1. art and entertainment
2. visual art and design
3. design

MECH 3492 Fluid Mechanics and Applications
Water Jetpack Design Project
MECH 3492: Fluid Mechanics and Applications
Prepared By: Gaurav Bankar (7678208)
Joe Tang (7617993)
Prince Soriano (7645250)
Prepared For: Dr. BingChen Wang
Submission Date: April 6, 2015
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MECH 3492 Fluid Mechanics and Applications
Contents
1 Introduction
1
1.1
Project Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Project Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.3
Project Exclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.4
Project Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
2 Background
3
2.1
Feasibility in Manitoba, Canada (Water Resources) . . . . . . . . . . . . . .
3
2.2
Marketing Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
3 Design Alternatives
6
4 Theoretical Calculations
7
4.1
Vertical Thrust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
4.2
Horizontal Thrust and Rotation . . . . . . . . . . . . . . . . . . . . . . . . .
9
4.3
Power and Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
5 Numerical Calculations
11
6 Nozzle Design CFD Analysis
12
7 Final Design
14
7.1
Design Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
7.1.1
Grips and Flow Control Handles . . . . . . . . . . . . . . . . . . . . .
15
7.1.2
Control Arms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
7.1.3
Torsion Bar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
7.2
CFD Analysis Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
7.3
Pump Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
7.3.1
Performance Curves . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
7.3.2
Pump Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
7.4
Cost Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
7.5
Safety Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
8 Conclusion
25
9 References
26
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MECH 3492 Fluid Mechanics and Applications
Appendices
28
APPENDIX A Sample Calculations, MATLAB Results, and CFD Results
28
A.1 Sample Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
A.2 MATLAB Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
A.3 Nozzle Design CFD Results . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
APPENDIX B Pump Performance Curves
38
APPENDIX C Engineering Drawings
40
List of Figures
1
Location of Provincial parks and beaches in Manitoba . . . . . . . . . . . . .
4
2
Various types of water jetpack configurations . . . . . . . . . . . . . . . . . .
6
3
An output sample from MATLAB . . . . . . . . . . . . . . . . . . . . . . . .
11
4
Nozzle 1 Design CFD Flow Simulation Results . . . . . . . . . . . . . . . . .
13
5
Water Jetpack Full Assembly Engineering Drawing . . . . . . . . . . . . . .
14
6
CAD model of the designed water jetpack system . . . . . . . . . . . . . . .
15
7
Flow Control Handle and Round Grip CAD Model . . . . . . . . . . . . . .
16
8
Butterfly valve that can control the flow of the nozzle . . . . . . . . . . . . .
16
9
Control Arm CAD Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
10
Location of the double seal dual ball bearings . . . . . . . . . . . . . . . . .
18
11
CAD model representation of the nylon torsion bar . . . . . . . . . . . . . .
18
12
Full Hydraulic Assembly CFD Results . . . . . . . . . . . . . . . . . . . . .
19
13
Performance curve of a peerless pump type 6AE18 [16] . . . . . . . . . . . .
20
14
8AE20G Performance Curve [14]
. . . . . . . . . . . . . . . . . . . . . . . .
22
A15 Nozzle 1 CFD Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
A16 Nozzle 2 CFD Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
A17 Nozzle 3 CFD Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
B18 Performance curve of 6AE14N [16] . . . . . . . . . . . . . . . . . . . . . . .
38
B19 Performance curve of 8AE17A [16] . . . . . . . . . . . . . . . . . . . . . . .
38
B20 Performance curve of 10AE16 [16] . . . . . . . . . . . . . . . . . . . . . . . .
39
B21 Performance curve of 8AE17A [16] . . . . . . . . . . . . . . . . . . . . . . .
39
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MECH 3492 Fluid Mechanics and Applications
List of Tables
I
WATER JETPACK PRICES . . . . . . . . . . . . . . . . . . . . . . . . . .
5
II
CFD WORKING PARAMETERS AND VARIOUS NOZZLE DIMENSIONS
12
III
CFD RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
IV
CALCULATED TOTAL HEAD AND VOLUMETRIC FLOW RATE FOR
DIFFERENT JET ANGLES . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
V
8AE20G SPECIFICATIONS [14] . . . . . . . . . . . . . . . . . . . . . . . .
21
VI
HIGH LEVEL COST SUMMARY OF THE WATER JETPACK DESIGN .
23
Page | iv
MECH 3492 Fluid Mechanics and Applications
Abstract
This report presents a preliminary design of a hydraulic system on a water jetpack
design. The current market share of the water jetpack recreational sport industry, as
well as the feasibility of implementing this recreational sport in Manitoba was further
examined. Moreover, the nozzle dimensions for the hydraulic system were determined
through theoretical (hand calculation) and numerical calculations (using MATLAB).
Subsequently, the theoretical and numerical results were validated and compared to the
Computational Fluid Dynamics (CFD) results that were determined using SolidWorks
Flow Simulation. Furthermore, the size of the pump required for the designed water
jetpack system was specified and justified through calculations and pump curves. For
this water jetpack design, a horizontal split case single stage double suction pump
type 8AE17Q was selected, as it suffice the overall volumetric flow rate and efficiency
required for our water jetpack design. Lastly, a high level cost estimate for the water
jetpack design was performed and determined that the preliminary design will cost
approximately $25 000 (CAD).
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MECH 3492 Fluid Mechanics and Applications
1.
Introduction
A jetpack is a device that is typically attached to a backpack that is powered by jets in
order to create thrust and lift. It was first investigated in 1949 by the U.S. army for the
purpose of having a device that can propel a single soldier up into the air [1]. One of the
major design concerns in designing a jetpack is how to generate enough thrust to overcome
gravity [2]. In the early jetpack designs, fuel tanks were not large enough to sustain the
weight in order to produce lift. Over the years, jetpack designs developed and now some
designs can be powered by liquid-fuel, hydrogen peroxide, water, and turbojets. For this
project, a water jetpack (also known as hydro jet packs) design was considered.
The main purpose of this design project is to create a preliminary design of a hydraulic system on a water jetpack using the knowledge learned in fluid dynamics. The project provides
an opportunity to apply the concepts of fluid motion, potential flow theory, and boundary
layer theory, learned in MECH 3492. It gives us a first-hand experience in designing water
sport equipment based on the theories learned in class. The project also presents us an
opportunity to study the feasibility of introducing the water jetpack recreational sport in
Manitoba, Canada.
1.1.
Project Objectives
The project objectives are as follows:
• To learn and apply the fluid mechanics principle to design the water jetpack. Concepts
of fluid motion, continuity equation, momentum, acceleration, thrust, drag will be used
in the design process.
• To check the feasibility of operating a water jetpack industry in Manitoba.
• To analyze the current market share of the water jetpack in the world of water sport
entertainment.
• To learn to incorporate safety features in a design.
1.2.
Project Scope
In order to ensure the safety of the water jetpack preliminary design, the team performed
the necessary engineering analysis (e.g. determined sizes of pumps, nozzles, and jets that are
acceptably safe to operate) on the components associated with the chosen hydraulic system.
However, the engineering analysis performed in this report is limited to the students’ current
knowledge in fluid mechanics. Therefore, the final design’s engineering analysis performed
in this report must be further analyzed by a Professional Engineer prior to purchasing any
components and implementing the system.
Furthermore, in order to fully understand what is needed for this project to be successful,
it is important to define the limitations of the project scope. Based on the availability of
resources and project schedule, this design project will cover the following work scope:
1. Produce a preliminary design of the hydraulic system for a water jetpack including
the determination of the size of the pump and the dimensions of key components
associated with the system.
2. Provide appropriate engineering rationale for all design decisions. Decisions must be
supported by detailed calculations, numerical approximations, and engineering experience.
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MECH 3492 Fluid Mechanics and Applications
3. Provide proper engineering drawings on key components of the designed hydraulic
system.
4. Provide a high level cost estimate of the chosen design.
5. Compare the theoretical (hand calculations), numerical, and CFD results that were
performed on some of the key components of the hydraulic system.
6. Investigate the feasibility of implementing the water jetpack system in Manitoba.
7. Investigate the current market and competitors’ prices of water jetpack systems.
1.3.
Project Exclusions
The following are exclusions from the project design scope:
1. Not responsible for designing the water pump needed in the hydraulic system. Based
on analysis and calculations, the pump will be chosen directly from the manufacturer’s
catalogue or market availability.
2. Design of the backrest to be excluded from the design process.
3. Machine design specifics will not be included (e.g. bolt sizes and specifications, straps,
and seat belt types)
4. Installation and assembly procedures in implementing the chosen hydraulic system are
not included.
5. Not responsible for outlining the necessary maintenance procedures of the hydraulic
system.
6. Not responsible for the procurement of the required components.
7. Not responsible for manufacturing the designed components.
8. Not responsible for determining the processes used to manufacture the water jetpack
design.
9. Engineering analysis such as fracture mechanics and vibrational influences on functional components are excluded.
10. Profit calculation in implementing the designed water jetpack in Manitoba.
1.4.
Project Assumptions
For every analysis, several assumptions must be made for simplicity. Some assumptions are
made to make calculations possible and not exceed the student’s current knowledge in fluid
mechanics. For this project’s analysis, the following assumptions were made:
• The studied flow was fully developed.
• The initial velocity of the water from the propulsion source on a separate unit tethered
behind the jetpack is horizontal. Thus, the water must be accelerated upward by the
upward-curving hose, which exerts an additional downward force on the jetpack.
• For this project, a hovering jetpack was assumed.
• Assume the total weight of the user and jetpack to be around 100 kg.
• All metals used in the water jetpack design are of Aluminum with Teflon coating.
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MECH 3492 Fluid Mechanics and Applications
2.
Background
Within the 21st century, jetpack designs have evolved into utilizing water as a high-density
propulsion fluid to produce thrust and lift [3]. The need of having a high-density propulsion
fluid requires a massive amount of fluid, in which makes it infeasible to have a self-contained
jetpack. Current water jetpack designs involve having a separate watercraft (such as a Jet
Ski) to store the necessary components (e.g. pump, engine, fuel, and fluid) that enables the
propulsion of the jetpack. The jetpack is then attached to the watercraft by a long flexible
hose that feeds the water into the jet nozzle connected to the pilot’s body. The flow rate
in the hydraulic system can be adjusted through a Jet Ski or a remote actuator from the
pilot. As of now, the water jetpack technology has been commonly applied as a recreational
sport. The following sections will discuss the feasibility of implementing this technology in
Manitoba, as well as the current market prices of some water jetpack systems.
2.1.
Feasibility in Manitoba, Canada (Water Resources)
Nowadays, most of the water jetpack design technology requires a body of water (e.g. beaches
and lakes) in order for it to operate. To ensure that the project can be implemented in the
province, a brief feasibility study of the water resources available in Manitoba was conducted.
Manitoba, Canada has an abundant amount of fresh water resources as the province is
comprised of many rivers and lakes. Manitoba is often referred to as the land of 100 000
lakes [4]. The three largest lakes that can be found in Manitoba are Lake Winnipeg (third
largest lake in Canada), Lake Winnipegosis, and Lake Manitoba [5]. Even though Manitoba
has one of the coldest winters and the lakes are frozen for long periods of time, there is
still significant tourism involved in these lakes. Numerous of Manitobans and tourists still
take advantage of the summer months and enjoy spending their leisure time outdoors. Some
of the common outdoor activities in Manitoba are camping, fishing, hiking, canoeing, and
often spending time relaxing at the beaches and lakes.
Manitoba has a significant amount of provincial parks and beaches, in which the water
jetpack recreational sports past time can possibly be implemented. Figure 1 depicts the
location of the provincial parks and beaches across Manitoba. Commercially, these parks
and beaches can be a potential location for a rental service of a water jet pack system
in Manitoba. Due to the abundance of fresh water resources and a significant amount of
potential location, it is therefore feasible to implement a water jet pack system in Manitoba.
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MECH 3492 Fluid Mechanics and Applications
Figure 1: Location of Provincial parks and beaches in Manitoba [6]
2.2.
Marketing Analysis
As determined in the previous section, it is feasible to implement a water jet pack system
in Manitoba due to the abundance of water resources in the province. However, due to the
limited summer months in Manitoba, the profitability to implement a water jetpack system
business here in the province is still questionable. Although, it is out of the scope of this
project on how much profit our design will potentially make. It is still imperative to have
an understanding and knowledge on the marketability of the product, as well as the prices
of the competitors.
Currently, the market for water jetpacks is mostly popular in warm weather places such
as Florida and California. However, the demand for this recreational hobby is currently
increasing and there is a potential that this technology can be implemented in Manitoba
due to the provinces’ abundance of water resources (e.g. rivers and lakes).
Subsequently, water jetpack systems come in various prices and the cost of the product
really depends on the type of design and configuration of the jetpack. TABLE I tabulates
the prices of various types of water jetpack configurations that are available in the market
Page | 4
MECH 3492 Fluid Mechanics and Applications
right now. Based on the selected final design configuration, the design team will aim to
design a water jetpack system that has a comparable (lower or similar) cost to the prices
outlined in TABLE I.
TABLE I: WATER JETPACK PRICES
Features/Configurations
Cost/Price
Need to be connected to a
X-Jetpack NX
jet ski and has a back strap $9495 (USD) [7]
design for the jet flow.
Need to be connected to a
jet ski and the jet flow is loZapata Flyboard
$6700 (USD) [8]
cated at the feet of the operator
Need to be added to a jet
Jetlev-Flyer (Jetpack only) ski. Has a back strap design $8900 (USD) [9]
for the jet flow.
Complete set with no jet ski
Jetlev-Flyer (JF-260)
required. Has a separate $111 000 (USD) [9]
boat for pumps.
Complete set with no jet ski
Jetlev-Flyer (SHARK)
required. Has a separate $30 000 (USD) [9]
boat for pumps.
Brand/Model Type
Page | 5
MECH 3492 Fluid Mechanics and Applications
3.
Design Alternatives
Prior to obtaining the final design selection of the water jetpack, the team researched various
design alternatives that could possibly be used as a reference design for our design project.
Figure 2a to Figure 2c depict the different types of water jetpack configurations and styles
that are currently available in the market. Basically, there are two types of water jetpack
configurations; a jetpack that is attached to a watercraft (Figure 2a), and a jetpack that is
connected to a Jet Ski (Figure 2b). However, the jet that propels the jetpack can either be
attached to a backrest located at the back of the pilot (Figure 2a and Figure 2b) or at their
feet (flyboard, Figure 2c).
(a) Jetpack (with backrest) attached to a watercraft
[9]
(b) Jetback (with backrest) attached to a Jet Ski [10]
(c) Jet located at the feet of the pilot [11]
Figure 2: Various types of water jetpack configurations
Page | 6
MECH 3492 Fluid Mechanics and Applications
4.
Theoretical Calculations
This section will present the theoretical analysis that will be used to calculate the required
dimensions in designing the water jetpack hydraulic system.
4.1.
Vertical Thrust
The vertical thrust generated in the jet pack design is a result of momentum exchange. As
a fluid exits a control system, there will be a change in momentum for that system, which
propels it in the opposite direction from the resulting force. To control this force, the velocity
of the exiting fluid must be controlled. To determine and control this velocity, equation (1)
and (2) are required.
Q = V1 A1 = V2 A2
(1)
A2
V1 = V2
(2)
A1
The volumetric flow rate for an incompressible liquid is constant and given by equation (1).
For a given velocity in a cross-sectional area, the volumetric flow rate must be kept constant,
and as such, any change in the cross-sectional area will result in a change in fluid velocity.
This principle is used in designing an appropriate nozzle to control the output velocity of
the jetpack. Knowing the output velocity from equation (1) and (2), a momentum equation
can be used to evaluate the resulting acceleration. This momentum equation is shown in
equation (3) in vector format.
Z
Z
∂
VρVdA
(3)
Vρd V– +
F = FS + FB =
∂t CV
CS
Associated with equation (3) is a continuity equation, (4):
Z
Z
∂
ρd V– +
ρVdA = 0
(4)
∂t CV
CS
Because our system sources its water from the environment, the total mass of the system
should remain constant. For the specific case of vertical thrust, equation (3) can be reduced
to (5).
Z
Z
Z
∂
Fy = FSy + FBy + arf y ρd V– =
vxyz ρd V– +
vxyz ρVdA
(5)
∂t CV
CS
The body force, FBy consists only of gravity, while the acting forces consist of the acceleration due to momentum exchange, arf y , the drag forces experienced by the system, FD ,
and any tensile forces experienced from the hose. One of the important cases needed to
be explored is the steady state case of no net acceleration, or floating. To compute the
momentum exchange, the inlet velocity and exit velocities of the nozzle are required and
can be found from equation (2).
Z
−M g + arf y M − FT y − FDy = −Ve
Z
ρVdA + Vi
CS
ρVdA
(6)
CS
where Ve = Ve cos θ
Page | 7
MECH 3492 Fluid Mechanics and Applications
With a constant mass flow rate, m, equation 6 can be reduced to 7.
−M g + arf y M − FT y − FDy = −Ve m
˙ e + Vi m
˙e
(7)
Rearranging to isolate arf y , the total acceleration for any given inlet and exit velocity, drag,
and tension can be found in equation (8).
m
˙
FD FT
arf y = (Vi − Ve )
+g+
+
(8)
M
M
M
If we take the simplified case where drag and tension are ignored, the case of hovering is
defined at a zero acceleration state.
0
0
7 FT
7
0
m
˙
FD
arf y = (Vi − Ve )
+g+ + M
M
M
m
˙
0 = (Vi − Ve )
+g
(9)
M
m
˙
−g = 9.81 m s−2 = (Vi − Ve )
(10)
M
Knowing that acceleration due to gravity is constant, we can determine the requisite inlet
and exit velocities to achieve an equivalent acceleration from the momentum exchange to
counteract this.
Vi = Ve
Ae
Ai
(From Equation (2))
Further simplifying the case using equation (2), the exit velocity and the referenced nozzle
dimensions can be determined for a given mass flow rate and user mass, to achieve the
floating condition.
˙
Ae m
−2
(11)
−g = 9.81 m s = Ve 1 −
Ai M
By adjusting the exit velocity and mass flow rate, thrust can be controlled and height
adjustments can be made by the user. This functionality would be performed with valves
that can adjust the mass flow rate achieved from the pump. The total mass of the system,
M, can be found from equation (12).
h
h
(12)
M = Mo + mj + mh + ρAh = Mo + Mj + Mh + ρπr2 h
L
L
The total mass to be accelerated is equal to the mass of the user, Mo , in addition to the
mass of the jetpack and the hose that is above water, assuming it is capable of floating for
the part that is not held in the air, and the mass of the water inside of the hose. Since the
height of the user can vary due to thrust, the total mass of the system will vary due to this
height, namely the amount of hose above water and its contents.
The gauge pressure at the entrance of the nozzle can be determined using equation (13), the
derivation of which can be found in the appendix sample calculations.
4 8ρQ2
Di
Pig = 2 4
−1
(13)
π Di
De
By evaluating these sets of equations, and factoring additionally drag and tension, the
specifications and requirements of the nozzles and pump should be determinable.
Page | 8
MECH 3492 Fluid Mechanics and Applications
4.2.
Horizontal Thrust and Rotation
Forward movement can either be controlled by separate jets in the horizontal direction,
or adjustment of the angle of the vertical jets with respect to the vertical direction. The
forward acceleration is derived from equation (3) and is similar to equation (5)
Z
Z
Z
∂
Fx = FSx + FBx + arf x ρd V– =
vxyz ρd V– +
vxyz ρVdA
(14)
∂t CV
CS
Using the same assumptions of steady state and negligible tension and drag, this can be
reduced to the following.
arf x M − FT x − FDx = −Ve m
˙ e + Vi m
˙e
(15)
where Ve = Ve sin θ
arf x M − FT x − FDx = (Ui − Ue ) m
˙e
(16)
0
0
7 FDx
m
˙ e FT x
− −
(17)
arf x = (Ui − Ue )
M
M
M
The acceleration in the forward direction can be similarly defined based on the inlet and
exit velocities in the horizontal plane. If two separate jets are used for forward propulsion,
angular movement should also be possible if only one of the two jets are active, or if one jet
is stronger than the other. For a single jet, depending on its radial distance from the center
of gravity, the torque, T, can be determined and the angular acceleration can be found in
equations (18) to (20).
m
˙e
T = (Ui − Ue )
r
(18)
2
T = Mα
(19)
2M
(20)
α=
(Ui − Ue ) m
˙ er
This angular acceleration and angular velocity should be considered for comfort as well as
ease of control. Other considerations in regards to rotation should be investigated for the
case of two vertical jets, where the user angles their center of mass to change propulsion.
Since it is ideal to work with fewer outlets due to complexity and losses, a design of two
nozzles used for both lift and propulsion is likely. In this case, the vertical and horizontal
components can be calculated using trigonometric identities from equations (6) and (15).
The vertical exit velocity required from equation (11) to achieve a floating state can then
be rearranged to account for an angled outlet stream.
v
u
g
M
u
2
·
(21)
Ve = t
Ae
ρA
e
cos θ 1 − Ai )
By controlling the outlet angle, the user will require an increased exit velocity to maintain
altitude, since there is a lower vertical component in the momentum exchange to combat
gravitational acceleration. However, this contributes a horizontal acceleration that allows
the user to propel themselves forward.
Page | 9
MECH 3492 Fluid Mechanics and Applications
4.3.
Power and Losses
When considering the power required for sustaining the desired functionality of the water
jetpack, modified Bernoulli equation is necessary.
1
P + ρV 2 + ρgz + h = C
(22)
2
The system can be separated into three distinct phases. The first phase, [A] will be the
state of the water source. Here, there is no elevation or velocity, with atmospheric pressure.
The second phase [B] will involve a pump, to add head to this water to achieve a specified
total pressure. The final phase [C] is the exit conditions of the water from the nozzles. Here,
there is some exit velocity necessary to sustain certain thrusts, as specified in equations
(8) and (17). Between phase [B] and phase [C], there will be some amount of losses from
the hose and hydraulic system, which will be further investigated. To summarize their
effects though, equation (23) for major head loss, and equation (25) for minor head loss
are considered. These losses should be factored in to the total head required from the
pump output to maintain the functions desired; i.e. sustained floating, vertical thrusts, and
horizontal thrusts.
L V2
(23)
hl = K
D 2
1
e/D 2.51
√ = −2.0 log
+
(24)
3.7
Ref
f
Le V 2
hlm = f
(25)
D 2
The major head loss comes from the nozzle’s gradual contraction. Using Table 8.3 [12],
the optimal parameters for a nozzle can be chosen to produce the least losses. The friction
coefficient for the turbulent flow inside the hose can be found iteratively with the Colebrook
equation, (24), assuming a very low roughness ratio for a material that minimizes losses.
The power of the pump can then be determined from the following equation.
"
#
2
2
p
V
p
V
˙ pump = m
W
˙
+
+ gz + htotal −
+
+ gz + htotal
(26)
ρ
2
ρ
2
f
i
Page | 10
MECH 3492 Fluid Mechanics and Applications
5.
Numerical Calculations
The equations derived from the theoretical calculations were assessed and configured into
a MATLAB script, the results of which are shown in Appendix A. The script iteratively
calculates required inlet and exit velocities, mass flow rates, power, and losses when given
associated nozzle dimensions to achieve a state of constant hovering at a certain height. An
output sample is presented in Figure 3.
Figure 3: An output sample from MATLAB
The analysis performed numerically through MATLAB provided an automated approach to
find required values with given input parameters. In the above sample, a given jet angle,
height, total mass, and inlet and outlet diameters were provided, and the following inlet and
outlet velocities, pressure, flow rate, head, etc. were obtained. This process was performed
for varying outlet diameters, ranging from 6 cm to 1 cm, at intervals of 1 CM, as well as
comparing jet angles of 0◦ , 30◦ , and 60◦ , to determine the required Power to achieve this
goal.
This output was verified using hand calculations to determine their accuracy with expected
results, which are included in the appendix. The design of the nozzles, and specifications
for the pump were based off these results.
Page | 11
MECH 3492 Fluid Mechanics and Applications
6.
Nozzle Design CFD Analysis
In order to verify the theoretical and numerical calculations for the nozzle design dimensions,
Computational Fluid Dynamics (CFD) analysis was performed using SolidWorks Flow Simulation feature. CFD analysis was conducted on three nozzle designs and compared it to the
analytical calculations. TABLE II tabulates the nozzle dimensions along with the working
parameters that were utilized to study the three nozzle designs.
TABLE II: CFD WORKING PARAMETERS AND VARIOUS NOZZLE DIMENSIONS
Parameters
User Mass :
100 kg (max)
Equipment Mass :
15 kg
Water Mass :
Total Mass
39.20 kg (max)
Environment Pressure :
101.325 kPa
Temperature :
293.2 K
: 154.2 kg (max)
Dimension Type
Nozzle 1
Nozzle 2
Nozzle 3
Inlet Diameter (m)
0.07
0.07
0.07
Outlet Diameter (m)
0.06
0.05
0.04
Nozzle Angle (deg)
10
10
10
Nozzle Length (m)
0.06
0.118
0.176
The velocity results from the CFD analysis of the three nozzle designs are summarized in
TABLE III. As indicated in TABLE III, the CFD results are within 1% to 4.18% compared
to the analytical calculations. It was observed in the results that the longer the nozzle length
the percentage difference between the analytical results and the CFD results decreases. This
is possibly because of the assumption of the flow being fully developed. The longer the nozzle
length the better the approximation it would be to be a fully developed flow.
TABLE III: CFD RESULTS
Nozzle Design
Parameters
Analytical Results
CFD Results
Percent Difference
1
Inlet Velocity
Outlet Velocity
22.28
30.94
22.28
32.26
N/A
4.18
2
Inlet Velocity
Outlet Velocity
13.89
27.78
13.89
28.43
N/A
2.31
3
Inlet Velocity
Outlet Velocity
9.53
29.78
9.53
29.48
N/A
1.01
Page | 12
MECH 3492 Fluid Mechanics and Applications
Figure 4 displays the CFD flow simulation results of the selected nozzle design. As expected,
the velocity increases as the flow diverges into the nozzle outlet diameter, as shown in the
flow lines in Figure 4. Furthermore, the nozzle 1 design was chosen because this particular
design dimensions provides a low exit velocity with a reasonable pressure at the nozzle
entrance and acceptable flow rate. Appendix A.3 presents the flow simulation results of all
the three nozzle designs.
Figure 4: Nozzle 1 Design CFD Flow Simulation Results
Page | 13
MECH 3492 Fluid Mechanics and Applications
7.
Final Design
SCALE:1:16
SHEET 1 OF 2
A4
WEIGHT:
2
8
D
C
B
A
9
1
1
5
2
6
4
3
7
J.T.
APPV'D
1-APR-2015
TITLE:
1-APR-2015
G.B.
CHK'D
1-APR-2015
DATE
NAME
P.S.
DRAWN
MATERIAL:
DO NOT SCALE DRAWING
PART NUMBER:
UNLESS OTHERWISE SPECIFIED:
DIMENSIONS ARE IN MILLIMETERS
TOLERANCES:
DWG NO.
Water Jetpack System
C
3
1
9
2
4
ITEM NO.
5
PART NAME
REVISION
2
ISO 7380 - M5 x 16 --16N
B
2
Flow Control Handle
8
2
Grip
7
2
Handle pipe
6
2
Straight Pipe
5
1
Nylon torsion bar
4
2
1
Nozzle
3
2
Y Branch
2
QTY.
Shoulder
1
6
A
After the design team’s careful deliberation of the design alternatives and calculations of
the necessary dimensions, the water jetpack design was finalized. Figure 5 displays a full
assembly engineering drawing (including the Bill of Materials) of the designed water jetpack
system. The detailed engineering drawings for certain components of the water jetpack design are presented in Appendix C.
Figure 5: Water Jetpack Full Assembly Engineering Drawing
Page | 14
MECH 3492 Fluid Mechanics and Applications
Figure 6 depicts a 3D Computer Aided Design (CAD) model of the designed water jetpack
system. The chosen water jetpack design has a similar configuration to Figure 2a, where
the jets nozzles are attached to the back rest and the jetpack is connected (through a
hose) to a watercraft. Several detailed components of the water jetpack system such as the
watercraft design, backrest, straps, seals, and bolts were not included in this design, as those
components were not part of the scope of this project.
Figure 6: CAD model of the designed water jetpack system
7.1.
Design Features
The following sections discusses several design features such as grips, flow control handles,
valves, control arms, and torsion bar that were implemented in the designed water jetpack
system.
7.1.1.
Grips and Flow Control Handles
The CAD model representation of the grip and the flow control handle for the water jetpack
design are displayed in Figure 7. The handle round grip is made out of a heavy duty vinyl
for water resistance and operator comfort. The round grip also provides a strong grasps
and control for the operator to hover and maneuver the jetpack system. Moreover, the
flow control handle mechanism controls how much flow will go through the nozzle. The
flow control handle mechanism has a similar concept design to a bicycle brake, where it is
attached to a cable and a valve that is similar to a butterfly valve. As soon as the handle
is pressed, the cable pulls the butterfly valve link and it opens the flow inside the water
jetpack design.
Page | 15
MECH 3492 Fluid Mechanics and Applications
Figure 7: Flow Control Handle and Round Grip CAD Model
Figure 8 shows a butterfly valve that can possibly be implemented (or serves as baseline
design) as the valve that controls the flow of the water jetpack design. The round grip,
flow control handle (bicycle brakes), cables, and the butterfly valve can be purchased from
McMaster-Carr.
Figure 8: Butterfly valve that can control the flow of the nozzle
Page | 16
MECH 3492 Fluid Mechanics and Applications
7.1.2.
Control Arms
Figure 9 depicts a CAD model representation of the control arms of the designed water
jetpack system. To attain a lightweight design of the system, the control arms are made out
of various sizes of schedule 40 Aluminum 6061 pipes (see Appendix C for the engineering
drawing and detailed dimensions). The holes in the pipes allow the operator to adjust the
control arms length for various operators. The holes will be connected by pins. Furthermore,
the control arm enables the operator to hold into the system, as well as control the forward
and backward motion of the water jetpack.
Figure 9: Control Arm CAD Model
In order for the water jetpack to move forward and backward, the jetpack shoulder has two
double sealed dual ball bearings inside to enable rotation on the jet nozzles. Figure 10a
and Figure 10b shows the dual ball bearing and its relative location on the designed water
jetpack system.
Page | 17
MECH 3492 Fluid Mechanics and Applications
(a) Location of the bearings
(b) Double seal dual ball bearings
Figure 10: Location of the double seal dual ball bearings
7.1.3.
Torsion Bar
Figure 11 displays the CAD model representation of the torsion bar that is attached to the
water jetpack system. The torsion bar is made out of nylon for flexibility and it provides the
appropriate amount of torsional force to prevent uncontrolled swivel or rotational movement
on the nozzles.
Figure 11: CAD model representation of the nylon torsion bar
7.2.
CFD Analysis Results
For the purpose of visualizing the water flow in the water jetpack design, CFD analysis was
performed in the hydraulic system assembly. Figure 12 presents the CFD flow results in
Page | 18
MECH 3492 Fluid Mechanics and Applications
the hydraulic system assembly. For this analysis, the inlet (larger diameter) flow velocity of
22.28 m s−1 and an outlet (nozzle) environmental pressure of 101.3 kPa parameters were used.
As shown in Figure 12, the water flow inside the jetpack pipe assembly is approximately
even throughout the two branches. This result indicates that there is an even distribution
of water flow in the designed Y-branch pipe. In addition, the CFD analysis determined
that the outlet velocity at the left nozzle is 25.68 m s−1 , while the outlet velocity at the
right nozzle is 25.77 m s−1 . Due to the minor losses in the hydraulic system assembly, the
values obtained from the hydraulic system analysis are lower than the outlet velocity results
32.26 m s−1 from the nozzle CFD analysis mentioned in Section 6.0, TABLE III.
Figure 12: Full Hydraulic Assembly CFD Results
7.3.
Pump Selection
In order to provide the necessary propulsion to drive the water jetpack, a centrifugal water
pump must be selected. This section presents the methodology in selecting the pump for
the water jetpack design.
Pumps are mechanical devices that use suction or pressure to transports fluids from one
location to another [14]. Pumps can be found in water distribution and wastewater collection
system [15]. To ensure efficiency and cost effectiveness of a pump, pumps must be sized
correctly. An improperly sized pump can caused failures and undesirable expenses. For
a specific application, pump curves are utilized to specify the correct size of the pump.
Furthermore, centrifugal pumps are applied in turbo machineries to increase the pressure
and drive the flow in a controlled volume.
In selecting the pump for this project, three characteristic properties were considered. The
characteristics that were considered are the overall head (H) that need to be achieved by the
pump, capacity or volumetric flow rate (Q), and the efficiency of the pump (η). Performance
curves provided by the manufacturer’s catalogue were used to select the pump. The chosen
pump was obtained from the Peerless Pump Catalogue.
Page | 19
MECH 3492 Fluid Mechanics and Applications
7.3.1.
Performance Curves
Centrifugal pump performance curves show graphical representations of how a pump performs in relation to the required head and flow of a system [15]. For a particular pump,
the pump curves are generated by plotting the possible combinations of total pressure and
volume flow rate into one graphical representation. Additionally, pump curves provides the
efficiency of the pump. Each pump has different maximum efficiency point and the pump’s
efficiency differs throughout a range of operating conditions. Typically, pump efficiency increases as the size of the impeller increases. On the other hand, pump efficiency decreases
when there is a reduction in the size of the impeller and rotational speed. Furthermore,
the generated curve indicates the ranges of operating conditions for the specific pump. In
a pump curve, the x axis (vertical) indicates the total head, while the y axis (horizontal)
indicates the flow capacity (in gpm). Figure 13 depicts an example of a performance curve.
Figure 13: Performance curve of a peerless pump type 6AE18 [16]
Generally, pumps can produce a specific pressure (commonly converted from psi or bar into
feet or meters head) at a particular flow (commonly represented in gpm) [15]. Dependent
upon the impeller speed and diameter, pumps can transport any fluid into a given height or
head. In addition, the amount of pressure in the pump is dependent on the weight of the
fluid being transported.
Page | 20
MECH 3492 Fluid Mechanics and Applications
7.3.2.
Pump Specification
To determine the horsepower needed for the water pump, the following calculation was made:
H ×Q
Php =
3960
Where:
H = Total head in feet = 227 ft
Q = Volumetric flow rate in gpm = 2774 gpm
Php = Water horsepower in hp
Water specific gravity ≈ 1000 kg m−3
Hence, horsepower is
Php = 159.17 hp
From the sample calculation above, TABLE IV tabulates the measurements for the total
head and overall volumetric flow rate required in the water jetpack design.
TABLE IV: CALCULATED TOTAL HEAD AND VOLUMETRIC FLOW RATE FOR
DIFFERENT JET ANGLES
Jet Angle (degrees) Total Head (feet) Volumetric Flow Rate (gpm)
0
227
2,774
30
260
2,980
60
433
3,921
From the calculated results, five pumps were considered from the manufacturer’s catalogue
and the pump curves for each these pumps are displayed in Appendix B. After analyzing
the design requirements, the peerless horizontal split case single stage double suction pump
(type 8AE20G) was selected, as it satisfies the requirements more efficiently than the other
available pumps. The specification for the 8AE20G model is represented in TABLE V and
Figure 14 shows the pump’s performance curve.
TABLE V: 8AE20G SPECIFICATIONS [14]
Specifications
Capacities
Head
Pressure
Over 8,000 gpm (1817 m3 h−1 )
Up to 675 ft (206 m)
Up to 510 psi (35 kg cm−2 , 3514 kPa)
Horsepower
Up to 550 hp (410 kW)
Temperature
Up to 250 ◦ F (121 ◦C)
Drive Combinations
Liquids
Materials
Motors, engines, steam turbines, combinations.
Water and clear liquids.
Cast iron, bronze fitted as standard. Other materials available
Page | 21
MECH 3492 Fluid Mechanics and Applications
Figure 14: 8AE20G Performance Curve [14]
As observed in the performance curve in Figure 14, as the total head increases, the efficiency
of the pump also increases. Subsequently, for jet angle at zero degrees the efficiency of the
pump is at 82%. As observed from the curve, the efficiency of the pump increases first, with
an increasing flow rate, then once it reaches the maximum, it then decreases to zero as soon
it reaches the maximum flow rate.
For this jetpack design, our team decided to use the horizontal split case single stage double
suction pump type 8AE17Q because it satisfies our requirements in terms of the overall
volumetric flow rate, and efficiency of the pump.
7.4.
Cost Summary
In order to compare the designed water jetpack relative to the current market prices, a high
level cost breakdown of the designed water jetpack was performed. TABLE VI summarizes
the high level cost estimate of the designed water jetpack. The costs are based on pricing
that were obtained from different suppliers. All the costs are an approximate and will have
± 20% variation. As shown in TABLE VI, the approximate total cost of the water jetpack
design is $25 158.00 CAD. The estimated cost does not include other component details
(such as watercraft, bolts, bearings, straps, backrests, and etc.) that were not part of the
water jetpack design.
Page | 22
MECH 3492 Fluid Mechanics and Applications
TABLE VI: HIGH LEVEL COST SUMMARY OF THE WATER JETPACK DESIGN
Cost Type
Vendor
Product Description
Raw Material
Metal
Depots
0.1 in Aluminium
Sheet Grade T6061
Dixie
packing and
seal
Teflon coating can
4 cans
Peerless
Pumps
Horizontal
split
case single stage
double
suction
pump type 8AE17Q
1
Pump Unit
Quantity
2 (4 ft
× 4 ft)
Cost
$
376.00 CAD [15]
$
232.00 CAD [16]
$18,000.00
CAD
[14] (approx.)
$1500.00
Cs
Engineering
Manufacturing
works
Frame of the jet
pack including the
nozzle
2-Nozzles
1-Frame
(Y-Structure)
Cs
Engineering
works
Teflon coating of
the frame
1
Jetlev-Flyer
Hose made up of
tightly woven textile, rubber-coated
1 ( dia - 10 cm,
length
1000 cm)
Miscellaneous
Estimated Total Cost
7.5.
(includes
manufacturing,
labour and
shipping charges)
[17]
$50.00 (excluding
the cost the spray
can) [17]
$5,000.00
CAD
(approx.) [18]
$ 25,158.00 CAD
Safety Considerations
When implementing any engineering design, safety is a prime concern. The water jetpack
design allows a user to propel themselves through the air with the use of momentum exchange
principles from nozzles. Because of the moving nature of the equipment, its overall mass, and
recreational intent, safety plays an important role in the overall experience in using water
jetpacks. A user must be able to trust their safety is protected when attempting a novel
recreational sport, particularly if it is intended to be a business. Many safety factors, such
as the maximum height achievable by the system, weight of the user, and jet exit velocity
were considered, and an appropriate developmental concept was formulated as follows.
One point to consider is the maximum height at which the user is allowed to achieve. We
have opted for a conservative maximum height of 5 m, which will first be enforced by the
maximum length of hose available. From this height, considering no air resistance, a user
will enter the water from freefall at a velocity of 9.9 m s−1 or 35.66 km h−1 . As an example,
FINA restricts the competitive diving height to a maximum of 5 m for children below 11
years of age . This appears to be a safe maximum height to allow the user to achieve. Aside
from the hose itself restricting height, the minimum and maximum flow rate of the system
can be lowered for participants who have lower mass, such has younger adults or children.
In regards to the scenario of free fall, it should be considered one of the ”worst case” scenarios,
where the pump loses power and cannot provide water to the jets anymore. Under normal
Page | 23
MECH 3492 Fluid Mechanics and Applications
conditions, the jets should always be active, and when the user wants to descend, there
should still be some jet that slows their decent to a comfortable level. This can be set as a
minimum value that can be reached by both the operator of the jetpack and the supervisor
on the float craft nearby.
The calculations set in this report apply to a user weight of 100 kg. It is not expected to
encounter users over the mass of 140 kg at the greatest, and while more power would be
required, it can be expected that the pump output can compensate to achieve the required
head, or the user will simply have to perform at a height lower than the allotted maximum.
In either case, there is no expected significant safety issue in regards to safety with weight
capacity. As discussed, a lower weight user may be interested in using water jetpacks, and
the flow rate from the pump, natively or with the use of secondary valves, can be adjusted
so they do not experience too much thrust or height compared to a heavier user.
In designing the momentum exchange for the nozzle, it is feasible to have a varying number
of exit velocities so long as the momentum exchange fits the acceleration required to stay
afloat. As such, it would be beneficial to have a design which uses a lower outlet velocity
while still maintaining adequate acceleration. This would reduce the likelihood of injury as
a result of being struck by the exit jet, should it occur.
Not included in the design set in this report is the protective equipment worn by the user. As
designing the protective equipment itself was outside the scope of this analysis, the general
overview of what should be achieved will be described. As the hydraulic equipment itself
is expected to weigh in the range of 10 to 20 kg, it has considerable mass when involved in
an impact. The jetpack should have some sort of shoulder padding to prevent hard impacts
between the user’s shoulders and the support bar between the grips and the backpack.
The backpack itself should be strapped securely to the user in such a way that does not
restrict circulation, and distributes the load evenly over their body to improve comfort.
Inexperienced users are suggested to wear flotation devices in the event they enter the water
and are unable to swim or float without assistance. There will be a supervisor on hand for
aid at all times, but there should be an immediate sense of safety to prevent panic in such
a situation.
As a summary of the safety considerations, the design considers a maximum height of 5 m
with an expected performance weight of 100 kg (though it should be capable of supporting
more at lower performance). The thrust jets are designed for lower velocity outputs and
should have some minimum flow rate at all times to prevent free fall from occurring due to
lack of user input. They should also have some maximum flow rate, set by the supervisor to
account for the user’s experience and weight class to prevent excessive thrust. Additional
protective equipment such as padding and flotation devices are considered to maximize the
user’s comfort.
Page | 24
MECH 3492 Fluid Mechanics and Applications
8.
Conclusion
In summary, water jetpacks are now trending in the recreational sports industry. Due to the
abundance of water resources in Manitoba, it was determined that it is feasible to implement
this technology in the province. The main purpose of this project is to provide a preliminary
design of the hydraulic system on a water jetpack design. The designed water jetpack system
can propel a 100 kg person at approximately 5 meters. Upon designing the water jetpack
system, the safety of the operator was carefully considered, as it is one of the reasons why the
5 meter hovering height was used in the design calculations. The nozzle dimensions for the
hydraulic system were determined using theoretical and numerical methods. Subsequently,
the theoretical and numerical results were validated through CFD analysis using SolidWorks
Flow Simulation. The percent difference for the theoretical, numerical, and CFD results are
less than 5% and has an approximately exit velocity of 30 m s−1 . Furthermore, a horizontal
split case single stage double suction pump (type 8AE17Q) was chosen, as it satisfies the
required efficiency and overall volumetric flow rate of our water jetpack design. Lastly,
the designed water jetpack system was estimated to cost $25 000 (CAD), excluding the
watercraft and other several detailed components such as belts, backrest, bolts, and straps.
Page | 25
MECH 3492 Fluid Mechanics and Applications
9.
References
[1]
E. Grabianowski, "How Jet Packs Work," Howstuffworks, 1998-2015. [Online]. Available:
http://science.howstuffworks.com/transport/engines-equipment/jet-pack2.htm.
[Accessed 2 March 2015].
[2]
Vince Lewis, "Jetpacks," Vince's Worthwile , 18 November 2012. [Online]. Available:
http://www.vincelewis.net/jetpack.html. [Accessed 2 March 2015].
[3]
Wikipedia, "Jet Pack," Wikipedia, 27 February 2015. [Online]. Available:
http://en.wikipedia.org/wiki/Jet_pack. [Accessed 4 March 2015].
[4]
J. Giannetta, "Manitoba," August 2011. [Online]. Available:
http://www.aitc.sk.ca/saskschools/canada/facts/mb.html. [Accessed 28 February 2015].
[5]
T. Weir, "Manitoba," Historica Canada, 12 January 2015. [Online]. Available:
http://www.thecanadianencyclopedia.com/en/article/manitoba/. [Accessed 28 February
2015].
[6]
Government of Manitoba, "Serviced Beaches in Manitoba Provincial Parks," [Online].
Available:
http://www.gov.mb.ca/conservation/parks/pdf/beach_safety_provincial_map_2012.pdf
. [Accessed 1 March 2015].
[7]
X-Jetpacks, "X-Jetpack NX from Stratospheric Industries, Inc.," Stratospheric Industries,
Inc. , 2015. [Online]. Available: http://www.x-jetpacks.com/. [Accessed 1 March 2015].
[8]
L. Blain, "Zapata's Outrageous US$6,600 Flyboard-Aquaman meets Iron Man," Gizmag, 7
December 2011. [Online]. Available: http://www.gizmag.com/zapata-flyboard-jet-packwatersport-boots/20772/. [Accessed 1 March 2015].
[9]
Jetlev-Flyer, "Products & Pricing," Watersports GmbH, 2015. [Online]. Available:
http://www.jetlev-flyer.com/products-pricing.html. [Accessed 1 March 2015].
[10] Flit Boating, "China hot selling flying water jetpack with jet ski," 1999-2014. [Online].
Available: http://jxflt.en.alibaba.com/product/60097358541218097754/China_hot_Selling_Flying_Water_Jetpack_with_Jet_Ski_high_quality_competit
ive_price.html. [Accessed 4 March 2015].
[11] Ocean Premium, "Toys for Superyachts," 2014. [Online]. Available:
http://www.oceanpremium.com/toys-sales/extreme. [Accessed 4 March 2015].
Page | 26
MECH 3492 Fluid Mechanics and Applications
[12] P. J. Pritchard, Introduction to Fluid Mechanics, John Wiley & Sons, 2011.
[13] Amazon Supply, "Dixon Ductile Iron Wafer Style Butterfly Valve," [Online]. Available:
http://www.amazonsupply.com/dixon-ductile-butterfly-valvestainless/dp/B00CSYELAG. [Accessed 1 April 2015].
[14] Wikipedia, "Pump," Wikipedia, [Online]. Available: http://en.wikipedia.org/wiki/Pump.
[Accessed 3 April 2015].
[15] Z. Satterfield, "Reading Centrifugal Pump Curves," 2013. [Online]. Available:
http://www.nesc.wvu.edu/pdf/dw/publications/ontap/tech_brief/tb55_pumpcurves.p
df. [Accessed 22 March 2015].
[16] Peerless Pump Company, "Horizontal Split Case Pumps Single Stage Double Suction Type
AE," [Online]. Available: 2015. [Accessed 2 April 2015].
[17] Metals Depot, "Pipe," [Online]. Available:
http://www.metalsdepot.com/catalog_cart_view.php?msg. [Accessed 2 April 2015].
[18] Dixie Packing & Seal Company, "Tef Coat-Case of 12," [Online]. Available:
http://www.dixiepackingandseal.com/productdetails.aspx?id=262. [Accessed 2 April
2015].
[19] Cs Engineering Works, "Products and Services," [Online]. Available: http://www.cserefra.com/cs-engineering-works.pdf. [Accessed 2 April 2015].
[20] Jetlev-Flyer, "Stop Dreaming! Start Flying!," [Online]. Available: http://www.jetlevflyer.com/product. [Accessed 2 April 2015].
[21] D. Potente, "General Design Principles for an Automotive Muffler," 9 November 2005.
[Online]. Available: daydesign.com.au. [Accessed 29 November 2014].
Page | 27
MECH 3492 Fluid Mechanics and Applications
APPENDIX A
A.1
Sample Calculations, MATLAB Results, and CFD Results
Sample Calculations
Given two jets, the required acceleration of each is only half that of gravity. Since the inlet
velocity is a function of the outlet velocity, equation (2) can be substituted into equation
(10).
m
˙
−g = 9.81 m s−2 = 2 (Vi − Ve )
M
˙
Ae m
= 2Ve 1 −
Ai M
Ae ρAe
9.81
2
= Ve 1 −
2
Ai M
Assuming the hose has a diameter of 10cm, and splits into two equal sized sections, the hose
area can be found, and its half can be set to the inlet area for the sections leading up to the
nozzle entrance.
πDo2 π(0.10)2
Ao =
= 0.007 854 m2
4
4
Ao
= 0.003 927 m2
Ai =
2r
r
Ai
0.003927
=2
= 0.0707 m
Di = 2
π
π
An exit diameter can then be chosen. In this case, an exit diameter of 6 cm will be evaluated.
The total mass of the system is 154.2 kg, and the density of water is taken at 998 kg m−3 .
The exit velocity can be found from equation (21).
πDe2
π(0.06)2
=
4
4
2
= 0.002 827 m
s
v
u
g
M
u
2
·
=
Ve = t
Ae
ρA
1−
e
cos θ 1 − Ai )
Ae =
9.81
2
0.002827
)
0.003927
·
154.2
(998)(0.002827)
= 30.9362 m s−1
Ae
Vi = Ve
Ai
= 22.2706 m s−1
Having found the inlet and exit velocities, the total pressure changes between the inlet and
exit of the nozzle can and work required can be determined.
Pi 1 2
Pe 1 2
+ Vi + gzi =
+ Ve + gze
ρ
2
ρ
2
2
Ve
Vi2
Pi − Pe = ρ
−
2
2
Because the inlet and outlet of the nozzle are at the same height, there is no contribution
from gravity. Along with this, the exit enters the atmosphere, meaning its gauge pressure
Page | 28
MECH 3492 Fluid Mechanics and Applications
can be reduced to zero.
Ve2 Vi2
Pig = ρ
−
2
2
2 Ai
2
ρ Ve − Ve Ae
=
2 2
ρVe2 1 − AAei
=
2
!
2
2
ρQ
Ai
=
−1
2A2i
Ae
ρQ2 Di4
= 2 4
−1
π Di De4
The overall gauge pressure for any nozzle system at constant height can be found from the
above equation derivation. Substituting known values, we can find the gauge pressure to be
Pig = 229.893 kPa
When considering the addition of losses, the gauge pressure must be increased to overcome
these effects at the nozzle. A loss coefficient of K = 0.05 was chosen for a nozzle design that
has an included angle of 10◦ . The losses here amount to
30.93622
V2
= 23.9262
hlm = K e = 0.05
2
2
= 23.9262 · 998 = 23.878 kPa
The power required for the pump to achieve the requisite nozzle entry pressure can be found
from equation (26)
"
#
2
2
V
V
p
p
˙ pump = m
+
+ gz + htotal −
+
+ gz + htotal
W
˙
ρ
2
ρ
2
f
i
2
229893 22.2706
+
+ 9.81 · 5
= 174.5637
998
2
= 96 240 W = 96.240 kW
= 129.058 hp
Without including the losses from the hose, the total power required for the pump is found.
Using a numerical approach through MATLAB, the loss from the hose using the Colebrook
equation can be determined.
Page | 29
MECH 3492 Fluid Mechanics and Applications
A.2
MATLAB Results
Output for sample 1
Jet Angle
:
0.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.060000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.061212 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.002827 [m^2]
Inlet Velocity :
22.276223 [m/s]
Oulet Velocity :
30.939199 [m/s]
Nozzle Pressure:
253.923934 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.087479
m^3/hr
:
314.922683
gpm
: 1386.534590
Nozzle Mass Flow Rate
kg/s
:
87.303566
Overall Volumetric Flow Rate
m^3/s
:
0.174957
m^3/hr
:
629.845366
gpm
: 2773.069180
Overall Mass Flow Rate
kg/s
:
174.607132
Major Head Loss:
23.930850 [N.m/kg]
Minor Head Loss:
127.187769 [N.m/kg]
Total Head
:
678.785623 [N.m/kg]
Total Head
:
69.193234 [m]
Work
:118520.810858 [W]
Work
:
158.936407 [HP]
-----------------------------Output for sample 1
Jet Angle
:
30.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.060000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.061212 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.002827 [m^2]
Inlet Velocity :
23.937359 [m/s]
Oulet Velocity :
33.246332 [m/s]
Nozzle Pressure:
293.206103 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.094002
m^3/hr
:
338.406446
gpm
: 1489.928380
Nozzle Mass Flow Rate
kg/s
:
93.813787
Overall Volumetric Flow Rate
m^3/s
:
0.188004
m^3/hr
:
676.812892
gpm
: 2979.856760
Overall Mass Flow Rate
kg/s
:
187.627574
Major Head Loss:
27.632966 [N.m/kg]
Minor Head Loss:
145.207911 [N.m/kg]
Total Head
:
774.550188 [N.m/kg]
Total Head
:
78.955167 [m]
Work
:145326.972719 [W]
Work
:
194.883470 [HP]
-----------------------------Output for sample 1
Jet Angle
:
60.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.060000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.061212 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.002827 [m^2]
Inlet Velocity :
31.503337 [m/s]
Oulet Velocity :
43.754634 [m/s]
Nozzle Pressure:
507.847867 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.123713
m^3/hr
:
445.367929
gpm
: 1960.856022
Nozzle Mass Flow Rate
kg/s
:
123.465887
Overall Volumetric Flow Rate
m^3/s
:
0.247427
m^3/hr
:
890.735859
gpm
: 3921.712044
Overall Mass Flow Rate
kg/s
:
246.931774
Major Head Loss:
47.861700 [N.m/kg]
Minor Head Loss:
241.018581 [N.m/kg]
Total Head
: 1295.164289 [N.m/kg]
Total Head
:
132.024902 [m]
Work
:319817.215747 [W]
Work
:
428.874886 [HP]
-----------------------------______________________________
Output for sample 2
Jet Angle
:
0.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.050000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.118362 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.001963 [m^2]
Inlet Velocity :
13.891666 [m/s]
Oulet Velocity :
27.783331 [m/s]
Nozzle Pressure:
308.147871 [kPa]
Page | 30
MECH 3492 Fluid Mechanics and Applications
Nozzle Volumetric Flow Rate
m^3/s
:
0.054552
m^3/hr
:
196.388797
gpm
:
864.656232
Nozzle Mass Flow Rate
kg/s
:
54.443339
Overall Volumetric Flow Rate
m^3/s
:
0.109105
m^3/hr
:
392.777594
gpm
: 1729.312464
Overall Mass Flow Rate
kg/s
:
108.886678
Major Head Loss:
19.297838 [N.m/kg]
Minor Head Loss:
53.385212 [N.m/kg]
Total Head
:
507.689801 [N.m/kg]
Total Head
:
51.752273 [m]
Work
: 55280.655670 [W]
Work
:
74.131359 [HP]
-----------------------------Output for sample 2
Jet Angle
:
30.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.050000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.118362 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.001963 [m^2]
Inlet Velocity :
14.927566 [m/s]
Oulet Velocity :
29.855133 [m/s]
Nozzle Pressure:
355.818512 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.058620
m^3/hr
:
211.033496
gpm
:
929.133588
Nozzle Mass Flow Rate
kg/s
:
58.503175
Overall Volumetric Flow Rate
m^3/s
:
0.117241
m^3/hr
:
422.066993
gpm
: 1858.267176
Overall Mass Flow Rate
kg/s
:
117.006350
Major Head Loss:
22.283223 [N.m/kg]
Minor Head Loss:
60.918653 [N.m/kg]
Total Head
:
577.916346 [N.m/kg]
Total Head
:
58.910942 [m]
Work
: 67619.882020 [W]
Work
:
90.678262 [HP]
-----------------------------Output for sample 2
Jet Angle
:
60.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.050000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.118362 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.001963 [m^2]
Inlet Velocity :
19.645782 [m/s]
Oulet Velocity :
39.291564 [m/s]
Nozzle Pressure:
616.295742 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.077149
m^3/hr
:
277.735700
gpm
: 1222.808570
Nozzle Mass Flow Rate
kg/s
:
76.994508
Overall Volumetric Flow Rate
m^3/s
:
0.154298
m^3/hr
:
555.471401
gpm
: 2445.617140
Overall Mass Flow Rate
kg/s
:
153.989016
Major Head Loss:
38.595675 [N.m/kg]
Minor Head Loss:
100.921508 [N.m/kg]
Total Head
:
960.480687 [N.m/kg]
Total Head
:
97.908327 [m]
Work
:147903.475944 [W]
Work
:
198.338561 [HP]
-----------------------------______________________________
Output for sample 3
Jet Angle
:
0.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.040000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.175512 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.001257 [m^2]
Inlet Velocity :
9.529604 [m/s]
Oulet Velocity :
29.780013 [m/s]
Nozzle Pressure:
419.348751 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.037423
m^3/hr
:
134.721603
gpm
:
593.149282
Nozzle Mass Flow Rate
kg/s
:
37.347822
Overall Volumetric Flow Rate
m^3/s
:
0.074845
m^3/hr
:
269.443207
gpm
: 1186.298563
Overall Mass Flow Rate
kg/s
:
74.695645
Major Head Loss:
22.171229 [N.m/kg]
Minor Head Loss:
26.763118 [N.m/kg]
Total Head
:
541.408924 [N.m/kg]
Total Head
:
55.189493 [m]
Page | 31
MECH 3492 Fluid Mechanics and Applications
Work
: 40440.888543 [W]
Work
:
54.231232 [HP]
-----------------------------Output for sample 3
Jet Angle
:
30.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.040000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.175512 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.001257 [m^2]
Inlet Velocity :
10.240226 [m/s]
Oulet Velocity :
32.000706 [m/s]
Nozzle Pressure:
484.222229 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.040213
m^3/hr
:
144.767784
gpm
:
637.380383
Nozzle Mass Flow Rate
kg/s
:
40.132847
Overall Volumetric Flow Rate
m^3/s
:
0.080427
m^3/hr
:
289.535568
gpm
: 1274.760766
Overall Mass Flow Rate
kg/s
:
80.265694
Major Head Loss:
25.601130 [N.m/kg]
Minor Head Loss:
30.527614 [N.m/kg]
Total Head
:
617.201342 [N.m/kg]
Total Head
:
62.915529 [m]
Work
: 49540.093806 [W]
Work
:
66.433266 [HP]
-----------------------------Output for sample 3
Jet Angle
:
60.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.040000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.175512 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.001257 [m^2]
Inlet Velocity :
13.476895 [m/s]
Oulet Velocity :
42.115298 [m/s]
Nozzle Pressure:
838.697502 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.052924
m^3/hr
:
190.525119
gpm
:
838.839758
Nozzle Mass Flow Rate
kg/s
:
52.817797
Overall Volumetric Flow Rate
m^3/s
:
0.105847
m^3/hr
:
381.050237
gpm
: 1677.679517
Overall Mass Flow Rate
kg/s
:
105.635594
Major Head Loss:
44.342458 [N.m/kg]
Minor Head Loss:
50.497310 [N.m/kg]
Total Head
: 1030.738922 [N.m/kg]
Total Head
:
105.070227 [m]
Work
:108882.717854 [W]
Work
:
146.011725 [HP]
-----------------------------______________________________
Output for sample 4
Jet Angle
:
0.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.030000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.232663 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.000707 [m^2]
Inlet Velocity :
6.508541 [m/s]
Oulet Velocity :
36.158562 [m/s]
Nozzle Pressure:
663.895819 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.025559
m^3/hr
:
92.012332
gpm
:
405.109849
Nozzle Mass Flow Rate
kg/s
:
25.507863
Overall Volumetric Flow Rate
m^3/s
:
0.051118
m^3/hr
:
184.024663
gpm
:
810.219699
Overall Mass Flow Rate
kg/s
:
51.015726
Major Head Loss:
32.686039 [N.m/kg]
Minor Head Loss:
13.337810 [N.m/kg]
Total Head
:
748.794635 [N.m/kg]
Total Head
:
76.329728 [m]
Work
: 38200.302032 [W]
Work
:
51.226605 [HP]
-----------------------------Output for sample 4
Jet Angle
:
30.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.030000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.232663 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.000707 [m^2]
Page | 32
MECH 3492 Fluid Mechanics and Applications
Inlet Velocity :
6.993883 [m/s]
Oulet Velocity :
38.854903 [m/s]
Nozzle Pressure:
766.600860 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.027465
m^3/hr
:
98.873685
gpm
:
435.318863
Nozzle Mass Flow Rate
kg/s
:
27.409983
Overall Volumetric Flow Rate
m^3/s
:
0.054930
m^3/hr
:
197.747370
gpm
:
870.637726
Overall Mass Flow Rate
kg/s
:
54.819965
Major Head Loss:
37.742587 [N.m/kg]
Minor Head Loss:
15.207631 [N.m/kg]
Total Head
:
856.851962 [N.m/kg]
Total Head
:
87.344746 [m]
Work
: 46972.594880 [W]
Work
:
62.990250 [HP]
-----------------------------Output for sample 4
Jet Angle
:
60.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.030000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.232663 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.000707 [m^2]
Inlet Velocity :
9.204467 [m/s]
Oulet Velocity :
51.135928 [m/s]
Nozzle Pressure: 1327.791638 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.036146
m^3/hr
:
130.125087
gpm
:
572.911843
Nozzle Mass Flow Rate
kg/s
:
36.073566
Overall Volumetric Flow Rate
m^3/s
:
0.072292
m^3/hr
:
260.250175
gpm
: 1145.823686
Overall Mass Flow Rate
kg/s
:
72.147132
Major Head Loss:
65.372079 [N.m/kg]
Minor Head Loss:
25.116597 [N.m/kg]
Total Head
: 1446.980247 [N.m/kg]
Total Head
:
147.500535 [m]
Work
:104395.474626 [W]
Work
:
139.994331 [HP]
-----------------------------______________________________
Output for sample 5
Jet Angle
:
0.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.020000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.289813 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.000314 [m^2]
Inlet Velocity :
4.096429 [m/s]
Oulet Velocity :
51.205359 [m/s]
Nozzle Pressure: 1365.417451 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.016087
m^3/hr
:
57.911897
gpm
:
254.973212
Nozzle Mass Flow Rate
kg/s
:
16.054465
Overall Volumetric Flow Rate
m^3/s
:
0.032173
m^3/hr
:
115.823794
gpm
:
509.946425
Overall Mass Flow Rate
kg/s
:
32.108929
Major Head Loss:
65.549720 [N.m/kg]
Minor Head Loss:
5.742752 [N.m/kg]
Total Head
: 1431.336874 [N.m/kg]
Total Head
:
145.905900 [m]
Work
: 45958.694737 [W]
Work
:
61.630610 [HP]
-----------------------------Output for sample 5
Jet Angle
:
30.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.020000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.289813 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.000314 [m^2]
Inlet Velocity :
4.401899 [m/s]
Oulet Velocity :
55.023739 [m/s]
Nozzle Pressure: 1576.648265 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.017286
m^3/hr
:
62.230383
gpm
:
273.986548
Nozzle Mass Flow Rate
kg/s
:
17.251645
Overall Volumetric Flow Rate
m^3/s
:
0.034572
m^3/hr
:
124.460766
gpm
:
547.973095
Overall Mass Flow Rate
kg/s
:
34.503290
Major Head Loss:
75.690297 [N.m/kg]
Page | 33
MECH 3492 Fluid Mechanics and Applications
Minor Head Loss:
6.544421 [N.m/kg]
Total Head
: 1645.090660 [N.m/kg]
Total Head
:
167.695276 [m]
Work
: 56761.040354 [W]
Work
:
76.116555 [HP]
-----------------------------Output for sample 5
Jet Angle
:
60.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.020000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.289813 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.000314 [m^2]
Inlet Velocity :
5.793225 [m/s]
Oulet Velocity :
72.415313 [m/s]
Nozzle Pressure: 2730.834901 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.022750
m^3/hr
:
81.899790
gpm
:
360.586575
Nozzle Mass Flow Rate
kg/s
:
22.704442
Overall Volumetric Flow Rate
m^3/s
:
0.045500
m^3/hr
:
163.799580
gpm
:
721.173150
Overall Mass Flow Rate
kg/s
:
45.408884
Major Head Loss:
131.099440 [N.m/kg]
Minor Head Loss:
10.787532 [N.m/kg]
Total Head
: 2812.925776 [N.m/kg]
Total Head
:
286.740650 [m]
Work
:127731.818938 [W]
Work
:
171.288369 [HP]
-----------------------------______________________________
Output for sample 6
Jet Angle
:
0.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.010000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.346963 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.000079 [m^2]
Inlet Velocity :
1.984524 [m/s]
Oulet Velocity :
99.226184 [m/s]
Nozzle Pressure: 5156.760287 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.007793
m^3/hr
:
28.055542
gpm
:
123.522319
Nozzle Mass Flow Rate
kg/s
:
7.777620
Overall Volumetric Flow Rate
m^3/s
:
0.015586
m^3/hr
:
56.111085
gpm
:
247.044638
Overall Mass Flow Rate
kg/s
:
15.555240
Major Head Loss:
246.145888 [N.m/kg]
Minor Head Loss:
1.546384 [N.m/kg]
Total Head
: 5219.660026 [N.m/kg]
Total Head
:
532.075436 [m]
Work
: 81193.062577 [W]
Work
:
108.879897 [HP]
-----------------------------Output for sample 6
Jet Angle
:
30.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.010000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Nozzle Length :
0.346963 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.000079 [m^2]
Inlet Velocity :
2.132509 [m/s]
Oulet Velocity :
106.625473 [m/s]
Nozzle Pressure: 5954.513879 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.008374
m^3/hr
:
30.147642
gpm
:
132.733370
Nozzle Mass Flow Rate
kg/s
:
8.357596
Overall Volumetric Flow Rate
m^3/s
:
0.016749
m^3/hr
:
60.295285
gpm
:
265.466739
Overall Mass Flow Rate
kg/s
:
16.715193
Major Head Loss:
284.224789 [N.m/kg]
Minor Head Loss:
1.760713 [N.m/kg]
Total Head
: 6019.531284 [N.m/kg]
Total Head
:
613.611752 [m]
Work
:100617.626008 [W]
Work
:
134.928236 [HP]
-----------------------------Output for sample 6
Jet Angle
:
60.0
[deg]
Height
:
5.0
[m]
User Mass
:
100.0
[kg] (Maximum)
Equipment Mass :
15.0
[kg]
Water Mass
:
39.2
[kg] (Maximum)
Total Mass
:
154.2
[kg] (Maximum)
Inlet Diameter :
0.070711 [m]
Oulet Diameter :
0.010000 [m]
Nozzle Angle
:
10.0
[deg] (Total)
Page | 34
MECH 3492 Fluid Mechanics and Applications
Nozzle Length :
0.346963 [m]
Inlet Area
:
0.003927 [m^2]
Oulet Area
:
0.000079 [m^2]
Inlet Velocity :
2.806540 [m/s]
Oulet Velocity :
140.327015 [m/s]
Nozzle Pressure: 10313.520573 [kPa]
Nozzle Volumetric Flow Rate
m^3/s
:
0.011021
m^3/hr
:
39.676529
gpm
:
174.686939
Nozzle Mass Flow Rate
kg/s
:
10.999215
Overall Volumetric Flow Rate
m^3/s
:
0.022043
m^3/hr
:
79.353057
gpm
:
349.373877
Overall Mass Flow Rate
kg/s
:
21.998431
Major Head Loss:
492.291775 [N.m/kg]
Minor Head Loss:
2.892815 [N.m/kg]
Total Head
: 10390.070100 [N.m/kg]
Total Head
: 1059.130489 [m]
Work
:228565.238855 [W]
Work
:
306.505985 [HP]
-----------------------------______________________________
Page | 35
MECH 3492 Fluid Mechanics and Applications
A.3
Nozzle Design CFD Results
Figure A15: Nozzle 1 CFD Results
Page | 36
MECH 3492 Fluid Mechanics and Applications
Figure A16: Nozzle 2 CFD Results
Figure A17: Nozzle 3 CFD Results
Page | 37
MECH 3492 Fluid Mechanics and Applications
APPENDIX B
Pump Performance Curves
Figure B18: Performance curve of 6AE14N [16]
Figure B19: Performance curve of 8AE17A [16]
Page | 38
MECH 3492 Fluid Mechanics and Applications
Figure B20: Performance curve of 10AE16 [16]
Figure B21: Performance curve of 8AE17A [16]
Page | 39
MECH 3492 Fluid Mechanics and Applications
APPENDIX C
Engineering Drawings
Page | 40
D
C
B
A
8
9
1
1
5
2
2
6
4
3
7
J.T.
APPV'D
WEIGHT:
MATERIAL:
G.B.
P.S.
NAME
CHK'D
DRAWN
DATE
Handle pipe
Grip
Flow Control Handle
ISO 7380 - M5 x 16 --16N
6
7
8
3
1
1-APR-2015
1-APR-2015
REVISION
Straight Pipe
5
SCALE:1:16
DWG NO.
TITLE:
2
2
2
1
2
SHEET 1 OF 2
A4
Water Jetpack System
PART NUMBER:
DO NOT SCALE DRAWING
2
Nylon torsion bar
4
9
2
Nozzle
3
1
Y Branch
2
QTY.
2
PART NAME
6
Shoulder
5
1
ITEM NO.
1-APR-2015
UNLESS OTHERWISE SPECIFIED:
DIMENSIONS ARE IN MILLIMETERS
TOLERANCES:
2
4
C
B
A
D
C
B
A
1
1
10
A
2
2
SECTION A-A
A
10
3
59.59
60
70
90
85.40
J.T.
APPV'D
WEIGHT:
MATERIAL:
G.B.
P.S.
NAME
CHK'D
DRAWN
DATE
1-APR-2015
1-APR-2015
1-APR-205
UNLESS OTHERWISE SPECIFIED:
DIMENSIONS ARE IN MILLIMETERS
TOLERANCES:
4
SCALE:1:2
DWG NO.
TITLE:
PART NUMBER:
REVISION
SHEET 1 OF 1
Nozzle
DO NOT SCALE DRAWING
5
6
A4
C
B
A
D
C
B
A
1
156.94
1
93.44
A
A
2
2
144.24
147.41
R6.35
19.05
R11.68
80
16.51
3
2X
J.T.
APPV'D
WEIGHT:
MATERIAL:
G.B.
P.S.
NAME
CHK'D
DRAWN
DATE
1-APR-2015
1-APR-2015
1-APR-2015
SCALE:1:4
DWG NO.
TITLE:
SECTION A-A
SCALE 1 : 3
5
REVISION
SHEET 1 OF 1
Shoulder
DO NOT SCALE DRAWING
R50.80
PART NUMBER:
70
80
90.80
UNLESS OTHERWISE SPECIFIED:
DIMENSIONS ARE IN MILLIMETERS
TOLERANCES:
230.78
273.38
3.18
4
6
A4
C
B
A
D
C
B
A
1
74.72
1
64.50
A
2
2
SECTION A-A
304.80
102.79
3
A
304.80
J.T.
APPV'D
WEIGHT:
MATERIAL:
G.B.
P.S.
NAME
CHK'D
DRAWN
DATE
1-APR-2015
1-APR-2015
1-APR-2015
UNLESS OTHERWISE SPECIFIED:
DIMENSIONS ARE IN MILLIMETERS
TOLERANCES:
4
SCALE:1:4
DWG NO.
TITLE:
PART NUMBER:
REVISION
SHEET 1 OF 1
Y BRANCH-7
DO NOT SCALE DRAWING
5
6
A4
C
B
A
D
C
B
A
1
1
50.80
101.60
203.20
279.40
R76.20
A
2
2
SECTION A-A
SCALE 1 : 3
23.11
3
19.05
44.45
152.40
69.85
J.T.
APPV'D
WEIGHT:
MATERIAL:
G.B.
CHK'D
P.S.
NAME
DATE
1-APR-2015
1-APR-2015
1-APR-2015
UNLESS OTHERWISE SPECIFIED:
DIMENSIONS ARE IN MILLIMETERS
TOLERANCES:
33.40
6.35
26.64
3X
DRAWN
A
4
SCALE:1:4
DWG NO.
TITLE:
PART NUMBER:
REVISION
SHEET 1 OF 1
Handle pipe
DO NOT SCALE DRAWING
5
6
A4
C
B
A
D
C
B
A
1
1
2
2
609.60
4
7X
J.T.
APPV'D
WEIGHT:
MATERIAL:
G.B.
CHK'D
P.S.
NAME
DATE
1-APR-2015
1-APR-2015
SCALE:1:8
DWG NO.
TITLE:
PART NUMBER:
6.35
1-APR-2015
UNLESS OTHERWISE SPECIFIED:
DIMENSIONS ARE IN MILLIMETERS
TOLERANCES:
DRAWN
19.05
EQUAL SPACING OF 25.40
3
40.89
48.26
REVISION
SHEET 1 OF 1
Straight Pipe
DO NOT SCALE DRAWING
5
6
A4
C
B
A
D
C
B
A
1
1
2
2
366.14
3
J.T.
APPV'D
WEIGHT:
MATERIAL:
G.B.
P.S.
NAME
CHK'D
DRAWN
DATE
1-APR-2015
1-APR-2015
1-APR-2015
UNLESS OTHERWISE SPECIFIED:
DIMENSIONS ARE IN MILLIMETERS
TOLERANCES:
4
SCALE:1:4
DWG NO.
TITLE:
PART NUMBER:
REVISION
19.05
6
SHEET 1 OF 1
Nylon torsion bar
DO NOT SCALE DRAWING
5
A4
C
B
A