level of the
building using an industrial elevator. The overhead cranes help with the construction
and maintenance of the station. Specifically, a gantry crane is located at each machine
center including the lower and upper turbine, and the pumping station to facilitate
maintenance, while the top of the facility is equipped with a jib crane which will help to
unload components and equipment. Finally, a helipad is added to allow remote access
to the facility. The helicopter is a scale model, to visually demonstrate the size of the
offshore storage system. This can be seen in the Figure 4.4 below.

Figure 4.4 - Top of the structure showing the helipad and jib crane
The final design proves to be more efficient than the original designs, by using less system
components, and concrete than its predecessors. The final design also mitigates the need
for continual maintenance to any of the mechanical components, and gives consideration
to access as well. Overall, this is the most feasible design option.
4.1.4 Design Comparison
Each of the designs described in Sections 4.1.1, 4.1.2, and 4.1.3 had merits and
drawbacks that needed to be considered. Overall the final design, as described in
Section 4.1.3, was found to have the greatest merits, as well as the fewest drawbacks.
Table 4.1 shown below summarizes the merits and drawbacks of each design.
Table 4.1 - Comparison of Designs
Design Merits Drawbacks
1 • Follows the schematic provided
by Humpback Hydro
• Provides an output power of 10
MW
• Design is very large, would require
a large amount of concrete to
construct.
• Penstock is 200 metres from the
upper reservoir to the upper
turbine resulting in high friction
loss

2 • Reasonable size
• Provides an output of 10MW
• Short penstocks results in less
friction loss
• Insufficient support for upper
reservoir
• Differs from the schematic
provided by Humpback Hydro Inc.
• Large base of dam
Final • Least amount of concrete
required for construction
• Uses less equipment
• Provides an output of 10MW
• Short penstocks results in less
friction loss
• Differs from the schematic
provided by Humpback Hydro Inc.
4.2 Dam Design
For the 10 megawatt pumped storage hydro facility designed for Humpback Hydro, the dam
dimensions needed to enclose the system are shown below in Figure 4.5.
Figure 4.5 - Dam Dimensions for 10 MW system with a Head Ratio of 2.5
The final design utilizes C35 concrete with a Strength of 23 MN/m2, which meets the strength
requirement to counteract the forces acting on the dam. A triangular cross section provides the
necessary strength while minimizing the volume of concrete required. A height of 76.67m is
specified for a head ratio of 2.5. An angle ‘β’ of 4.5° is the minimum angle allowed, while
maintaining compressive forces in the dam. This slope produced a base dimension of 7.65m.
For the 10MW facility, this dam design required a final volume of concrete of 220,000 ݉ଷ
.

4.3 Hydraulic Components
The hydraulic components of the system include the penstock, piping, pumps, and turbines.
4.3.1 Penstock and Piping
Two penstock and one piping system are used in the design of the ocean hydro storage
system. One penstock circuit conveys water from the external reservoir (such as an
ocean) through the lower turbine, and then into the lower reservoir. The other penstock
circuit will convey water from the upper reservoir, through the upper turbine, and expel
the water back to the external reservoir. The piping system will convey fluid from the
lower reservoir to the upper reservoir. Each of these systems are highlighted in the Figure
4.6.
Figure 4.6 - Penstock and Piping Components - a) Lower Penstock b) Upper Penstock c) Piping System
Considering the sea water conditions the system will be operating in, Fibre-reinforced,
plastic penstocks should be utilized to minimize the erosion and attachment of sea debris
to the penstocks. Fibre-reinforced plastic penstocks have been utilized in traditional
seawater pumped storage stations. This is beneficial in seawater environments as marine
creatures will not adhere on the inside of the penstock (Water Power and Dam
Construction, 2000). This will allow the system to meet its low life cycle cost requirement
and have less impact on the marine life.
4.3.2 Turbine Selection
The turbines selected for use in the ocean hydro storage system are Kaplan turbines,
which will be used for both the upper and lower turbine. Kaplan turbines are a low head,

high flow turbine which are suited to the range of heads (15-70) meters required for this
project. Additionally, Kaplan turbines have a maximum power output of 300 MW (Dixon
& Hall, 2010, p. 306), while the required power ratings for the lower and upper turbine
are 2.86 and 7.14 Megawatts respectively. This allows the design to only require one
turbine per generating circuit. The turbines are connected via a shaft, and possibly a gear
box, depending on the selected rotational speed to a generator to produce electricity.
Section 4.4 will discuss the selection of the generators for the use with the turbines.
4.3.3 Pumping selection
The pumping system in this design requires 72 meters of dynamic head and a flow rate of
7.9 cubic meters per second. It was determined that two pumps, such as the SPP XF-400-
436 pumps, could be used in series (SPP Pumps, 2015). The use of pumps in series
provides the same flow rate as one pump, but doubles the amount of head that can be
achieved. Using two of the previously mentioned pumps, facilitates the required 72
meters of head and 7.9 cubic meters per second of flow rate required for the 10 MW
facility. Figure 4.7 below shows the series arrangement of the centrifugal pumps.
Figure 4.7 - Series Pumping Arrangement

4.4 Power Transmission Selection
A power generator and transformer are selected based on the turbine output of 1-10
megawatt, and a rotational speed range of 1,000 to 2,000 RPM. These parameters are used to
select equipment with specified rated voltage and frequencies, however, this can vary by
region.
The generator selection is based on the power output range of the turbine. TMEIC (Toshiba
Mitsubishi-Electric Industrial systems Corporation) produces a 4-pole turbine generator that
has the rated output of 10,000-50,000kVA. The detailed specifications of the generator are
shown in Table 4.2 below.
Table 4.2 - TMEIC Turbine Generator Specifications (CORPORATION)
Ratings
Rated Output 10,000 – 50,000 kVA
Rated Voltages 6.6kV, 11kV or 13.8kV
Frequency 50 z or 60 Hz
Poles 4
Rated Speed 1,500 min-1 or 1,800 min-1
Rated Power Factor 80% - 90% lagging
The turbine has a range between 1000-2000 RPM, and the generator has the rated speed at
1500 or 1800 RPM. It may be possible that the turbine will be directly coupled to the generator,
but may require a gearbox to match the speed of the generator. This generator also has two
frequency options, either 50 or 60 Hz, and several rated voltage options that will be convenient
to most of the power companies in the world (North America has the power transmission
frequency of 60 Hz and Europe has the frequency of 50 Hz ).
The transformer selection is made based on the generator. After research of commercially
available transformers, the dry-type medium voltage distribution transformer produced by HPS
(Hammond Power Solutions) proved to be a viable option. Using the ratings of the TMEIC

generator, the three phase model of this transformer is selected. The three phase transformer
will operate at a greater stability and efficiency, as compared to the single phase option. Table
4.3 shows the transformer efficiency for different applied loads. The input of this transformer
can be varied between 500 – 15,000 kVA, and the efficiency is 99.48% at full load.
Table 4.3 - HPS Dry-Type Medium Three Phase Voltage Distribution Transformer (Systems, 2014)
kVA 20-45 kV BIL
Efficiency (%)
46-95 kV BIL
Efficiency (%)
≥≥≥≥ 96 kV BIL
Efficiency (%)
1000 99.14 99.03 98.99
1500 99.22 99.12 99.09
2500 99.31 99.23 99.20
3000 99.34 99.26 99.24
3750 99.38 99.30 99.28
5000 99.42 99.35 99.33
7500 99.48 99.41 99.39
The generator and transformer set satisfy the design parameters of a 1-10 megawatt power
output and 1,000-2,000 RPM turbine speed. Additionally, the system can be modified based on
certain regional regulations, to make the system adaptable to a variety of locations.
4.5 Graphical User Interface Design
A computer program was developed to aid in the sizing of the Humpback Hydro system. The
computer program was designed as a graphical user interface (GUI) using MATLAB. As specified
by the requirements of the project, the user inputs include: power delivery time required,
power output, and low peak duration in order to size the system. A snapshot of the graphical
user interface is shown in Figure 4.8. There are three steps to using the GUI which include the
following.
1. The user enters the three inputs
2. The user clicks the push button labelled “calculate” to execute the program
3. The calculated values are shown, which can aid in sizing a facility

Figure 4.8 - Screenshot of the Graphical User Interface 1) user inputs 2) push button to execute program
3) Outputs to size the facility
Two of the most important values the GUI will provide the user with is, the expected system
efficiency and total amount of concrete needed to build the facility. A complete overview of all
GUI outputs are described in depth in Appendix E. The GUI typically requires the use of the
MATLAB program which may not be available to all end users. Fortunately, the GUI can be
exported into a standalone executable file using the MATLAB compiler application, so it can be
distributed to users without access to MATLAB.
The calculations that are used in the background of the GUI were adapted directly from
calculations performed, which evaluate the hydraulic operation of the system and design the
gravity dam which enclose the structure as described in detail in Appendix B and C respectively.
Appendix A also displays the MATLAB code for the GUI.
1
2
3

5 Results and Verification
The section will discuss the hydraulic calculations, dam design calculations, and finite element
analysis completed to verify the design.
5.1 Hydraulic Calculations
Hydraulic calculations were performed on the system to determine the efficiency, reservoir
sizes, head losses, required power, flow rate, required head, and penstock diameters. The
majority of the theory was adapted from “Fluid Mechanics: Fundamentals and Applications” by
Cengel and Cimbala (2006) and “Fluid Mechanics and Thermodynamics of Turbomachinery” by
Dixon and Hall (2010). In order to understand the results presented in this discussion, Figure
5.1 below visually identifies the hydraulic components.
Figure 5.1 - Offshore Hydro Energy Storage System Hydraulic Schematic
The results presented in this section were calculated for a facility with a 10 megawatt power
output, a power delivery time of three hours that replenishes the upper reservoir over six hours
during low demand. As specified in the constraints and specifications section, the range of
lower turbine heads was given as 15 – 70 meters. This is the approximate depth of water in
which the structure will be placed. The efficiency was calculated throughout this range of heads

which is defined as the energy output of the system, (energy created by the turbines) divided
by the energy input, (energy input required to pump the water between the reservoirs) as
expressed in Equation 1 below. The full hydraulic analysis is detailed in Appendix B.
ߟ௢ =
ܲ௧ܶ௦
ܲ௣ܶ௣
Equation 1
Figure 5.2 below graphs the efficiency versus lower turbine head for various head ratios. The
head ratio is the ratio between the lower turbine head and upper turbine head.
Figure 5.2 - Efficiency vs. Lower Turbine Head for the 10 MW Facility
For clarity, not all of the data was displayed on this chart. Specifically, head ratios greater than
3.5 are neglected, as they were not efficient options. Typically, each of these curves showed an
increase in efficiency until a point, where they reached a maximum efficiency, and then
decreased. The head ratios 0.5 and 2.5 produced the highest efficiencies of 70.19%, which is a
desirable performance characteristic for the energy storage system. Table 5.1 below listed the
best efficient result for each head ratio, with the parameters required to achieve the efficiency.
The 2.5 head ratio (highlighted in the table) was the selected design for the 10 megawatt
67.0%
67.5%
68.0%
68.5%
69.0%
69.5%
70.0%
70.5%
0 20 40 60 80
Efficiency(%)
Lower Turbine Head (m)
Efficiency vs. Lower Turbine Head
0.5 Head
Ratio
1.0 Head
Ratio
1.5 Head
Ratio
2.5 Head
Ratio
3.5 Head
Ratio

facility described in Section 4.
Table 5.1 - Results of Hydraulic Calculations for the 10 MW Facility
Head
Ratio
Best
Efficiency
Lower
Turbine
Head (m)
Upper
Turbine
Head (m)
Lower
Turbine
Power (MW)
Upper
Turbine
Power (MW)
Lower Turbine
Flow Rate
(࢓૜
/s)
Upper Turbine
Flow Rate
(࢓૜
/s)
0.5 70.186% 45 22.5 6.67 3.33 16.33 16.34
1.0 70.195% 35 35 5.0 5.0 15.76 15.58
1.5 70.189% 25 37.5 4.0 6.0 17.62 17.37
2.0 70.177% 20 40 3.33 6.67 18.35 18.06
2.5 70.195% 20 50 2.86 7.14 15.76 15.47
3.0 70.177% 15 45 2.5 7.5 18.35 18.35
3.5 70.186% 15 52.5 2.22 7.78 16.34 16.34
4.0 70.173% 15 60 2 8 14.73 14.73
4.5 70.139% 15 67.5 1.82 8.18 13.41 13.41
Head
Ratio
Lower
Penstock
Diameter (m)
Upper
Penstock
Diameter (m)
Lower
Reservoir
Volume (࢓૜
)
Upper
Reservoir
Volume (࢓૜
)
Pump
Flow Rate
(࢓૜
/s)
Total
Pump
Head (m)
Pump
Power
(MW)
0.5 1.65 1.65 176432 176432 8.17 69.25 7.1239
1.0 1.61 1.61 168254 168254 7.88 71.78 7.1231
1.5 1.71 1.70 190325 187629 8.81 64.20 7.1236
2.0 1.75 1.73 198169 195075 9.17 61.67 7.1248
2.5 1.62 1.60 167098 167098 7.88 71.78 7.1231
3.0 1.75 1.73 198169 194732 9.17 61.67 7.1248
3.5 1.65 1.63 176432 173048 8.17 69.25 7.1239
4.0 1.56 1.55 159037 155710 7.36 76.84 7.1252
4.5 1.50 1.47 144801 141531 6.70 84.44 7.1287
It can be seen from the table, that the 2.5 and 1.0 head ratio both achieved the same efficiency,
however, a head ratio of 2.5 requires smaller reservoir, which can reduce the capital cost to
construct the system. This selection is further justified using the dam design calculations
outlined in Section 5.2 of the report.
5.2 Dam Design Calculations
The objective of the dam design for the offshore ocean hydro storage system is to estimate the
volume of concrete required for the dam structure, while maintaining an ample safety factor
against sliding, and in compression. There are three major forces acting on the dam. These

include the hydrostatic load (W), dead lead (G), and uplift load (U) as shown in Figure 5.3.
Figure 5.3 - Forces acting on a Gravity Dam
The hydrostatic load (W) is the static load exerted on the dam by the weight of the water, and is
assumed to be linearly distributed along the vertical surface of the dam. The dead load (G) is
the vertical force acting on the dam due to the weight of the concrete. The Uplift load (U) is
produced by the hydrostatic pressure of the ocean water, that seeps through the pores and
cracks of the foundation and base of the dam, and produces an upward force along the base of
the dam.
The calculated loads G, W, U acting at a distance ‘c’ (Figure 4.5) on the dam, produce contact
stresses on the dam on the upstream side 1 (ߪଵ), and downstream side 2 (ߪଶ). These stresses
are calculated using the following stress equation.
ߪீି௎ାௐ =
‫ܩ‬ − ܷ
‫ܤ‬
ቌ1 ±
6(ܿ −
஻
଺
)
‫ܤ‬
ቍ
Contact stresses must maintain compressive values at all times in the dam structure, as tensile
stresses in concrete are undesirable. Utilizing the upstream stress (ߪଵ), a safety factor in
compression greater than 3 is obtained using the following equation.

ܵ. ‫ܨ‬௖௢௠௣௥௘௦௦௜௢௡ =
ܴ௖
ߪଵ
> 3.0
To ensure the dam will remain fixed on the ocean floor, a safety factor against sliding greater
than 1.5 is utilized through the following equation.
ܵ. ‫ܨ‬௦௟௜ௗ௜௡௚ =
‫ܩ‬ − ܷ
ܹ − ‫ܥ‬
‫ߔ݊ܽݐ‬ > 1.5
A complete overview of the dam design is provided in Appendix D. The dam design results for a
10 MW facility at various head ratios is shown in Table 5.2 below.
Table 5.2 - Dam Design Results for a 10 MW facility at Different Head Ratios
Head
Ratio
Best
Efficiency
Height
of Dam
H (m)
Angle of
Dam β
(deg)
Contact Stress
Upstream
(MN/࢓૜
) ࣌૚
Contact Stress
Downstream
(MN/࢓૜
) ࣌૛
Safety
Factor
S.F.
Sliding
Safety
Factor S.F.
Compression
Volume of
Concrete
Vc (࢓૜
)
1 70.195% 81.67 10.7 1.5992 0.0084 2.9188 14.3822 363609
1.5 70.189% 70.83 7.6 1.4405 0.0077 3.6008 15.9665 266574
2 70.177% 66.67 5.7 1.375 0.0236 4.287 16.7267 221932
2.5 70.195% 76.67 4.5 1.6283 0.0103 4.397 14.125 221327
3 70.177% 65 3.5 1.3728 0.0361 5.5172 16.7537 180533
3.5 70.186% 72.5 2.9 1.5566 0.0324 5.5774 14.7761 181749
4.0 70.173% 80 2.5 1.6837 0.0853 5.8132 13.6607 185277
4.5 70.139% 87.5 2.1 1.9189 0.03 5.7597 11.986 184895
It can be seen from the table that a head ratio of 2.5 produces the highest efficiency at 70.2
percent, while requiring only 221,327 ݉ଷ
of concrete. A similar efficiency is obtained through a
head ratio of 1, but this design was not pursued as it requires a significant amount of concrete
to construct. Efficiency and head ratio values are further discussed in Table 5.1. A positive value
for contact stresses (ߪଵ, ߪଶ) signifies compressive stresses in the dam. It is important to
maintain compressive contact stresses at all times, as tensile stresses in concrete are
undesirable. Angle ‘β’ is the minimum angle possible, while maintaining positive (compressive)
values for contact stresses. A small value for ‘β’, decreases the cross-sectional area, ultimately
decreasing the volume of concrete required in the dam.

5.3 Finite Element Analysis
To verify the structural integrity of the final model, a finite element analysis (FEA) was
completed using the Autodesk Inventor Stress Simulation software. A FEA is a computerized
method of predicting how real-world forces act on a structure, and whether the structure will
break, wear-out, or work the way it is designed.
The FEA simulated the equivalent pressure exerted on the structure by the fluid when the
upper reservoir is full. The pressure (P) is obtained by utilizing the required volume (V) of water
stored in the upper reservoir. The volume is converted to an equivalent force, which is equally
distributed along the bottom of the upper reservoir as shown in Equation 30 in Appendix E. For
the design of a 10 MW facility, with a head ratio or 2.5, a volume of water in the upper
reservoir of 170,000 ݉ଷ
is required. This volume produces a distributed pressure of 0.4 MPa
along the surface of the upper reservoir which produced the following FEA results.
Figure 5.4 - Von Mises Stress in Structure of a 10 MW Facility Using a 0.4 MPa Stress Distribution
The Von Mises Stress values showed a stress concentration of 2.55 MPa at the Upper Reservoir
supports, which is acceptable compared to a compressive strength of concrete of 23 MPa. The
remaining structure produced no significant stress concentrations.

Figure 5.5 - Minimum Safety Factor for a 10 MW Facility Using a 0.4 MPa Stress Distribution
The Safety factor results produced a minimum safety factor of 10 at the reservoir support,
which is sufficient, as required safety factor of 3 in compression must be maintained. The
remaining structure upheld a safety factor of 15.
Figure 5.6 - Deflection in the Structure of a 10 MW Facility Using a 0.4 MPa Stress Distribution

The deflection results showed a maximum deflection of 2.672 millimeter acting at the center of
the upper reservoir. This deflection is within the allowable limit for concrete over the given area
for practical concrete design. A deflection of 1.6 millimeter was obtained at the crest of the
dam, which is acceptable as this section has no other external forces acting on it. The remaining
structure produced no significant deflection.

6 Organizational Approach
The organization approach is described in this section, including an overview of the approach,
project schedule, and work distribution.
6.1 Overview of Organizational Approach
The organizational approach of the project involved continual collaboration between the team
members, scheduling time to meet the milestones required by the course, continually
evaluating the team’s progress, and by distributing the work load based on each individual
member’s strengths and interests.
The team continually collaborated on the project by having weekly meetings. During these
weekly meetings topics concerning upcoming milestones, design specifications, and design
ideas were discussed. During these meetings tasks were divided among the team members so
that all project milestones could be reached. These meetings also allowed for communication
between parts of the project where team members had design considerations which affected
other aspect of the project. The majority of the organization of the project occurred in these
meetings and allowed the group to complete the project on time.
6.2 Project Schedule
The project schedule involved three main phases including; project definition, conceptual
design, and final design. Each of these phases were broken down into a series of sub-tasks
which needed to be accomplished before the end of the project phase, where the group
typically wrote a report and gave a presentation on what the group had completed. A Gantt
chart that provides the entire project schedule, and the time period in which the tasks were
completed can be found in Appendix F.
6.3 Work Distribution
The work was distributed between the group based on the member’s interest and expertise. As
the group contained one electrical student and three mechanical students, the electrical scope
was completed by the electrical student while the mechanical scope of the project, which was

large, was completed by the three mechanical students and divided based upon each member’s
strengths and interests. Table 6.1 below list all the tasks completed in the project and the group
member(s) which were responsible for the task.
Table 6.1 - List of Tasks with the person(s) responsible
Task Group Member(s) Responsible
Project Definition Tasks All
Creating Project Definition Presentation All
Creating Project Definition Report All
Project Definition Presentation All
Project Definition Report All
Power Transmission Selection Billy Su
Conceptual CAD Modelling Shariq Codabux
Conceptual Design Presentation All
Conceptual Design Report All
Efficiency and Hydraulic Analysis Mitchell Lamoureux
Dam Design David Martens
Graphical User Interface Billy Su
Final CAD Model Shariq Codabux
Create Flow Animation David Martens
Create Final Design Presentation All
Submit Poster All
Poster Presentation All
Create Final Report All

7 Conclusion
The objective of the offshore hydro energy storage system project is, to complete a proof of
concept design, and outline the operating principles of the system. Humpback Hydro is
interested in a design which is scalable, with low life cycle, operation, and maintenance costs.
The project was completed by fulfilling the four objectives/deliverables set out at the beginning
of the project, which include:
• Providing a 10 megawatt offshore pump storage hydro facility, which achieved a
maximum overall efficiency of 70.2%, and would require 220,000 cubic meters of
concrete to construct.
• Selecting the power transmission equipment required to operate this facility including a
4-pole TMEIC turbine generator, with a rated output of 10,000-50,000 kVA, and a HPS
dry-type medium three phase voltage distribution transformer, with an efficiency of
99.48%.
• Developing a user-friendly, graphical user interface (GUI), to assist the user with sizing
system components of the pumped storage hydro facility, by prompting the user for the
required power output, storage time, and low demand time. For the scalable facility, the
GUI outputs include penstock diameters, turbine heads, flow rates, pump head, pump
flow rate, reservoir volumes, system efficiency and the total volume of concrete
required.
• Creating a CAD model that provides the layout of all system components for the 10
megawatt facility, along with a flow simulation utilizing the CAD model, to show the
operating principles of the system in the offshore environment.

8 References
Cengel, Y. M. (2006). Fluid Mechanics: Fundamentals and Applications. New York: McGraw Hill.
CORPORATION, T. M. (n.d.). http://www.tmeic.com/Repository/Others/4P%20TG.pdf.
Dixon, S. L., & Hall, C. A. (2010). Fluid Mechanics and Thermodynamics of Turbomachinery.
Oxford: Elsevier.
Herzog, M. A. (1999). Practical dam analysis. London: Thomas Telford Publishing.
Humpback Hydro. (2014). Humpback Hydro Inc, Grid Scale Energy Storage Technology.
Vancouver, BC, Canada.
Matysko, R. (2014, December 15). GrabCAD Kaplan turbine. Retrieved January 2, 2015, from
GrabCAD: https://grabcad.com/library/kaplan-turbine-2
Salam. (2014, June 05). GrabCAD Centrifugal Pump. Retrieved January 2, 2015, from GrabCAD:
https://grabcad.com/library/centrifugal-pump-12
SPP Pumps. (2015, April 7). SPP Pumps Autoprime: XF-400-436 Performance Curve. Reading,
Berkshire, United Kingdom. Retrieved April 7, 2015, from
http://www.spppumps.com/linkservid/620C65DF-9EFF-4445-
AECF5EE220E96331/showMeta/0/
Systems, H. P. (2014). Dry-Type Medium Voltage Distribution [Power] Transformer . Hammond
Power Solutions Inc. .
Water Power and Dam Construction. (2000, August 14). Water Power and Dam Construction.
Retrieved from Japanese pumped storage embraces the ocean waves:
http://www.waterpowermagazine.com/features/featurejapanese-pumped-storage-
embraces-the-ocean-waves/

Appendix A: MATLAB Code
function varargout = GUI_Mar_7(varargin)
% GUI_MAR_7 MATLAB code for GUI_Mar_7.fig
% GUI_MAR_7, by itself, creates a new GUI_MAR_7 or raises the existing
% singleton*.
%
% H = GUI_MAR_7 returns the handle to a new GUI_MAR_7 or the handle to
% the existing singleton*.
%
% GUI_MAR_7('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in GUI_MAR_7.M with the given input arguments.
%
% GUI_MAR_7('Property','Value',...) creates a new GUI_MAR_7 or raises
the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before GUI_Mar_7_OpeningFcn gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to GUI_Mar_7_OpeningFcn via varargin.
%
% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one
% instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help GUI_Mar_7
% Last Modified by GUIDE v2.5 10-Mar-2015 23:40:33
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @GUI_Mar_7_OpeningFcn, ...
'gui_OutputFcn', @GUI_Mar_7_OutputFcn, ...
'gui_LayoutFcn', [] , ...
'gui_Callback', []);
if nargin && ischar(varargin{1})
gui_State.gui_Callback = str2func(varargin{1});
end
if nargout
[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT
% --- Executes just before GUI_Mar_7 is made visible.
function GUI_Mar_7_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)

% varargin command line arguments to GUI_Mar_7 (see VARARGIN)
% Choose default command line output for GUI_Mar_7
handles.output = hObject;
% Update handles structure
guidata(hObject, handles);
% UIWAIT makes GUI_Mar_7 wait for user response (see UIRESUME)
% uiwait(handles.figure1);
bg = imread('bg-2.jpg');
axes(handles.axes2);
imshow(bg)
% --- Outputs from this function are returned to the command line.
function varargout = GUI_Mar_7_OutputFcn(hObject, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% Get default command line output from handles structure
varargout{1} = handles.output;
function edit1_Callback(hObject, eventdata, handles)
% hObject handle to edit1 (see GCBO)
% Hints: get(hObject,'String') returns contents of edit1 as text
% str2double(get(hObject,'String')) returns contents of edit1 as a
double
% --- Executes during object creation, after setting all properties.
function edit1_CreateFcn(hObject, eventdata, handles)
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'),
get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end

double
end
double
end
% --- Executes on button press in pushbutton1.
function pushbutton1_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton1 (see GCBO)
p1 = str2num(get(handles.edit1,'String'));

P=p2*10^6; % Desired Power MW (This Will be a User Input)
ts=p1; %Stored Energy Duration in Hours (This Will be a User Input)
tp=p3; % Pumping/Low Demand Time (This Will Be User Input)
%% CONSTANT VALUES
vp=5; % velocity in piping
ro=1027; % Sea Water Desity in kg/m^3
etat=0.93; % Efficiency of Turbine (Kaplan Reaches as High as 94%)
etap=0.80; % Efficiency of Pump
etag=0.99; % Efficiency of Generator (Guess is 99%)
kv=1.0*10^-6; %Kinematic Viscosity of Sea Water
g=9.81; % Acceleration due to gravity m/s^2
eps=0.015; % Roughness Factor for steel varies from 0.015 to 0.045 depending
on type
Hi=3; %Head previous to inlet is equal to 3 meters Can vary this later to see
results
vut=sqrt(2*g*Hi); % Velocity in Penstock of Upper Turbine
vlt=sqrt(2*g*Hi); % Velocity in Penstock of Lower Turbine
gammaw=0.01007; % Specfic Gravity of Water for dam analysis
gamma=1.025; % Specific Gravity of Water
gammac=0.024; %Specific Gravity of Concrete
Rc=23; % Strength of Concrete 30 MPa
%% THIS SECION TAKES INPUTS AND MAKES THEM SCRIPT FRIENDLY
%% DECLARING CALCULATION VARIABLES AND THEIR SIZES
Hlt=15:5:70; % Head range of lower turbine heads
Hlt=Hlt'; % Transposing Head To Be a Column

hrat=0.5:0.5:4.5; % Head Ratio which is upper turbine head dived by lower
turbine head
hrat=hrat'; % Transposing head ratio into column
Hut=zeros(length(Hlt),length(hrat)); % Upper Turbine Head
Hutnet=zeros(length(Hlt),length(hrat)); % Net Upper Turbine Head
Hltnet=zeros(length(Hlt),length(hrat)); % Net Lower Turbine Head
Hlut=zeros(length(Hlt),length(hrat)); % Upper Turbine Head Loss
Hllt=zeros(length(Hlt),length(hrat)); % Lower Turbine Head Loss (m)
hlp=zeros(length(Hlt),length(hrat)); % Head Loss In Pumping (m)
Pp=zeros(length(Hlt),length(hrat)); % Pump Power (Watts)
TPE=zeros(length(Hlt),length(hrat)); % Total Pump Energy (MW-hr)
TUTE=zeros(length(Hlt),length(hrat)); % Total Upper Turbine Energy (MW-hr)
TLTE=zeros(length(Hlt),length(hrat)); % Total Lower Turbine Energy (MW-hr)
TTE=zeros(length(Hlt),length(hrat)); % Total Turbine Energy (AKA Total Output
Energy) (MW-hr)
erat=zeros(length(Hlt),length(hrat)); % Energy Ratio (AKA Efficiency)
Qut=zeros(length(Hlt),length(hrat)); % Upper Turbine Flow Rate (m^3/s)
Qlt=zeros(length(Hlt),length(hrat)); % Lower Turbine Flow Rate (m^3/s)
Qp=zeros(length(Hlt),length(hrat)); % Flow Rate in Pumping System (m^3/s)
dut=ones(length(Hlt),length(hrat)); % Upper Penstock Diameter
dlt=zeros(length(Hlt),length(hrat)); % Lower Penstock Diameter
dp=zeros(length(Hlt),length(hrat)); % Pipe Diameter
Reut=zeros(length(Hlt),length(hrat)); % Reynolds Number in Upper Penstock
Relt=zeros(length(Hlt),length(hrat)); % Reynolds Number in Lower Penstock
Rep=zeros(length(Hlt),length(hrat)); % Reynold Number in Pipe
put=zeros(length(Hlt),length(hrat)); % Upper Turbine Inlet Pressure
plt=zeros(length(Hlt),length(hrat)); % Lower Turbine Inlet Pressure

Hlltit=zeros(length(Hlt),length(hrat)); % Head Loss Iteration for Lower
Turbine
Hlutit=zeros(length(Hlt),length(hrat)); % Head Loss Iteration for Upper
Turbine
frut=0.00011*ones(length(Hlt),length(hrat)); %Upper Turbine Friction Factor
Initialized
frlt=0.00011*ones(length(Hlt),length(hrat)); %Lower Turbine Friction Factor
Initialized
frp=0.00011*ones(length(Hlt),length(hrat)); %Piping Friction Factor
Initialized
del=0.0001; % Iteration size
deldut=0.1; % Iteration size for Penstock
delb=0.1; % Iteration size for Upper Reservoir Height
difut=ones(length(Hlt),length(hrat)); % Upper Turbine Iteration Difference
diflt=ones(length(Hlt),length(hrat)); % Lower Turbine Iteration Difference
Vut=zeros(length(Hlt),length(hrat)); % Upper Reservoir Volume
Vlt=zeros(length(Hlt),length(hrat)); % Lower Reservoir Volume
heightlt=zeros(length(Hlt),length(hrat)); % Height of the Lower Reservoir
Alr=zeros(length(Hlt),length(hrat)); % Lower Reservoir Area
dimut=zeros(length(Hlt),length(hrat)); % Dimensions of the Upper Reservoir
dimlt=zeros(length(Hlt),length(hrat)); % Dimension of the Lower Reservoir
Ar=zeros(length(Hlt),length(hrat)); % Upper Reservoir Area
Ap=zeros(length(Hlt),length(hrat)); % Pump Pipe Area
Zp=zeros(length(Hlt),length(hrat)); % Pumping Elevation Distance
Hp=zeros(length(Hlt),length(hrat)); % Total Pump Head Required
w=zeros(length(Hlt),length(hrat)); % Dead Load in Dame
Vutc=zeros(length(Hlt),length(hrat)); % Volume of Concrete
beta=zeros(length(Hlt),length(hrat)); % Slope of Dam
DH=zeros(length(Hlt),length(hrat)); % Height of the Dam

B=zeros(length(Hlt),length(hrat)); % Base Length of Dam
G=zeros(length(Hlt),length(hrat)); % Dead Load Acting on Dam
W=zeros(length(Hlt),length(hrat)); % Hydrostatic Load
U=zeros(length(Hlt),length(hrat)); % Uplift Load
c=zeros(length(Hlt),length(hrat)); % Distance of Resultant Force
sigma1=zeros(length(Hlt),length(hrat)); % Contact Stress 1
sigma2=zeros(length(Hlt),length(hrat)); % Contract Stress 2
C=zeros(length(Hlt),length(hrat)); % Adhesion Coefficient
sfs=zeros(length(Hlt),length(hrat)); % Safety Factor of Sliding
sfc=zeros(length(Hlt),length(hrat)); % Compressive Safety Factor
Plt=zeros(length(Hlt),length(hrat)); % Lower Turbine Power
Put=zeros(length(Hlt),length(hrat)); % Upper Turbine Power
ESU=zeros(length(Hlt),length(hrat)); % Energy Produced
TC=zeros(length(Hlt),length(hrat)); % Total Amount of Concrete
smallh=zeros(length(Hlt),length(hrat)); % The height of Water
for j=1:length(hrat)
for i=1:length(Hlt);
Hut(i,j)=hrat(j,1)*Hlt(i,1); % Calculating the Upper Turbine Head
Plt(i,j)=P/(1+hrat(j,1)); % Calculating Lower Power Required
Put(i,j)=P-Plt(i,j); % Calculation Upper Power Required
ESU(i,j)=(Put(i,j)*ts)/(10^6); % Energy Output
Hb(i,j)=Hut(i,j); % Base Head
end
end
for j=1:length(hrat)
for i=1:length(Hlt);

while abs(diflt(i,j)) > 0.001
Hllt(i,j)=Hlltit(i,j); %Head Loss Iteration for Lower Turbine
Hltnet(i,j)=Hlt(i,1)-Hllt(i,j); % Net Head in Lower Turbine
Qlt(i,j)=Plt(i,j)/(etat*etag*ro*g*Hltnet(i,j)); % Flow rate
through a turbine to generate specified power
dlt(i,j)=sqrt((4*Qlt(i,j))/(pi*vlt)); % Diameter of Penstock in
meters to produce desired flow rate
Relt(i,j)=(vlt*dlt(i,j))/kv; % Calculation of Reynolds Number
plt(i,j)=gamma*(Hltnet(i,j)-(vlt^2/(2*g))); % Pressure at Turbine
Inlet
while 1/sqrt(frlt(i,j)) > -
2.0*log((eps/dlt(i,j))/3.7+2.51/(Relt(i,j)*sqrt(frlt(i,j))))
frlt(i,j)=frlt(i,j)+del; % This while loop iteratively solves
for the friction factor
end
Hlltit(i,j)=frlt(i,j)*((1.75*Hlt(i,1))/dlt(i,j))*((vlt^2)/(2*g));
% Head Loss Calculation
diflt(i,j)=Hllt(i,j)-Hlltit(i,j); % Difference between Iterations
for While Loop
end
Vlt(i,j)=Qlt(i,j)*ts*3600; % Volume of Resevoir in m^3
heightlt(i,j)=(1/3)*(Hlt(i,1)); % Height of Lower Resevoir
Alr(i,j)=Vlt(i,j)/heightlt(i,j); % Lower Reservoir Area
dimlt(i,j)=sqrt(Alr(i,j)); % Square Dimensions of the Reservoir
TLTE(i,j)=(Plt(i,j)*ts)/1000000; % Total Lower Turbine Energy Produced in
W-hr
% Pumping Calculations
Zp(i,j)=Hlt(i,1)+Hut(i,j); % Elevation that must be pumped
Qp(i,j)=Vlt(i,j)/(tp*3600); % The required Pump Flow Rate
dp(i,j)=sqrt((4*Qp(i,j))/(pi*vp)); % Diameter of the Piping

Rep(i,j)=(vp*1.25*Zp(i,j))/kv; % Calculation of Reynolds Number
while 1/sqrt(frp(i,j)) > -
2.0*log((eps/dp(i,j))/3.7+2.51/(Rep(i,j)*sqrt(frp(i,j))))
frp(i,j)=frp(i,j)+del; % This while loop iteratively solves for
the friction factor
end
hlp(i,j)=frp(i,j)*((1.1*Zp(i,j))/dp(i,j))*((vp^2)/(2*g)); % Major
Head Losses in the pumping system
Hp(i,j)=Zp(i,j)+hlp(i,j)+(vp^2)/(2*g); % Total Pump Head Required
Pp(i,j)=(Qp(i,j)*Hp(i,j)*g*ro)/etap; % Pump Power Required
TPE(i,j)=(Pp(i,j)*tp)/10^6; % Total Energy to Pump
while abs(difut(i,j)) > 0.001
Hlut(i,j)=Hlutit(i,j); %Head Loss Iteration
Hutnet(i,j)=Hut(i,j)-Hlut(i,j); % Net Head Lower Turbine
Qut(i,j)=Put(i,j)/(etat*etag*ro*g*Hutnet(i,j)); % Flow rate
through a turbine to generate specified power
dut(i,j)=sqrt((4*Qut(i,j))/(pi*vlt)); % Diameter of Penstock in
meters to produce desired flow rate
Reut(i,j)=(vlt*dlt(i,j))/kv; % Calculation of Reynolds Number
put(i,j)=gamma*(Hutnet(i,j)-(vlt^2/(2*g))); % Pressure at Turbine
Inlet
while 1/sqrt(frut(i,j)) > -
2.0*log((eps/dut(i,j))/3.7+2.51/(Reut(i,j)*sqrt(frut(i,j))))
frut(i,j)=frut(i,j)+del; % This while loop iteratively solves
for the friction factor
end
Hlutit(i,j)=frut(i,j)*((1.75*Hut(i,1))/dut(i,j))*((vlt^2)/(2*g));
% Head Loss Calculation
difut(i,j)=Hlut(i,j)-Hlutit(i,j); % Difference between Iterations
for While Loop
end

Vut(i,j)=Qut(i,j)*ts*3600; % Upper Turbine Volume
TUTE(i,j)=(Put(i,j)*ts)/1000000; % Total Lower Turbine Energy Produced in
W-hr
erat(i,j)=(TLTE(i,j)+TUTE(i,j))/TPE(i,j);
while sfs(i,j) < 1.5 || sfc(i,j) < 3 || sigma1(i,j) < 0 || sigma2(i,j) <
0 % While Loop increases the angle until all three design conditions are met
beta(i,j)=beta(i,j)+0.1; % Angle Increase Iteration
DH(i,j)=Hlt(i,1)+heightlt(i,j)+10; % Dam Height
smallh(i,j)=DH(i,j)-heightlt(i,j)-10; % Dam Water Level
B(i,j)=1+DH(i,j)*tan(beta(i,j)*(pi/180)); % Dam Base Length
G(i,j)=(gammac*(B(i,j)*DH(i,j)))/2; % Calculating Dam Dead Load
W(i,j)=gammaw*(smallh(i,j)^2/2); % Calculating Horizontal Hydrostatic
Load
U(i,j)=gammaw*((smallh(i,j)*B(i,j))/2); % Calculating Uplift Load
c(i,j)=(smallh(i,j)/3)*(W(i,j)/(G(i,j)-U(i,j))); % The Acting
Distance of Resulting Force
sigma1(i,j)=((G(i,j)-U(i,j))/B(i,j))*(1+(6*(c(i,j)-
B(i,j)/6))/B(i,j)); % Resulting Contact Stress
sigma2(i,j)=((G(i,j)-U(i,j))/B(i,j))*(1-(6*(c(i,j)-
B(i,j)/6))/B(i,j)); % Resulting Contact Stress
C(i,j)=0.1*B(i,j); % Coefficient of Adhesion
sfs(i,j)=(G(i,j)-U(i,j))/(W(i,j)-C(i,j)); % Calculation of Safety
Factor of Sliding
sfc(i,j)=Rc/sigma1(i,j); % Calculation of Compressive Safety Factor
end
TC(i,j)=(DH(i,j)*1+(DH(i,j)*B(i,j)/2))*4*dimlt(i,j); % Total Concrete
Required for the system
end
end

%% GUI OUTPUTS
[x,y]=find(erat==max(erat(:)));
if length(x)>1
x = x(1);
end
if length(y)>1
y = y(1);
end
Hltout=Hlt(x,1); % Lower Turbine Head Output (m)
Qltout=Qlt(x,y); % Lower Flow Rate Output (m^3/s)
Vltout=Vlt(x,y); % Lower Reservoir Volume (m^3)
Pltout=Plt(x,y); % Lower Turbine Power Output (MW)
dltout=dlt(x,y); % Lower Penstock Diameter (m)
Hutout=Hut(x,y); % Upper Turbine Head Output (m)
Qutout=Qut(x,y); % Upper? Flow Rate Output (m^3/s)
Vutout=Vut(x,y); % Upper? Reservoir Volume (m^3)
Putout=Put(x,y); % Upper? Turbine Power Output (MW)
dutout=dut(x,y); % Upper? Penstock Diameter (m)
Hpout=Hp(x,y); % Total Pump Head Output (m)
Ppout=Pp(x,y)/10^6; % Total Pump Power Output (MW)
Qpout=Qp(x,y); % Pump Flow Rate Output (m^3/s)
TCout=TC(x,y); % Total Concrete Output m^3
efficiency=erat(x,y); % System Efficiency (Total Energy Out/Total Energy
Consumed)
set(handles.edit4,'String',Hltout)
set(handles.edit12,'String',Qltout)
set(handles.edit13,'String',Vltout)
set(handles.edit14,'String',Pltout)
set(handles.edit18,'String',dltout)
set(handles.edit8,'String',Hutout)
set(handles.edit9,'String',Qutout)
set(handles.edit10,'String',Vutout)
set(handles.edit11,'String',Putout)

set(handles.edit19,'String',dutout)
set(handles.edit16,'String',Hpout)
set(handles.edit20,'String',Ppout)
set(handles.edit17,'String',TCout)
set(handles.edit21,'String',efficiency)
set(handles.edit15,'String',Qpout)
set(handles.pushbutton1,'String','Calculate');
double
end
double

end
double
end
double
end

double
end
double
end

double
end
double
end
double

end
double
end
double

end

Appendix B: Hydraulic Analysis of System
The analysis of the system is based on the power generated by a turbine and power consumed
by a pump as shown in Equation 2 and Equation 3 respectively.
ܲ = ߟߩ݃ܳ‫ܪ‬௡௘௧ Equation 2
ܲ =
ߩ݃ܳ‫ܪ‬௡௘௧
ߟ
Equation 3
It is possible to have different heads for the lower or upper turbine and an equal flow rate is
desired so water can be pumped during low peak time to the upper reservoir, then on the next
cycle the lower reservoir can be completely refilled. All terms of the power equation are
constant with the exception of the head; the power that each turbine will generate is expressed
in terms of head ratio as shown in Equation 4 and Equation 5.
ܲ௟௧ =
ܲ
1 + ℎ௥௔௧
Equation 4
ܲ௨௧ = ܲ − ܲ௟௧ Equation 5
Analyzing the power through the lower turbine is completed by solving the power equation to
specify the required flow. Re-arranging Equation 2 to solve for the flow rate is shown in
Equation 6.
ܳ௟௧ =
ܲ௟௧
ߟߩ݃‫ܪ‬௟௧
Equation 6
Using the flow rate, it is possible to determine the volume of water which the reservoir must
hold by multiplying the volume flow rate by the specified storage time (Equation 7).
ܸ௟௧ = ܳ௟௧ × ܶ௦ Equation 7
The velocity in the penstock can be expressed as a function of the height from the water level
to the inlet of the penstock as shown in Equation 8.
‫ݒ‬ = ඥ2݃‫ܪ‬௜ Equation 8
The penstock diameter required to deliver this flow rate is calculated by relating the flow rate,
velocity, and area of pipe. This is shown in Equation 9.

‫ܦ‬ = ඨ
4ܳ
ߨ‫ݒ‬
Equation 9
To truly capture the losses through the system, the major head loss in the penstock must be
considered. To calculate the head loss, the friction factor is calculated using the Colebrook
Equation shown in Equation 10. This equation cannot be solved directly and is instead
iteratively solved in MATLAB.
1
ඥ݂
= −2݈‫݃݋‬ଵ଴(
ఢ
஽
3.7
+
2.51
ܴ݁ඥ݂
)
Equation
10
To determine major the head loss, the Darcy-Weisbach equation is used as shown in Equation
11. The length is assumed to be 1.75 times that of the head. This would allow for a 55 degree
sloped pipe from the intake to the turbine. This was a necessary assumption to make at the
time of calculation, however needs to be determined further. Once a model is completed the
actual lengths will be checked against the physical model to determine the true length.
ℎ௟ = ݂
‫ܮ‬
‫ܦ‬
‫ݒ‬ଶ
2݃
Equation 11
The net head is calculated by subtracting the losses from the total head as shown in Equation
12.
‫ܪ‬௡௘௧ = ‫ܪ‬௟௧ − ℎ௟ Equation 12
The previous set of equations would not be able to fully produce the required power, as the
initial flow rate calculation does not take into effect the effects of head loss. By implementing a
simple while loop, these equations can be solved again, using the net head until the change in
head losses between iterations is negligible. In order to accurately perform these iterations, the
calculations were implemented into a MATLAB code which is available in Appendix A.
The upper turbine requires a different analysis. When analyzing the upper turbine the head
cannot be considered constant. The head decreases as the upper reservoir is drained. Figure
B.0.1 below shows the schematic used in this analysis.

Figure B.0.1 - Upper Turbine Analysis Schematic
The head in the reservoir will change as a function of time. Assuming the reservoir starts
completely full e.g. ‫)0(ݕ‬ = ‫ܪ‬௨௧ then the head level as a function of time, flow rate, and
reservoir area can be expressed as Equation 13.
‫)ݐ(ݕ‬ = ‫ܪ‬௨௧ −
ܳ௨௧
‫ܣ‬௨௥
‫ݐ‬ Equation 13
The flow rate can be expressed as function of velocity and pipe diameter as shown in Equation
14.
ܳ௨௧(‫)ݐ‬ =
ߨ
4
‫ܦ‬௨௧
ଶ
‫ݒ‬௨௧(‫)ݐ‬
Equation 14
The velocity can be expressed as function of the head level and bottom of the reservoir as
shown in Equation 15.
‫ݒ‬௨௧(‫)ݐ‬ = ඥ2݃(‫)ݐ(ݕ‬ − ‫ܪ‬௕)
Equation 15
Combining Equation 13, Equation 14, and Equation 15 and solving a quadratic equation (and
rejecting the positive solution) the head level can be expressed in the final form as shown in
Equation 16.
‫)ݐ(ݕ‬ = ‫ܪ‬௨௧ + ݃ ቎
గ஽ೠ೟
మ
ସ
‫ܣ‬௨௥
‫ݐ‬቏
ଶ
−
గ஽ೠ೟
మ
ସ
‫ܣ‬௨௥
ඩ݃(‫ܪ‬௨௧ − ‫ܪ‬௕ + ݃ ቎
గ஽ೠ೟
మ
ସ
‫ܣ‬௨௥
‫ݐ‬቏
ଶ
)
Equation 16

Using this, along with the Colebrook Equation (Equation 10) and the Darcy-Weisbach Equation,
(Equation 11) the net head can be calculated for each point in time, and then, using Equation 2
the power can be calculated for each point of time. To calculate the total energy produced, we
approximate, by summing each power term at every second, as shown in Equation 17.
‫ܧ‬௨௧ = න ܲ(‫ݐ݀)ݐ‬ ~ ෍ ܲ(‫)ݐ‬
்௦
଴
்௦
଴
Equation 17
To determine the power required by the pump, the required flow rate, and net pumping head is
required. The specified flow rate for pumping, is the reservoir volume divided by the low peak
time (6 hours in this analysis). This relationship is expressed in Equation 18.
ܳ௣ =
ܸ௟௧
ܶ௣
Equation 18
Using the flow rate it is possible to calculate the diameter of pipe required to pump this amount
of water at the specified velocity shown in Equation 19.
‫ܦ‬௣ = ඨ
4ܳ௣
ߨ‫ݒ‬
Equation 19
The Colebrook equation (Equation 10) is used to calculate the friction factor, and the Darcy
Weishbach equation (Equation 11) is used to calculate the head losses in the piping system. The
total pump head is calculated using Equation 20.
‫ܪ‬௣ = ܼ௣ + ℎ௟ +
‫ݒ‬ଶ
2݃
Equation 20
Knowing the volume flow rate and the net head, Equation 3 is used to calculate the power
input of the pump.
Using the power of the pump, the overall system efficiency can be calculated. This is defined as
the energy produced by the two turbines, divided by the energy consumed by the pump.
ߟ௢ =
(ܲ௟௧ܶ௦) + ‫ܧ‬௨௧
ܲ௣ܶ௣
Equation 21

Appendix C: Dam Design Procedure
The following equations (Equation 22-Equation 30) adapted from the book Practical dam
analysis, (Herzog, 1999) are used to calculate the forces acting and applicable safety factors for
a gravity dam.
The objective of the dam design for the offshore ocean hydro storage system is to estimate the
volume of concrete required for the dam structure. Figure C.0.1 below shows a cross-section of
the dam that is used in the analysis.
Figure C.0.1 - Dam Cross-Section with dimensions
For the cross section shown in Figure C.0.1, the dead load G of the dam structure is the force
due to the weight of the concrete as shown in Equation 22.
‫ܩ‬ = ߛ௖
‫ܪܤ‬
2
Equation 22
The hydrostatic load W, as shown in Equation 23 is the horizontal static load exerted on the
dam by the weight of the water, and is assumed to be linearly distributed along the vertical
surface of the dam.
ܹ = ߛ௪ ቆ
ℎଶ
2
ቇ Equation 23
The up-lift force U as shown in Equation 24 is produced by the hydrostatic pressure of the
ocean water that seeps through the pores and cracks of the foundation and base of the dam,
and produces an upward force along the base of the dam.

ܷ = ߛ௪ ൬
ℎ ∗ ‫ܤ‬
2
൰ Equation 24
If the up-lift load produced by the hydrostatic pressure is large, it can cause the dam to slide
and fail, therefore the dead load of the dam needs to be sufficient to counteract this up-lift
load. The dead load, hydrostatic load, and uplift load as shown in Figure C.0.2 are the major
forces acting on a gravity dam.
Figure C.0.2 - Forces Acting on a Gravity Dam
The distance of the resulting force ܿீି௎ାௐ (Equation 25) is measured from the base of the
upstream side of the dam and should have a value less than
஻
ଷ
as shown in Figure C.0.1.
ܿீି௎ାௐ =
ℎ
3
൬
ܹ
‫ܩ‬ − ܷ
൰ Equation 25
Using the calculated loads G, W, U and distance ܿீି௎ାௐ, the contact stresses acting on the
upstream side 1 (ߪଵ), and downstream side 2 (ߪଶ) as shown in Figure C.0.2 of the dam are
determined using Equation 26.
ߪீି௎ାௐ =
‫ܩ‬ − ܷ
‫ܤ‬
ቌ1 ±
6(ܿ −
஻
଺
)
‫ܤ‬
ቍ Equation 26
It is critical for these stresses to be compressive on both sides of the dam. The adhesion C

between the base of the dam and the bed rock can be calculated as shown in Equation 27.
‫ܥ‬ = ܽ‫ܤ‬ Equation 27
The magnitude of adhesion ‘a’ has a range 0 < ܽ < 3‫݉/ܰܯ‬ଶ
based on practical design. The
safety factor against sliding (Equation 28) between the base of the dam and the bedrock is
determined as a ratio between the vertical forces (G, U) over the horizontal forces (W, C) and
must be greater than 1.5.
ܵ. ‫ܨ‬௦௟௜ௗ௜௡௚ =
‫ܩ‬ − ܷ
ܹ − ‫ܥ‬
‫ߔ݊ܽݐ‬ > 1.5 Equation 28
The coefficient of friction ‫݊ܽݐ‬ ߔ between the concrete dam and the bedrock is generally small,
where ‫݊ܽݐ‬ ߔ = 0.7. The safety factor against compression (Equation 29) is a ratio of the
strength of concrete ܴ௖ and the upstream stress ߪଵ. This safety factor must be greater than 3.
ܵ. ‫ܨ‬௖௢௠௣௥௘௦௦௜௢௡ =
ܴ௖
ߪଵ
> 3.0 Equation 29
Once the proper dimensions are chosen, the volume of concrete ܸ௖ needed for the dam can
now be calculated from the area of the dam’s cross-section multiplied by the sum of the lengths
of the dams’ sides as shown in Equation 30.
ܸ௖ = ‫ܣ‬ ∗ ‫ܮ‬ Equation 30

Appendix D: Dam Design Sample Calculations
Given
Density of Concrete γc 0.024 (MN/m3)
Density of Salt Water γw 0.01007 (MN/m3)
Strength of C35 Concrete Rc 23 (MN/m2)
Magnitude of Adhesion a 0.1 (MN/m2)
Coefficient of Base
Friction
tan
φ 0.7
Height of Dam H 30 (m)
Height of Water h 20 (m)
Angle on Dam β 17 (degrees)
Base of Dam B 6.38 (m)
Length of Short Side L1 100 (m)
Length of Long Side L2 200 (m)
Dead Load G
‫ܩ‬ = ߛ௖
‫ܪܤ‬
2
Equation 21
‫ܩ‬ = 0.024
‫ܰܯ‬
݉ଷ
൬
6.38݉ ∗ 30݉
2
൰
‫ܩ‬ = 7.20
‫ܰܯ‬
݉
Hydrostatic Load W
ܹ = ߛ௪ ቆ
ℎଶ
2
ቇ Equation 22
ܹ = 0.024
‫ܰܯ‬
݉ଷ
ቆ
20݉ଶ
2
ቇ
ܹ = 2.01
‫ܰܯ‬
݉
Up-Lift Load

ܷ = ߛ௪ ൬
ℎ ∗ ‫ܤ‬
2
൰ Equation 23
ܷ = 0.01007
‫ܰܯ‬
݉ଷ
൬
20݉ ∗ 6.38݉
2
൰
ܷ = 0.64
ெே
௠
Distance of Resultant Force c
ܿீି௎ାௐ =
ℎ
3
൬
ܹ
‫ܩ‬ − ܷ
൰ Equation 24
ܿ‫ܹ+ܷ−ܩ‬ =
20݉
3
ቌ
2.01
‫ܰܯ‬
݉
7.20
‫ܰܯ‬
݉
− 0.64
‫ܰܯ‬
݉
ቍ
ܿ‫ܹ+ܷ−ܩ‬ = 2.05݉
ܿ‫ܹ+ܷ−ܩ‬ <
‫ܤ‬
3
=
6.38݉
3
2.05݉ < 2.13݉
Contact Stresses σ
ߪீି௎ାௐ =
‫ܩ‬ − ܷ
‫ܤ‬
ቌ1 ±
6 ቀܿ −
஻
଺
ቁ
‫ܤ‬
ቍ Equation 25
ߪ‫ܹ+ܷ−ܩ‬ =
7.2
‫ܰܯ‬
݉
− 0.64
‫ܰܯ‬
݉
6.38݉
ቌ1 ±
6 ቀ2.05݉ −
6.38݉
6
ቁ
6.38݉
ቍ
Upstream Stress σ1
ߪ1 = 1.0282
‫ܰܯ‬
݉2
(1 − 0.926)
ߪ1 = 0.76
‫ܰܯ‬
݉2
Downstream Stressσ2
ߪ2 = 1.0282
‫ܰܯ‬
݉2
(1 − 0.926)
ߪ2 = 1.98
‫ܰܯ‬
݉2

Adhesion C
‫ܥ‬ = ܽ‫ܤ‬ Equation 26
‫ܥ‬ =
0.1‫ܰܯ‬
݉ଶ
∗ 6.38݉
‫ܥ‬ = 0.638
‫ܰܯ‬
݉
Safety Factor in Sliding
ܵ. ‫ܨ‬௦௟௜ௗ௜௡௚ =
‫ܩ‬ − ܷ
ܹ − ‫ܥ‬
‫ߔ݊ܽݐ‬ > 1.5 Equation 27
ܵ. ‫ܨ‬‫݈݃݊݅݀݅ݏ‬ = ቌ
7.2
‫ܰܯ‬
݉
− 0.64
‫ܰܯ‬
݉
2.01
‫ܰܯ‬
݉
− 0.638
‫ܰܯ‬
݉
ቍ ∗ 0.7 > 1.5
ܵ. ‫ܨ‬‫݈݃݊݅݀݅ݏ‬ = 3.34 > 1.5
Safety Factor in Compression
ܵ. ‫ܨ‬௖௢௠௣௥௘௦௦௜௢௡ =
ܴ௖
ߪଵ
> 3.0 Equation 28
ܵ.‫ܨ‬ܿ‫݊݋݅ݏݏ݁ݎ݌݉݋‬ =
23
‫ܰܯ‬
݉2
1.98
‫ܰܯ‬
݉2
> 3.0
ܵ.‫ܨ‬ܿ‫݊݋݅ݏݏ݁ݎ݌݉݋‬ = 11.61 > 3.0
Volume of Concrete Vc
ܸ௖ = ‫ܣ‬ ∗ ‫ܮ‬்௢௧௔௟ Equation 29
ܸܿ = ቆ
‫ܪܤ‬ + ‫ܪ‬
2
ቇ ∗ (2‫ܮ‬1 + 2‫ܮ‬2)
ܸܿ = ቆ
6.38݉ ∗ 30݉ + 30݉
2
ቇ ∗ (2 ∗ 100݉ + 2 ∗ 200݉)
ࢂࢉ = ૟૟, ૜ૢ૙ ࢓૜

Appendix E: Calculation for FEA Values
The following calculations are used to produce the Pressure acting on the surface of the upper
reservoir due to a full column of fluid.
Given Value Units
Head Ratio 2.5
Volume (V) 170,000 ݉ଷ
Density (ρ) 1027 ‫݃ܭ‬ ݉ଷ⁄
Gravity (g) 9.81 ݉ ‫ݏ‬ଶ⁄
Area of Reservoir (A) 4264 ݉ଶ
ܲ (‫)ܽܲܯ‬ =
ܸ ∗ ߩ ∗ 9.81
‫ܣ‬
∗ 10ି଺ Equation 30
ܲ (‫)ܽܲܯ‬ =
170,000݉ଷ
∗ 1027 ‫݃ܭ‬ ݉ଷ⁄ ∗ 9.81 ݉ ‫ݏ‬ଶ⁄
4264݉ଶ
∗ 10ି଺
ܲ (‫)ܽܲܯ‬ = 0.402 ‫ܽܲܯ‬

Final_Report_Humpback_Hydro

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