solar powered well pump, mechanical system design, cai williams
DESCRIPTION
3rd Year Report preceding "System Modelling of Rope Pump powered by hand, wind and solar. MEng Masters Thesis for Bristol University" thesisTRANSCRIPT
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Declaration
The accompanying research project report entitled: Solar Powered Well Pump: Mechanical System
Design is submitted in the third year of study towards an application for the degree of Master of
Engineering in Mechanical Engineering at the University of Bristol.
The report is based upon independent work by the candidate. All contributions from others have been
acknowledged at the start of the report. The supervisors are identified at the start of the report. The
views expressed within the report are those of the author and not of the University of Bristol.
I hereby declare that the above statements are true.
Name: Cai Williams
Date:
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Work Distribution
PV Cell and Motor Research
Pump and Mechanical System Review
Selection of Variable Universal Drill Motor
Theoretical Model Pump Generation
Prediction of Final Power Demands and Discharge Flow-rates
for Full Head
Analyse Results and Decipher which Motor
and PV Cell
Comparison of Theoretical Model to
Empirical Data
Design, Build and Test Model Rig
and Results Analysis
Assembly of all electronic parts with
Cost Analysis
Joint Work
Joint Work
Design, Build and Test Model Rig
and Results Analysis
Product Design Specification Generation
Product Design Specification Generation
Ben Stitt Cai Williams
Project Supervisor: Dr J.D. Booker
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Summary
The concept of integrating a well pump with a solar power installation was proposed as an
economically viable method of improving access to water for drinking and irrigation in areas with
poor infrastructure.
The rope-pump was selected as the most appropriate design for integration with a solar panel based on
cost, maintenance requirements, efficiencies, achievable heads and flow-rates. To assess the power
demands of the pump a theoretical model was developed and compared to a physical model based on
those supplied by the charity Pump Aid.
The model rope-pump was tested at an approximately constant rope velocity of 1m/s, rope diameter of
8mm, rising main diameters of 21mm and 40mm OD and for a range of heads up to 3m.
The slip flow for one of the specific configurations tested was turbulent leading to the breakdown of
the theoretical flow model in that case. Analysis of the empirical data proved that the frictional shear
force of the slip flow was. A constant systematic error between the expected and recorded torque (and
therefore power) reading was noted and integrated into the model. The mechanical power and
discharge rates of the rope-pump were extrapolated up to the full 10m head designed for and found to
be approximately 140W and 0.6l/s for the 40mm OD rising main.
The 40mm rising main was found to have an efficiency over 3 times that of the 21mm OD rising main.
Considerable scope for improvements to the rope-pump efficiency was also apparent.
Acknowledgements
The author wishes to acknowledge the vital role of Dr Booker, Bobby Lambert, Pump-Aid, Solar-
Centurary and the technical staff in the workshop and hydraulics laboratory whose expertise provided
an indispensable resource and without which this project would not have been completed. Benjamin
Stitts hard work and lateral thinking were also key in overcoming the many problems encountered
during the project.
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Contents Summary........................................................................................................................................................ 1 Acknowledgements........................................................................................................................................ 1 Contents ......................................................................................................................................................... 2 Notation.......................................................................................................................................................... 3 1. Introduction........................................................................................................................................... 4 1.1. Background .......................................................................................................................4 1.1. Objectives .........................................................................................................................4 1.2. Research Methodology .....................................................................................................5 1.3. Summary of Chapters .......................................................................................................5
2. Research and Review............................................................................................................................ 6 2.1. Product Design Specification............................................................................................6 2.2. Pump Review....................................................................................................................7 2.2.1. Pump Classification 7 2.2.2. Linear Motion Pumps 7 2.2.3. Rotary Motion Pumps 9
2.3. Concept Comparison and Selection ................................................................................11 2.4. Failure Modes and Effects Analysis (FMEA) ................................................................12 2.5. Research and Review Summary .....................................................................................13
3. Theoretical Model ............................................................................................................................... 13 3.1. Pressure Gradient Model.................................................................................................13 3.2. Slip Velocity Profile Model Derivation..........................................................................14 3.3. Slip Velocity Profile Model Analysis and Modification ................................................15 3.4. Slip Flow Derivation.......................................................................................................17 3.5. Torque and Power Demand Derivation ..........................................................................19 3.6. Theoretical Model Summary ..........................................................................................21
4. Design & Build .................................................................................................................................... 21 4.1. Preliminary experiment...................................................................................................22 4.2. Model Parts .....................................................................................................................22 4.3. System Integration Problems ..........................................................................................24 4.4. Design and Build Summary............................................................................................25
5. Experimental Methodology................................................................................................................ 25 5.1. Initial Methodology ........................................................................................................25 5.2. Methodology Modifications............................................................................................25 5.3. Model characteristics ......................................................................................................26 5.4. Experimental Methods Summary ...................................................................................26
6. Results and Analysis ........................................................................................................................... 27 7. Discussion ............................................................................................................................................ 29 7.1. Error Analysis .................................................................................................................29 7.1.1. Torque and Power Errors 29 7.1.2. Delivered Flow-rate Errors 29 7.1.3. Rope Slip Errors 29 7.1.4. Efficiency and Power Errors 30
7.2. Comparison of Model with Empirical Data....................................................................30 7.2.1. Model of Delivered Volume Flow-rate 30 7.2.2. Model of Torque and Power Demands 30 7.2.3. Model of Efficiencies 31
8. Conclusions and Future Work........................................................................................................... 33 8.1. Findings...........................................................................................................................33 8.2. Future Work ....................................................................................................................35
Appendix A .................................................................................................................................................. 36 Appendix B .................................................................................................................................................. 37 References .................................................................................................................................................... 39
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( )( )
( )
2
-2
2 2
2
Cross Sectional Area ( )
Aspect Ratio
Diameter
Tensional Force
Gravitational Constnt ( )
Head Lost to Friction
Current ( )
Correction factor
Spring constant ( )
Length (
f
A m
AR
D m
F N
g ms
H m s
I A
k
K kgs
L m
=
=
=
=
=
=
=
=
=
=
( )
-1
-1
3 -1
)
Mass ( )
Number Of Pistons Per Unit Length ( )
Power ( )
Re Rynolds Number
Time Period ( )
Torque
Velocity ( )
Volume Flow Rate ( )
Voltage ( )
Spring Extension For 0.5kg Load
m kg
N m
P W
t s
T Nm
u ms
v m s
V V
=
=
=
=
=
=
=
=
=
=
-3
1
( )
Efficiency (%)
Dynamic Viscocity or Friction Coefficient
Density ( )
Argument ( )
Rotational Velocity ( )
m
kgm
rad
rads
=
=
=
=
=
1
2
Indexes
Position Under Lower Washer
Position Above Lower Washer
Position Under Upper Washer
Rising
Return
Bearing
Delivered
Electrical Or Motor
Distance From Final Water Level To Ri
b
d
e
fl
i
ii
iii
x
x
x
x
x
x
=
=
=
=
=
=
=
=
= sng Main
Guide
Head
Distance From Initial Water Level To Risng Main
Ideal Volume Flow Rate
Mechanical
Null
Normalised
Original
Pulley
Piston Or Washer
Rope
Rising Main
g
h
il
id
m
nu
no
o
p
pi
r
rm
s
x
x
x
v
x
x
x
x
x
x
x
x
x
=
=
=
=
=
=
=
=
=
=
=
=
Shaft
Slip
Spring
Tachometer
Volumetric
Water
Water in Gap Between Piston and Rising Main
Water in Main Section of Rising Main
h
sl
sp
t
v
w
wg
wm
x
x
x
x
x
x
x
=
=
=
=
=
=
=
=
Notation
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1. Introduction
1.1. Background I have always had a keen interest in world politics and development in particular. My perception of gross global
inequalities has inspired me into the field of development engineering (engineering for developing counties),
which I believe is vital to help alleviate poverty. After several enquiries to various intermediate technology
NGOs I was fortunate to find a third year project from Bobby Lambert (ex-CEO of Red-R) which gave me a
real opportunity to develop my skills and has solidified my commitment to working in this field. Lambert was
the CEO of Registered Engineers for Disaster Relief (Red-R) and has over twelve years practical experience
developing water supplies and other basic amenities for rural communities in developing countries including 8
years of academic and field based research, mainly in Zimbabwe in the late 1980s [1].
Based on this experience Lambert put forward his proposal, in the Solar Pumping for Sustainable Food
Production concept paper [1], for the integration of a small solar photovoltaic panel with simple proven
pumping technology to draw water from a well. Lambert proposed that the fall in the cost of photovoltaic cells
meant that it might now be an economically viable method of producing sufficient water for irrigation and
domestic use at household or small community level. Income from the irrigated land would mean that the
package would have a payback period of several years [1]. The package would be aimed at developing
countries where water scarcity is a major constraint on food production, where modest amount of groundwater
is available within 30 metres of the surface and where there is poor access to electric or other sources of
power. [1]. Lamberts research lead him to the conclusion that the package would the following outcomes:
- Improved family nutrition through economically viable household food production
- Improved health associated with sufficient clean water
- Improvements in household economics through sale of irrigation produce
- Improved opportunities for education & other economic activities through reduction in labour
required for food production & water collection
- Improved electricity availability for domestic and small community use
- Enhanced attractiveness of solar power as a viable energy source, through adding another level of
economically viable functionality
- Improved environment through reduced soil erosion associated with well watered soil [1]
The design brief, therefore, was to investigate the technical package and to produce a detailed prototype design.
Solar-Aid, a solar power charity set up by the UKs leading solar panel supplier, Solar-Century, also pledged
their technical support for the project.
1.1. Objectives My research partner Ben Stitt concentrated on the electrical system i.e. solar panel and motor, this report
concentrates on the mechanical system i.e. pump and coupling. To fulfil the project brief this reports objectives
were to:
Generate a Product Design Specification (PDS) through a dialogue with Bobby Lambert, Solar-Aid and
other stakeholders
Carry out a review of appropriate designs, to generate a range of concepts for the mechanical system and to
make a final selection.
Generate detailed drawings of the selected system
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Model, both theoretically and physically, the selected integrated design to determine the power and flow-
rate characteristics
Analyse the final design based on the findings
1.2. Research Methodology
A Gantt chart was generated to explicitly identify a timescale for the project to ensure effective co-
ordination with my research partner Ben Stitt.
A shared access folder on the G: drive facilitated effective knowledge management of our project.
Relevant information was gathered from a breadth of resources
A Failure Modes and Effects Analysis (FMEA) of the selected system was carried out
A CAD model was generated in order to explicitly identify the chosen design and to aid the manufacture of
the model.
A theoretical model of the torque and flow characteristics of the pump was generated
A prototype was assembled and analysed to confirm and develop the concept selection
1.3. Summary of Chapters
2 Research and Review Product Design Specification (PDS) Mechanical system selection from a comprehensive review of pump, manual drive and coupling
mechanisms
3 Theoretical Model Slip and delivered fluid flow model of the rope-pump Force and moment model of the integrated system
4 Design & Build
Details of the manufacture of a third scale physical model rope-pump and the problems overcome
5 Experimental Methodology
Details of the methods used to obtain empirical data from the physical model and the problems overcome
6 Results and Analysis Illustration of the analysis and results of both the empirically recorded data and the data predicted by
the theoretical model
7 Discussion
Analysis of the errors inherent to the recorded data Comparison of empirical data and the theoretical model Extrapolated estimations of the delivered flow-rates and the full torque and power requirements for the
full 10m head 8 Conclusions & Future Work
Final conclusions of the report findings based on the original objectives Recommendations for the most effective future research based on experience from the project
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2. Research and Review
2.1. Product Design Specification The Product Design Specification (PDS) detailed in
Table 1 was generated through a dialogue with Bobby Lambert (the project proposer), Solar-Aid and Pump-Aid
(NGO stakeholders).
Table 1 - Product Design Specification (PDS)
The pump will need to be powered primarily by photovoltaic cells but with a fail safe capability to be easily driven manually.
The pump will need to provide between 1000 and 5000 litres of water per day to irrigate an area of 0.1 of a hectare, which is sufficient to provide food for one family.
The water will need to be pumped from an operating depth of 10m and a maximum 30m depth and supplied though a simple surface irrigation system (pipe with holes in) 20m long with a minimum 40mm diameter.
The electricity from the solar panel will potentially be required for lighting, battery charging and low power uses.
Performance
The package will need to be put together with security in mind as theft may be a problem in the target areas
The package is designed to fit into the social, economic, agricultural, hydrological and environmental circumstances in large parts of rural Eastern Africa and other semi arid areas.
Where water scarcity is a major constraint on food production
Where modest amount of groundwater is available within 30 metres of the surface
Where there is poor access to electric or other sources of power Environment
The specific operating climate of Tanzania may be designed for as this is where the field trials will take place
Product Life
Span
Aim at a minimum of 15 years allowing for minor maintenance work, considering that the package may only be self financing after a 10 year period
Life in Service /
Duty Cycle
Expected to be in use constantly during day light hours as well as up to 1 hour of manual use a day during peak dry season which may be up to 150 days a year
Target Costs Must be kept to an absolute minimum, with a target of 500
Focused on the prototype Quantity
The long term intention however is for the production of several thousand
Maintenance It is essential that the package is maintainable using basic artisan skills (with the exception of the photo-voltaic cells)
Marketing Not concerned with marketing
Packaging None
Size and Weight
Restrictions
The package will be assembled by a few trained individuals without any specialist lifting equipment.
Shipping The package will be assembled on or in close proximity to the target site
It is essential that the package is as simple to fabricate as possible (using basic light engineering and welding shop technology) and to minimising the number of electrical components.
The package will be manufactured one at a time.
Manufacturing
processes
The photo-voltaic cells and motor will be bought in.
Materials Made using readily available materials in the target location.
Safety Serious consideration must be given to the fact that the package will be used by untrained individuals and sometimes by children.
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2.2. Pump Review The most important design consideration is to keep cost, complexity and maintenance to a minimum. Much
work has gone into the design of hand pumps with exactly these considerations in mind. To this end a
comprehensive review of available hand pumps along with pumps already utilised in automated systems
follows.
2.2.1. Pump Classification
All pumps can be divided into two broad categories, dynamic pumps and displacement pumps, the latter are
pumps:
In which energy is periodically added by application of force to one or more movable boundaries of any
desired number of enclosed, fluid-containing volumes, resulting in a direct increase in pressure up to the
value required to move the fluid through valves or ports into the discharge line [2]
All displacement pump involve enclosed, fluid-containing volumes [2] which are then forcibly moved to
create the pumping action. To create these enclosed volumes mechanical contact or very close fits are required
leading to inevitable friction losses, these losses are, however, mediated by the lubrication from back or slip
flow. At high pumping heads these frictional losses can be relatively low compared to dynamic pumps.
Dynamic pumps are pumps:
In which energy is continuously added to increase the fluid velocities within the machine to values greater
than those occurring at the discharge such that subsequent velocity reduction within or beyond the pump
produces a pressure increase [2]
A displacement pumps discharge rate is not affected as greatly by head compared to dynamic pumps making
the former more suited to higher heads.
2.2.2. Linear Motion Pumps
Nearly all linear motion pumps are positive displacement pumps.
Conversion from the rotational output of the motor would add
complexity and therefore whole life time cost. The most widely used
conversion method is that of the nodding donkey design (see
Figure 1).
Reciprocating positive displacement pumps create a cyclic
load on the motor which, for efficient operation, needs to be
balanced. Hence, the above ground components of the solar
pump are often heavy and robust, and power controllers for
impedance matching often used. [3]
This added complexity should be balanced against the familiarity of linear positive displacement pumps to the
end user. Positive displacement pumps are the most common type of hand pump, and are therefore common
within the target communities. Existing support networks could therefore be taken advantage of to ease market
penetration. Linear motion positive displacement pump designs can be split in to three main types based on their
pumping method.
Figure 1 - Reciprocating positive
displacement pump system [3]
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Figure 3 - The low lift treadle pump [5]
Reciprocating Piston Pumps
These pumps involve a reciprocating piston that forms a seal
with a cylindrical casing (see4Figure 2). The piston carries a
non-return valve that allows water past the piston on the
downward stoke while the non-return foot (also known as
the suction or check) valve at the bottom of the cylinder
keeps the fluid from escaping. The piston valve then closes
on the upward stroke forcing the fluid up and out of the
cylinder while the foot valve at the bottom of the cylinder
opens allowing fluid in.
This is by far the most common form of hand pump; several
different pumps utilize the design including:
o Treadle pump This pump employs twin cylinders driven by a treadle
(see5Figure 3). These pumps utilise the most powerful
muscles in the body, the leg muscles, they also have a
relatively constant output compared to a single cylinder
pump making them one of the most efficient hand
pumps available. Much work has gone into developing
the efficiencies of the pump, over 60,000 have been sold
in Tanzania, Mali and Kenya [6]. However, the treadle
pump is designed to be located at ground level and is
therefore a suction pump which have a maximum
practical lift height of approximately 8m [2]. This limit
is imposed by the maximum head achievable by a
vacuum from atmospheric pressure compounded by
practical manufacturing limits.
o Tara Direct Action Hand Pump7 This pump involves the user directly lifting the piston
which is located under the water via a long connector
rod running the length of the borehole, see Figure 5.
This removes the limits of a suction pump but introduces
the limit of the maximum weight a human can lift; this
pump is therefore best suited to heads from 7-15m [7].
The design is very simple and therefore low in cost and
maintenance.
o Afridev Hand pump The Afridev Hand pump employs a mechanical multiplier (see Figure 6) increasing the maximum lift
to over 45m [7]. This adds to the complexity and therefore the cost and maintenance of the design.
o Rower Hand Pump The rower pump attempts to utilise more muscle power from a rowing action (see Figure 4). However,
the pump has been found to be under half as efficient as the treadle pump at heads above 5m [8]. The
rower pump is also designed to be located at ground level and so is limited to heads under 8m.
Figure 2 - Basic design of a reciprocating
positive displacement pump [4]
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Figure 7 - Diaphragm hand pump [10]
Diaphragm Hand Pump
This is a compact design that can fit into
awkward shaped wells (see Figure 7). The
design is simpler than a piston type pump,
is not adversely affected by abrasive
sediment in the pumped fluid and
therefore requires far less maintenance.
However the pump is designed to be
installed at ground level and is therefore
limited to heads under 8m.
Shaduf
A counterweight is employed similar to a
nodding donkey, essentially a rope and
bucket [9]. Too difficult to mechanise.
2.2.3. Rotary Motion Pumps
The main advantage of these pumps is that no mechanical conversion to the motor is needed (other than
gearing) cutting down the complexity of the design. The main types are:
Centrifugal Pump
A centrifugal pump is a rotating machine in which flow and pressure are generated dynamically. The
inlet is not walled off from the outlet as is the case with positive displacement pumps, whether they are
reciprocating or rotary in configuration. Rather, a centrifugal pump delivers useful energy to the fluid or
pumpage largely through the velocity changes that occur as this fluid flows through the impeller and
the associated fixed passageways of the pump [see Figure 8]; that is, it is a rotodynamic pump. All
impeller pumps are rotodynamic, including those with radial-flow, mixed flow, and axial-flow
impellers: the term centrifugal pump tends to encompass all rotodynamic pumps. [2]
Figure 5 - The medium lift 'Tara'
direct action handpump [7]
Figure 6 - High lift 'Afridev'
hand pump [7]
Figure 4 - The low lift rower pump [5]
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Figure 8 - End suction, single-stage centrifugal pump [7]
Figure 10 - Example 'Mono' solar pump system schematics [11]
By far the most widely used pump, it is a dynamic
as opposed to a displacement pump. To achieve
large heads centrifugal pumps can be connected in
series, this obviously adds complexity and cost to
the design. The impeller and casing of the pump
are complex and therefore manufacture and
maintenance are costly compared to other simpler
designs. Centrifugal pumps also have a high
running speed requiring considerable gearing if
powered by a human.
Helical Progressive Cavity (Mono) Pump
The "helical progressive cavity" alias "Mono"
pump [see10Figure 9] is unique in being a
commercially available rotary positive
displacement pump that readily fits down
boreholes. It also has a reputation for
reliability, particularly with corrosive or
abrasive impurities in the water. The reasons
for this relate to good construction materials
combined with a mechanically simple mode of operation. [10]
The Mono pump consists of a solid single helix which rotates between a
flexible double helix stator. Figure 9 shows how this creates a water filled
cavity which progresses a long a helical loci, hence the name.
Pumps of this kind are usually driven at speeds of typically 1000 rpm
or more, and when installed down a borehole they require a long drive
shaft which is guided in the rising main by water lubricated "spider
bearings" usually made of rubber. [10]
The lubricating slip flow combined with the small radius of the mechanical
contact between the stator and rotor
minimises the frictional torque losses
resulting in a high efficiency. The
Mono Pump company is the market
leader in solar powered water pumps.
The complex design does however
make the pump expensive. A rough
quote of 4000 was given from Mono
[11] for a similar solar pump system
to that shown in Figure 10 for a 10m
head (PV included).
Figure 9 Helical progressive
cavity or 'Mono' pump [10]
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Figure 14 - 'Permaprop'
tooth pump [10]
Vane, Gear and Lobe Pumps
Many different types of a flexible vane, lobe and gear pumps exist (see Figure 11, Figure 12, Figure 13 and
Figure 14 for a selection of typical designs) they are all positive displacement pumps and employ a simple
revolving door type pumping action. They are generally suited to surface mounting and therefore are
limited to an 8m lift height and tend to have considerable frictional losses. Their cost vary according to
complexity but tend not to be competitive with other pumps of comparable efficiencies, they are most suited
to viscous liquids.
Rope-Pump
The rope-pump is a positive displacement pump adapted from of an ancient
design and has taken on many incarnations including the chain and washer
pump. The simple rope-pump has proven to be a highly successful low whole
life time cost well pump with over one hundred thousand models inuse
worldwide [10].
The simple pumping action is achieved by pistons that pass up a vertical pipe
section which doubles as the rising main, the bottom end of which is
submersed in the reservoir of water (see12Figure 15). As the pistons pass into
the rising main they force water along with them due to the close fit of the
pistons in the rising main; the internal diameter of the pipe is just 1-2mm
greater than the outer-diameter of the pistons. The pistons are attached at
regular intervals along an endless loop of rope that passes over a v-section
pulley attached to the drive shaft, the rope then returns to a guide which turns
the rope 180 degrees and aligns it with the bottom of the pipe.
The pumping force is divided between each piston meaning the pressure
remains relatively low throughout. This not only results in drawn heads of up
to 60m [13], but also allows the use of plastic as the rising main and piston
material easing removal and therefore maintenance. Uniquely for a
displacement pump the maximum torque is only achieved once the rope-pump
has fully primed. This makes the pump particularly suited to motors that have a
lower start up torque than at full speed.
2.3. Concept Comparison and Selection The full mechanical systems were compared in Table 2 against the four most important categories identified and
weighted through in line with the PDS.
Figure 11 - Flexible
vane pump [10]
Figure 13 - Single (left) and
Multiple (right) lobe pumps [2] Figure 12 - External (left) and
internal (right) gear pump [2]
Figure 15 - Rope-pump [12]
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Table 2 - System Comparison
Bobby Lamberts original suggestion (the rope-pump) was therefore proven to be the most suitable design. The
relatively low efficiency was far outweighed by its:
suitability to both motor and manual operation
high achievable head
simple, light design resulting in
o low cost
o easy removal and maintenance
The linear motion pumps costly requirement for a mechanical conversion to be driven by a motor left them at
serious disadvantage despite their other wise low cost and ease of manual operation. At the other end of the
scale the other rotary motion pumps high cost and large gearing requirement to be driven by hand made them
unsuitable. The rope-pump uniquely satisfies the majority of the demands of the PDS.
In accordance with the PDS the simplest and cheapest ancillary components were selected from the options
reviewed in Table 3 (see Appendix A):
A simple bolt pinning the solid drive shaft to the tubular driven shaft; as no dynamic decoupling
requirement of the crank or motor from the shaft was identified in the PDS.
A two limb crank; the strongest and most easily manufactured option.
The simple and cheap journal bearing; despite of the inherent low relative efficiency.
Plastic pipe spacers either side of a set-screw fixed pulley-hub for flexibility during testing
2.4. Failure Modes and Effects Analysis (FMEA) Due to the emphasis on minimising cost and the ease of repair of the selected system a FMEA in its usual
capacity was not deemed necessary. The most important function identified by the PDS was the supply of
enough drinking water. Therefore the manual drive, coupling and pump must be reliable with simple
maintenance and spare part requirements.
Using the FMEA framework the attractive simplicity of the rope-pump and selected mechanical system create a
low score for detect-ability (D) and severity (S) due to the ease of repair. Therefore, despite the relatively high
occurrence (O) score for the cheaper selected system components the over all risk priority number (RPN) is low
compared to other more reliable but complex system component options.
Pump Type Cost
(low)
Maintenance
Requirement
Manual [8]
Operation
Drawable
Head
Efficiency Total
Treadle Pump Tara Pump Afridev Pump
Rower Pump
Diaphragm Pump
Centrifugal Pump
Mono Pump Vane, Gear and Lobe Pumps
Rope-pump
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2.5. Research and Review Summary The PDS identified cost, maintainability, a 10m achievable head and a fail safe supply of drinking water as the
most important design specifications. The rope-pump bolted to either a simple hand crank or motor shaft
employing journal bearings was selected as the system that best satisfied the PDS.
3. Theoretical Model Although over 100 000 mainly hand powered rope-pumps have been installed worldwide no detailed hard data
is available describing the power demands and achievable discharge flow-rates for the rope-pump. In an attempt
to understand the power and flow characteristics of the rope-pump a theoretical model was generated. The only
other hydrodynamic model of the rope-pump was proposed by Smulders et al. [14]. This model, although
reasonable, is based on large simplifications the largest of which are that
the wall friction (hydrodynamic and mechanical) is assumed to be zero.
the tension force in the rope above the outflowis simply the weight of the water column above the level
in the well. [14]
i.e. the pump is assumed to be perfectly mechanically efficient and all frictional losses over the guide, at the
bearings and from the slip flow on the pistons are ignored.
In addition the absence of wall friction [14] leads to an assumed zero velocity gradient between the piston and
rising main. Water is not inviscid it has a dynamic viscosity of 0.00089kg/ms, as a result it will have no velocity
at the rising main and will equal the rope velocity at the piston.
3.1. Pressure Gradient Model A pressure gradient, created by the weight of the water above the piston, exists across each piston (see Figure
16). Assuming that the pressure difference between the head and rising main is negligible the pressure at entry
and exit are equal.
The pressure of the weight of water in the pump must therefore be fully supported by the rope and pistons. The
pressure must therefore only vary between each piston. Therefore starting from Bernoulli [15] and assuming a
constant water density and pipe diameter.
2 2
,2 2ii ii iii iii
ii iii f wm
w w
p u p ugz gz H
+ + = + + + (1)
Based on conservation of mass and assuming pi is small
w rm ii w rm iiiA u A u = (2)
ii iiiu u = (3)
( ) ,ii iii iii ii f wmw
p pg z z H
= + (4)
,w
ii iii w f wm
gp p H
N
= + (5)
For both laminar and turbulent flow the velocity gradient (du/dr) at the wall is higher in the entry than for fully developed flow and so the shear stress at the wall is greater. The value of dH/dl is also greater, so the total head loss [near pipe entry] is somewhat larger than if the flow were fully developed [15]
Therefore the total frictional loss must be very small to be negligible, assume (confirmation in section 3.4)
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F1p F2p
Dp/2
Dg/2
Lh
1/N
Pulley
Rising Main
Guide
Piston
pi
pi
Dpi
Drm
Lp
iii
ii i
ur
Free Water Surface
Free Water Surface
Lrm
Figure 16 - Model and geometric definitions of the rope-pump
fwm
gH
N (6)
w
ii iii
gp p
N
= (7)
As stated earlier
iii ip p= (8)
w
ii i
gp p
N
= (9)
Approximating a linear pressure gradient
wg ii i
pi
dp p p
dz L
= (10)
wg w
pi
dp g
dz NL
= (11)
3.2. Slip Velocity Profile Model Derivation
To model the slip flow a free body diagram of an
infinitesimal annular section between the piston
and the rising main was analysed (see Figure 17).
Assuming:
laminar flow
a constant density
negligible heating due to friction and
therefore a constant viscosity
steady state conditions
Conservation of momentum states that:
( )
( )
20 2 2 2
2 2 2
wg
wg wg w
wg
wg wg
p r rp r r p r r z g r r z
z
r zr z r r z
r
= +
+ +
(12)
2 2 2 0wg wgw
p rr r z g r r z z r
z r
+ = (13)
( )0
wgwg
w
rpr gr
z r
+ = (14)
The shear force of the slip flow is related to the slip velocity [15] by:
wg
wg w
u
r
= (15)
Combining with equations 11 and 14
wg ww w
pi
u gr r gr
r r NL
=
(16)
-
15
Defining
1 1wpi
w
gB
NL
= +
(17)
2
2wgu r
r B Cr
= + (18)
12wgB
u r r C rr
= + (19)
2 ln4wgB
u r C r E = + + (20)
Boundary conditions defines
; 02rm
wg
Dr u= = (21)
2
0 ln4 4 2
rm rmD DB C E = + + (22)
2
ln4 4 2
rm rmD DBE C = (23)
22 1ln 1 ln
4 4 4 2w rm rm
wgpi
w
g D DBu r C r C
NL
= + +
(24)
22 2ln44
rmwg
rm
B rDu r C
D
= +
(25)
Boundary condition defines
;2pi
wg r
Dr u u= = (26)
22
ln4 44pipirm
r
rm
DDB Du C
D
= +
(27)
( )2 216
ln
r rm pi
pi
rm
Bu D D
CD
D
+ = (28)
Combining with equations 17 and 27
( )2 222
1 116 21 1 ln44
ln
wr rm pi
piw wrmwg
pi piw rm
rm
gu D D
NLg rDu r
NL D D
D
+ + = + +
(29)
3.3. Slip Velocity Profile Model Analysis and Modification At 25C water density (w) is 997kg/m
3, viscosity (w) 0.00089kg/ms and the gravitational constant (g) is
9.80665m/s2 [16]. Defining the piston spacing (N) as 1/0.7m, the piston length (Lpi) as 0.005m, The rising main
diameter (Drm) as 0.036m, the piston diameter (Dpi) as 0.035m and a rope speed (ur) of 1m/s. The velocity
distribution predicted by the model (shown in Figure 18) was dominated by the pressure gradient across the
piston, resulting in flows peaking at around 47m/s. This is most likely down to the assumption that the pressure
gradient exists only across the length of the piston. In fact the slip flow will extend beyond the bottom of the
piston and will not return to the static pressure until the flow has been dissipated as shown in Figure 19. Based
on the average flows predicted by Smulders et al [14]
pwg2rr
pwg2rr+((pwg2rr)/z)z
C l
r=D/2
2rz+((wg2rz)/r)r
wg2rz g2rrz
r
z
z
Figure 17 - Free body diagram of an infinitesimally small annular
section between the piston and the rising main
-
16
-5
-4
-3
-2
-1
0
1
2
0.0175 0.0176 0.0177 0.0178 0.0179 0.018
Radius (m )
Slip
velo
cit
y (
m/s
)
Mode Predictionl
Smulders et al.
Figure 20 - Graph of water velocity against radius between the piston
and the rising main for kLpi=0.05m
(30) A reasonable estimation of the length over which the
pressure gradient truly acts is one 10 times the length
of the piston (i.e. if k= 10, Lpi now replaced with
kLpi=0.05m). Based on this modification we obtain a
much more reasonable water velocity distribution
(shown in Figure 18) with a much more realistic
velocity profile than that predicted by Smulders et al.
The laminar flow assumption if false would lead to the
breakdown of the model. Smulders et al. also assume
laminar flow
The flow velocity can be estimated from
[(2g/N)] and for N = 1 is equal to about 4
m/s. If the gap width [is equal to] 0.3 mm, then
the Reynolds number of the gap flow is:
Re = [(2g/N)*0.3*w /w]1200, well within the
laminar flow range. [14]
A test of the laminar flow assumption for the model now
follows:
By definition [15]:
( )Re
2w wg rm pi
wg
w
u D D
= (31)
2
2
2
-
rm
pi
D
wg
D
wg
rm pi
u r
uD D
=
(32)
From equation 27
2
2 2
2
2 21
1
h rm hwg
pi rm pi rm
rm
gL D gLu
D L N D L N
D
= = =
-50
-40
-30
-20
-10
0
10
0.0175 0.0176 0.0177 0.0178 0.0179 0.018
r (m)
u (
m/s
)
Figure 18 - Graph of water velocity against radius
between the piston and the rising main
Lpi
Dpi
Drm
Flow Lines
Rising Main
Piston
Effective length of total
pressure drop 10Lpi
Figure 19 - Modelled flow through gap
between piston and rising main
-
17
2 2 2 222
2 2 2 2
2ln44
rm rm rm rm
pi pi pi pi
D D D D
rmwg
D D D D rm
B rDu r r r r C r
D
= +
(33)
The inverse function rule [17] states:
( ) ( )1f x dx xy f y dy = (34) Where lny x= (35)
ln ln Constanty yx x xy e y xy e Constnt x x x = = + = + (36)
3 32 2
3
2
44 3 2 2
2 ln ln ln
2 2 2 2 2 2 2
rm
pi
D
rm pi rm pirmwg
D
rm pi pi pi pirm rm rm
rm
D D D DB Du r
D D D D DD D DC
D
=
+ +
(37)
( )
3 32 2
2
84 24
2 ln 1 ln ln
2 2 2
rm
pi
D
rm pi rmwg rm pi
D
pirmrm pi rm pi
rm
D DB Du r D D
DDCD D D D
D
=
+ +
(38)
Combining with equations 31 and 32
( )( )
3 32
2 2
1 1
32 3Re
216 ln 1 ln ln2 2
2ln
w
wg pi rm piwrm rm pi
wwg
w r rm pipirm
rm pi rm pipi rm
rm
g
Nk L D DD D D
Bu D D DD
D D D DD D
D
+ =
+ + +
(39)
For the aforementioned parameters Re 1644wg =
Therefore it is feasible that the Reynolds number could be under the limit of laminar flow (2000) and that the
laminar flow assumption and model could therefore hold for reasonable geometric configurations. The velocity
profile on its own, however, is not useful. To find the power torques required by the pump and the delivered
flow-rate further analysis is necessary.
3.4. Slip Flow Derivation Assuming piston volume is negligible
( )2 2 22 2
2 2
24 4
rm rm
pi pi
D D
r rm r r rmd id sl wg wg
D D
u D D u Dv v v u A u r r
= + = + = + (40)
From equation 27
2 2 2 223
2 2 2 2
2ln44
rm rm rm rm
pi pi pi pi
D D D D
rmwg
D D D D rm
B rDu r r r r r r C r r
D
= +
(41)
2 2 2 2 223
2 2 2 2 2
2ln ln44
rm rm rm rm rm
pi pi pi pi pi
D D D D D
rmwg
D D D D Drm
B Du r r r r r r C r r r r r
D
= + +
(42)
-
18
Integration by parts [17] states: v u
u x uv v xx x
= (43)
Where ln ; v
u x xx
= = (44)
21;
2
u xv
x x
= = (45)
2 2 2 2 21ln ln ln ln Constant
2 2 2 2 2 4
x x x x x xx x x x x x x x
x
= = = +
(46)
4 4 2 22 2
4 2
2
2 2 2 2 2
2
2
44 4 2 2 2
2 ln ln Constant
2 2 2 4
rm
pi
rm
pi
D
rm pi rm pirmwg
D
D
rm pi
Drm
D D D DB Du r r
D D r rC r
D
=
+ + +
(47)
4 4 2 22 2
2
2 2 2 22 2
2 2 2 2
44 64 8
2 ln ln ln
2 4 2 2 2 2 2 2 2 2
rm
pi
D
rm pi rm pirmwg
D
rm pi pi pi pirm rm rm
rm
D D D DB Du r r
D D D D DD D DC
D
=
+ +
(48)
( )
4 422 2 2
2
2 2 2 2
128 2
2 1 ln ln ln28 2 2
rm
pi
D
rm pi
wg rm rm pi
D
pirmrm pi rm pi
rm
D DBu r r D D D
DDCD D D D
D
=
+ +
(49)
Combining with equation 40
( )
( )
4 42 2 2 2 2
2 2 2 2
16 2
4 2 1ln ln ln2 2 2
rm pi
r rm r rm rm pi
d
pirm
rm pi rm pi
rm
D DBu D D D D D
vDD
C D D D DD
+ =
+ +
(50)
Combining with equations 17 and 28
( )
( )( )
4 42 2 2 2 2
2 2
2 2 2 2
1 116 2
1 14 16 2 1ln ln ln2 2 2ln
rm piw
r rm r rm rm piwg piw
wd
r rm piwg pi piw rm
rm pi rm pi
pi rm
rm
D Dgu D D D D D
Nk L
gv u D DNk L DD
D D D DD D
D
+ +
= + + + +
(51)
As stated earlier in equation 6
fwm
gH
N
By definition [15]:
Re2
w wm rm
wm
w
u D
= (52)
2d d
wm
rm rm
v vu
A D= =
(53)
-
19
Re2
d w
wm
w rm
v
D
=
(54)
For the aforementioned parameters Re 4230wm (55)
is turbulentwmu (56) For turbulent flow in a smooth pipe, Blasius formulae [15] states:
14
0.079
Ref = (57)
For fully developed flow the frictional head loss [15] 2
,
4
2wm
f wm
rm
fuH
ND= (58)
For the aforementioned parameters 2
, 2 5
4 0.079 0.70.135
2d
f wm
rm
vH
D
= =
(59)
9.81 0.7 6.867 0.135fg
HN
= = = (60)
Therefore equation 6 holds
3.5. Torque and Power Demand Derivation The friction over the guide was first calculated as follows (see Figure 21 for parameter definitions).
1, 2,g g
g gF F e = [18] (61)
, 1, 2,2 o g g gF F F= + [18] (62) Combining with equation 61
( )1, , 1,2 g gg o g gF F F e = (63) ,
1,
2
1
g g
g g
o g
g
F eF
e
= + (64)
Combining equations 61 and 62 also
, 2, 2,2g g
o g g gF F F e = (65)
,2,
2
1g go g
g
FF
e = +
(66)
Subtracting from equation 65
( ),1, 2,
2 1
1
g g
g g
o g
g g
F eF F
e
=
+ (67)
The frictional torque from the bearings was decided to be equal to the
coefficient of friction of the bearing (b) multiplied by the shaft radius
(Dsh/2) multiplied by the normal force which
( )( )1, 2,2sh
b p sh p p
Dm m g F F= + + + (68)
A free body diagram of the pulley, rope and guide depicted in Figure
21 was based on the following assumptions
The angle of rope overlap around guide (g) is radians
No slip of the rope over the pulley
Steady state conditions.
Negligible frictional force of water on the rising main and the of
the flow in and out of the rising main relative to the weight of
F1,p F2,p
Dp/2
Dg/2
Guide
Pulley
F1,g F2,g
Fo,g(e-1)/
((e+1)Dg)
((msh+mp)g+F1,p+F2,g)Dshb/2
T
mrg/2 mwg
F1,g F2,g
F2,p
F1,p
Return Rope mrg/2
NLrmpi
Rising Rope
Figure 21 - Free body diagrams of
rope-pump parts
-
20
the water, shear frictional force on slip flow on pistons and friction of rope over guide
No mechanical contact between pistons and rising main due to lubricating slip flow
A moment balance for the pulley yielded
( )1, 2, 1, 2,( )
2 2p p p sh b
sh p p p
F F D DT m m g F F
= + + + + (69)
A force balance for the rising rope then yielded
1, 1, 2r
p g w rm pi
mF F m g NL = + + +
(70)
A force balance for the return rope then yielded
2, 2, 2r
p g
mF F g
= +
(71)
Subtracting from equation 70
1, 2, 1, 2, 2 2r r
p p g g w rm pi
m mF F F F m g g NL = + + +
(72)
Combing with equation 67
( ),1, 2,
2 1
1
g
g
o g
p p w rm pi
F eF F m g NL
e
= + ++
(73)
Combining with equation 69
( )
( )
,
1, 2,
2 1
2 1
2 2 2
g
g
o gp
w rm pi
sh b r rsh p g w rm pi g
F eDT m g NL
e
D m mm m g F m g NL F g
= + + +
+ + + + + + + +
(74)
Combining with equation 62
( ) ( )
( )
2 2,
2 2
,
2 1
2 41
22 4
g
g
o g w h rm rp
rm pi
w h rm rsh bsh p r rm pi o g
F e L D D gDT NL
e
L D DDm m m g NL F
= + + +
+ + + + + +
(75)
From equation 15
2pi
wg
pi pi pi w
Du
L Dr
= (76)
From equation 27
1
2wgu B
r Cr r
= + (77)
2 2
4
piwg
pi
pi
Du
DB C
r D
= + (78)
Combining with equation 76
2
4pi
pi pi pi w
pi
DL D B C
D
= +
(79)
Combining with equation 75
-
21
( ) ( )
( )
2 2
2 2
1
81
4 2
2 -
2 4
g
g
og w h rm r
p
w h rm r
sh b sh p r og
p sh b pi
rm pi pi w
pi
F e L D D gT D
e
L D D gD m m m F
D D DNL L D B C
D
= + +
+ + + + +
++
(80)
2 rm
p
TuP
D= (81)
( ) ( )
( )
2 2,
2 2
,
2 1
41
24
2 1
4
g
g
o g w h rm r
m r
w h rm rsh b rsh p r o g
p
pish br rm pi pi w
p pi
F e L D D gP u
e
L D DD um m m g F
D
DDu NL L D B C
D D
= + +
+ + + + +
+ +
(82)
d d w hm
m m
P v gL
P P
= =
(83)
( )
( )
( ) ( )
4 42 2 2 2 2
2 2 2 2
2 2,
16 2
4 2 1ln ln ln2 2 2
2 1
41
g
g
rm pi
r rm r rm rm pi
w h
pirmrm pi rm pi
rm
m
o g w h rm r
r
wsh b rsh p r
p
D DBu D D D D D
gL
DDC D D D D
D
F e L D D gu
e
D um m m
D
+
+ + =
+ +
+ + + +( )2 2
,24
21
4
h rm r
o g
pish br rm pi pi w
p pi
L D Dg F
DDu NL L D B C
D D
+
+ + (84)
3.6. Theoretical Model Summary Based on several assumptions, the most important of which was that of laminar slip flow, a theoretical flow
model was generated for the flow within the rope-pump. A force balance also yielded a model of the torque and
therefore power demands of the system. Combing the two models the theoretical efficiency of the pump was
then calculated.
4. Design & Build To accurately determine the torque and speed requirements of the pump on a motor a third scale model of the
full 10m head was constructed. To ease analysis heads in multiples of 1/N were chosen, the maximum therefore
-
22
equalling 2.8m. Two pipe diameters were chosen of 21mm and 40mm outer diameter and a pulley diameter of
40cm was selected in accordance with Bobby Lamberts design [19].
A computer aided design of the model was generated (see Appendix B) to easily communicate the model
requirements to those involved in its construction. The design was based on the model installed by Pump Aid, a
NGO who install hand powered rope-pumps across Zimbabwe and the surrounding countries. Correspondence
via a series of model provided all the information necessary for an appropriately accurate reproduction of the
pump installed in the field. The designs detailed by Bobby Lambert [19] were also used as an aid. The selection
of the pump was largely based on its ease of construction, therefore, most model parts were easily sourced or
manufactured from off the shelf items.
4.1. Preliminary experiment Ben Stitt selected a hand drill as the most appropriate
motor for our model based on cost and flexibility over a
range of running speed and torques. A preliminary
experiment was decided to be the most accurate initial
estimate of the torque demands, which dictated exactly
which hand drill to purchase.
A single piston was attached to a spring balance and
pulled through a section of rising main at approximately
1m/s. The rising main was submerged at the bottom end
and the top positioned 1/N (0.7m) above the water level. It would therfore, when kept topped up by a hose,
create a load representative of the load on each piston.
The speed was measured using a stop watch over a marked distance. The force in the spring balance was
determined using a rubber grommet inserted into a spring balances scale such that it was moved to the
maximum value when loaded. The experiment was repeated to reduce the affect of variance and a non-constant
rope speed. The results (see Figure 22) showed that for a speed of 1m/s a tension of approximately 14.7N was
required. It was decided that this was likely to be greater
than the force at steady state as it would include the forces
needed to accelerate the water, however, this was likely to
be balanced by the un-modelled frictional forces at the guide
and bearings. Therefore, for the full 2.8m head
12.8 14.7 0.30.7 8.82
2 2p
N mF DT Nm
= = (85)
4.2. Model Parts The rig depicted in Figure 23 was constructed using the
following materials
To allow for the mentioned errors inherent to our
preliminary experiment Ben Stitt selected a Silverline
cordless hand drill (see20Figure 26) for our motor, quoted
as providing torques of 12Nm. The drill was powered by a
10
11
12
13
14
15
16
17
18
0.8 0.9 1.0 1.1R ope Velocity (m /s)
Ten
sio
n (
N)
Figure 22 - Graph of rope velocity against rope tension
for a 34.9mm OD piston and 36.4mm OD rising main
Figure 23 - Model assembly
Rising main
Guide
Tubular plastic bag overflow guide
Piston
-
23
Figure 26 - Selected hand drill [20] Figure 27 - Power Supply Unit (PSU)
Figure 29 - Greased wooden bearings
Metal bracket
Drill
12V DC battery which matched what could be expected from a photovoltaic unit. I the experiment the battery
was simulated by a power supply
unit or PSU (see Figure 27).
The rising main and side delivery arm
were formed from a length of 40mm
or 21mm outer diameter (OD) PVC
waste pipe and corresponding pipe
connectors. The rising main was
supported via 40mm or 21mm ID
waste pipe fixings to an up ended
table (see Figure 23). The pipe was
made vertical using a simple plumb-line.
8mm outer diameter nylon rope was used. The length of
rope needed was based on a length twice that of the rising
main length, plus one extra metre to allow for the distance
around the guide, plus the angle of lap around the pulley
multiplied by the pulley radius
2 12
p
r rm
DL L
= + + (86)
Defining Lr = 2.8m and Dp = 0.3m
7rL m (87)
The rope ends were connected using
tape and the pistons located using
knots 1/N (0.7m) apart.
The water reservoir was a PVC bin
located in a drainage channel (see
Figure 23)
Ben Stitt assembled a bottom rope guide (see Figure 24) from scrap metal
The journal bearings were drilled from unfinished pine wood and greased (see
Figure 29), the bearings were then bolted to mild steel brackets constructed by Ben Stitt that were then
clamped to steel girders (see Figure 25)
The shaft was constructed from scrap stainless steal water piping of 20mm inner diameter (ID) (see
Appendix B)
To ensure accurate alignment of the rope at exit and therefore remove any mechanical friction of the pistons on
the rising main, lengths of PVC pipe were placed over the shaft (see Figure 32) as spacers and the rising main
carefully adjusted.
Ben Stitt designed the coupling drill-bit, which was a simple bolt pinning the shaft to a solid mild-steel
cylinder with a hexagonal projection that could easily be fixed by the hand drills three way vice (see Figure
28)
Figure 24 - Bottom guide
Figure 25 - Mild steel
brackets
Girder
Metal Bracket
Figure 28 - Shaft and
coupling to machined drill
Drill
-
24
Figure 30 - Pulley tyre part construction [19]
The pistons were manufactured based on an example piston, designed for a 40mm OD PVC pipe, sent over
from Zimbabwe. The pistons for the 21mm OD pipe were simply a scaled down design of the 40mm pistons
and were manufactured by the university workshop. To calculate the number of pistons needed the length of
rope was multiplied by N, one added for safety and then rounded up to the nearest integer i.e.
For the aforementioned parameters
1 11.1 12rNL + = (88)
The pulley was constructed based on Bobby Lamberts design
(see Figure 30). The hub was constructed from two wooden
discs which clamped the tyre and then were bolted to a
specially designed metal hub (see Figure 30 and Figure 31 ).
The engineering drawing used to order the mild-steel hub from
the university workshop is depicted in Appendix B. It was
generated directly from the Ideas11 CAD model of the pump
assembly (also in Appendix B).
4.3. System Integration Problems
The torque, once the pipe was fully primed, was too great for the motor. This
was most likely due to the torque quoted for the motor being a break torque
rather than a running torque (which would be lower).
o The larger pulley wheel (see Figure 31) was therefore replaced by a
smaller pulley (see Figure 32) which solved the problem.
The tyre used for the smaller pulley was softer and created a more obtuse
profile which not only occasionally allowed the rope to jump out of the
pulley but also exacerbated the slip in the system making the pump
ineffective.
o The Duck tape used to connect the ends of the rope was replaced with
electrical tape and used sparingly to reduce the tape area (which had a
lower coefficient of friction).
o The smaller pulley was modified with larger wooden hubs to make the
profile of the pulley more acute.
o The rising main was flared at the bottom to avoid the problems of misalignment at entry, i.e. pulsing
higher torques generated by the pistons knocking on entry.
o The guide was also adjusted to
ensure accurate alignment of the
rope at entry.
o The doubled over rope at the
joints created significant friction
in the 21mm pipe. The electrical
tape was therefore tied tight and
used sparingly to reduce the
diameter of the joints.
The 21mm pipe had an ID smaller than the OD of the knots in the rope
o The knots were therefore replaced with electrical tape wrapped tightly around the rope (see Figure 33).
Figure 31 - Larger Pulley
Tyre part
Figure 32 Smaller pulley assembly
Pipe spacer
Metal hub
-
25
Figure 34 - Static wired torque gauge [21]
Figure 36 - Tachometer
Figure 33 - Smaller pistons fixed
with electrical tape
Electrical tape
Small piston
4.4. Design and Build Summary A physical third scale model was successfully constructed, the rope-pump
proved to be a very simple and easily constructed design. The addition of the
motor created two main problems, rope slip and the motor stalling. Altering
the pulley design proved to be the most effective solution to both.
5. Experimental Methodology Using the model automated rope-pump rig detailed above the torque, slip flow-rate, delivered flow-rate,
electrical power demands were empirically determined for a range of heads and pipe diameters at a rope speed
of 1m/s (specified by Bobby Lambert).
To do this we took readings of head, torque, rope velocity, delivered flow-rate, shaft speed, voltage and current
supplied.
5.1. Initial Methodology
A set of five readings for each configuration of head and rising
main diameter were recorded. The rising main was trimmed from
2.8m down to 1.4m, in 1/2N or 0.35m intervals, to give six
different graph points (including the zero head configuration).
Direct torque gauges were investigated; only static torque gauges
existed within a realistic budget (see21Figure 34) and were
therefore not useful. The large cost of dynamic torque gauges is
mainly attributed to the electrical brushes required to transmit the
data from the sensor. The rope tension was instead converted into a torque using:
1,
2p p
p
F DT = (89)
To take readings for tension in the rope a spring balance was integrated into the
loop of rope. A range of spring balances were sourced (see Figure 35) from
which the most appropriate was used. Once at steady conditions a video clip of
the balance at exit from the rising main was taken to obtain readings of tension
(F1,p).
To measure the rope linear velocity the total length of rope was measured and the time taken for one
complete rotation using a stop watch.
To achieve a rope velocity of 1m/s the current supplied by the PSU was varied iteratively
The delivered flow-rate was obtained by measuring the time taken to pump 20l from the reservoir again
using a stopwatch.
The shaft speed was measured using a tachometer (see Figure 36) that
was placed in direct contact with the shaft.
The PSU used had inbuilt amp and volt meters.
For each combination of rising main diameter and length a minimum of five valid readings were recorded.
5.2. Methodology Modifications
The spring balance, due to its size and rigidity caused unrealistic jerk loads during each cycle. The balance
would also not fit down the 21mm OD rising main
Figure 35 - 'Globe' spring
balances [21]
-
26
Figure 38 - Calibrated
source reservoir
Figure 39 - Fixed hand
drill
Figure 37 - Spring from
balance tied into rope loop
o The balance casing was, therefore, removed and the spring integrated into the loop of rope using wire to
maintain the flexibility of the rope loop (see Figure 37). The spring was characterised to convert the
observed aspect-ratio to a tensile force.
At faster speeds the images obtained of the spring from a video camera were
blurred making it impossible to analyse the aspect ratio.
o A lamp was, therefore, installed to introduce more light and thus increase the
images sharpness. A still camera was also used which allowed a series of
sixteen images to be taken in quick succession (rapid image array) with a
far better resolution.
The flow-rate achieved was too great for the side arm to comfortably cope with
and water was spilt out of the top of the rising main
o The side arm was therefore removed and the delivered flow directed, via a tubular channel of plastic bin
liners, away from the source reservoir (see Figure 23). The reservoir was then calibrated to measure
volume within a 2l accuracy (see Figure 38) and the drawn (rather than delivered) flow-rate measured.
The volume flow-rate achieved using the 21mm OD rising main was
considerably slower than that achieved with the 40mm rising main.
o The time taken for 10l to be pumped was therefore taken for the smaller
diameter
The hand drill was designed for use in short bursts and therefore encountered
increased inefficiencies after prolonged use due to Ohmic losses.
o The drill was therefore allowed to cool between readings and only used for
short periods
The location of the drill proved to be a significant influence on frictional losses.
The number of readings required also proved too great for just one person to take
o The previously hand held drill was therefore clamped between mating blocks of wood which were then
attached to a girder via a metal bracket (see Figure 39).
5.3. Model characteristics The model characteristics were recorded using a vernier gauge and digital weighing scales
0.0890
0.151
0.008
0.025
3.1
g
p
r
sh
p sh
D m
D m
D m
D m
m m kg
=
=
=
=
+ =
5.4. Experimental Methods Summary Five readings of flow-rate, rope torque, rope speed and slip and power drawn were recorded for a range of
heads up to 3m and for two different rising main diameters. The main development in the experimental
methodology was the integration of a spring into the rope loop to measure tension.
-
27
6. Results and Analysis As mentioned readings were repeated five times for each combination of rising main diameter and length, then
averaged to reduce the affect of variance on the data.
The water level obviously dropped during each experiment, an average head was therefore calculated.
2il fl
h rm
L LL L
+= (90)
The coefficients of friction () for the rope on the guide, and the bearings were determined by placing a
representative load on pair of parallel surfaces similar to those being investigated (i.e. the same materials and
under the same lubrication) and inclined until slip occurred (at sl).
sintan
cossl
sl
sl
mgF
N mg
= = = (91)
2
2
0.268
0.487b
g
kgs
kgs
=
=
1 2pD
T F= (92)
sp
sp
LAR
D= (93)
FK
x=
(94) 0.5
no
sp
gK
D
=
(95)
, , ,1
0.5 sp nu sp o sp nusp sp sp
sp
L L LgF AR
D D DD
= (96)
See Figure 40 for parameter definitions
( )1 ,0.5 sp sp ogF D AR L = (97)
( ),4p
sp sp o
D gT D AR L =
(98)
r
r
r
Lu
t= (99)
For the larger pipe diameter 30.02
d
w
mv
t= (100)
For the smaller pipe diameter 30.01
d
w
mv
t= (101)
4r rm
id
u Dv
= (102)
eP VI= (103)
1m rP Fu= (104)
Lsp
Dsp
Lnu
Figure 40 - Definitions of
spring geometric parameters
-
28
2
Du = (105)
sh t
t sh
D
D
= (106)
t
sh t
sh
D
D = (107)
2pt
sl t r
sh
DDu u
D = (108)
d d w hP v gL= (109)
1
d d w h
m
m r
P v gL
P Fu
= =
(110)
The recorded and predicted data was then plotted (see Figure 41) along with the most appropriate type of lines
of best fit (based on the highest R2 value). The physical model characteristics defined in section 5.3. were
inputted into the theoretical model and also plotted.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.6 0.8 1.0 1.2
Rope Speed (m/s)
De
livere
d F
low
rate
(l/s
)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 0.5 1 1.5 2 2 .5 3
He ad (m )
Delivere
d F
low
rate
(l/s)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0 0.5 1 1.5 2 2.5 3
Head (m)
To
rqu
e o
f R
op
e (
N)
0
10
20
30
40
50
60
70
80
90
100
0 0.5 1 1.5 2 2.5 3
Head (m)
Po
wer
(W)
0%
5%
10%
15%
20%
25%
30%
35%
0 0.5 1 1.5 2 2.5 3
Head (m)
Eff
icie
nc
y
R
y Ry = 00
005
Head (m)
Po
wer
(W)
Recorded Electrical (40mm OD)
Recorded Mechanical (40mm OD)
Predicted Mechanical (40mm OD)
Ideal Mechanical (21mm OD)
Recorded Electrical (21mm OD)
Recorded Mechanical (21mm OD)
Predicted Mechanical (21mm OD)
Ideal Mechanical (21mm OD)
Figure 41 - Graphs of recorded and predicted results
-
29
7. Discussion
7.1. Error Analysis
7.1.1. Torque and Power Errors
As mentioned the aspect ratio of the spring was
determined from photographic images of the
spring. Due to the motion of the spring, the length
of the images exposure lead to a blurring affect
(see Figure 42) making accurate definition of the
spring length difficult. A few images were
obtained with a much faster shutter speed (see
Figure 43), these images were obtained when the
rapid image array camera function was turned
off and were therefore much harder to capture.
The carefully considered method of inspecting the
images was validated when the forces obtained from the two different camera functions were compared and the
standard deviation calculated to be just 2.5N about an average of 22N.
The rapid image array had a relatively low resolution; comparison between images within each captured array
confirmed the spring length to within + 2 pixels (an error of + 2.4-5.7%) and the width to within 1 pixel (an error
of + 4.2-5.6%). More than one image array for each reading was also captured, further reducing the affects of
variance and increasing the accuracy of the data.
The torque readings (shown in Figure 41) obviously do not include the torque necessary to overcome the
bearing friction, a comparison was therefore made with the model by setting the bearing friction coefficient in
our model to zero.
The electrical power demands (see Figure 41) gave further confirmation of the power readings. The recorded
electrical power demands were at all times at realistic levels based on reasonable electrical and bearing power
losses.
7.1.2. Delivered Flow-rate Errors
Although every effort was made to keep the rope speed constant at 1m/s the resolution of the power supply,
which determined the pump speed, was such that this was impossible. This lead to standard deviations of
0.0193l/s about an average of 0.107l/s for the 21mm OD rising main and 0.0498l/s about an average of 0.611l/s
for the 40mm OD rising main. This is, however, not too large for a useful comparison of the recorded and
predicted delivered flow-rates against head (see Figure 41). This variation in rope speed did however allow
comparison of the recorded delivered flow-rates to those predicted by the model (see Figure 41) over the small
range of rope speeds. Every effort was also made to prevent leakage of the delivered flow-rate back into the
source reservoir; some leakage was unavoidable but was assumed negligible.
7.1.3. Rope Slip Errors
The low accuracy of the tachometer and the variation of shaft velocity during the readings lead to a standard
deviations of 10rpm about an average of 110rpm for the 21mm OD rising main and 7.7rpm about an average of
110rpm for the 40mm OD rising main. The average rope slip over all our data was -0.053m/s (implying the rope
moved faster than the pulley, obviously impossible), confirming, if rather unsatisfactorily, the assumption of no
rope slip. A more satisfactory confirmation of the no slip assumption was the observation that not only was
Figure 43 - Higher quality single photo of spring in
motion
Figure 42 - Example blurred image of spring from image array
-
30
there no visual sign of slip during the readings but that when slip did occur, it would be permanent and totally
disable the pump, preventing any readings being taken.
7.1.4. Efficiency and Power Errors
As mentioned the recorded torque (and therefore mechanical power) omitted any bearing friction.
7.2. Comparison of Model with Empirical Data
7.2.1. Model of Delivered Volume Flow-rate
The models assumption that the pressure would be equal throughout the rising main, at corresponding locations
between the pistons, appeared to hold. This can be seen clearly in Figure 41 by the graph of delivered flow-rate
against head. A constant slip flow-rate lead to a constant delivered flow-rate at any head and was illustrated by
the lines of best fit for the recorded data; the gradients for the 40mm OD and 21mm OD rising mains were a
mere 0.0005l/sm and 0.020l/sm respectively.
Based on the empirical data the average delivered flow-rate for the 40mm and 21mm OD rising mains were
0.61l/s and 0.11l/s respectively, considerably less than the ideal volume flow-rate. The predicted and recorded
absolute delivered flow-rates appeared to be very similar for the 21mm OD rising main, confirming the
estimated and blunt correction factor (k=10), which was defined for geometries nearly twice that of the 21mm
OD rising main. However, the absolute predicted delivered flow-rates for the 40mm OD rising main were
considerably less than those recorded. This was most likely due to the laminar flow model holding far better for
the 21mm OD than for the 40mm OD rising main, which had a predicted Reynolds numbers of 3090 and 6460
respectively. Turbulent slip flow is considerably slower than that predicted by a laminar flow model based on
the same geometries and fluid properties. This explains why the predicted slip flow was over twice that
recorded. In addition if the assumption of negligible leakage (of the delivered flow back into the source
reservoir) was incorrect this may have also caused the predicted flow-rates to be lower than those recorded;
based on observation this is unlikely to have been significant.
The graph of delivered flow-rate against rope speed (see Figure 41) also appears to confirm the model for the
21mm OD rising main, which is more likely to have been laminar, but again shows the model to overestimate
the slip flow in the turbulent 40mm OD rising main.
7.2.2. Model of Torque and Power Demands
The empirical data backed equation 80s prediction that the affect of the slip flow would be negligible
(accounting for just 0.4% of the total torque) and that the torque gradient (of the rope on the pulley) would be
approximately:
( )2 28
p w h rm rp
h
D L D D gdT
dL
= (111)
However, the y-axis intercept was underestimated (see Figure 41). A corrective guide friction coefficient of 2
was iteratively determined as the closest fit for the 21mm OD rising main. A corrective coefficient for the
guide-friction was decided on through a process of elimination. The torque of the bearings was omitted from the
empirical data, the torque of the water could be confidently predicted and the shear force of the slip flow was
predicted to be negligible (a corrective coefficient of over 90 would be required to justify the model based on
the shear force of the slip flow) leaving the guide-friction term.
( )( ) ( )2 21 0
0 281
g
g
og w rm r
p p
F e D D gT D
e
= + +
(112)
However, the same corrective factor underestimated the empirically recorded torques for the 40mm OD rising
main. Despite the breakdown of the laminar assumption for the 40mm OD rising main it was decided that any
-
31
possible increased frictional force of the slip flow could not account for this underestimation. It was therefore
decided that an even larger underestimation of the guide-friction had been made for the 40mm OD rising main.
This was attributed to some accidental change in the guide or rope tension configuration created when the
pistons were swapped. Therefore, to overcome this systematic error a new corrective coefficient of 3 for the
guide frictional force was defined for the 40mm OD rising main.
( ) ( )2 2, 13
81
g
g
o g w h rm r
p p
F e L D D gT D
e
= + +
(113)
Therefore, combining equation 80 and 112 the predicted frictional force of for the bearings for the 21mm OD
rising main was:
( ) ( ) ( )2 2 2 2,,
2 1
8 4 21
g
g
o g w h rm r w h rm r
p p sh b sh p r o g
F e L D D g L D D gT D D m m m F
e
= + + + + + +
+
(114)
From equation 81
( ) ( ) ( )2 2 2 2,,
2 1
8 4 21
g
g
o g h w rm r w h rm r
m p sh b sh p r o g
F e L D D g L D D gP D D m m m F
e
= + + + + + +
+
(115)
For the 40mm OD rising main from equations 80 and 113
( ) ( ) ( )2 2 2 2,,
3 1
8 4 21
g
g
o g w h rm r w h rm r
p p sh b sh p r o g
F e L D D g L D D gT D D m m m F
e
= + + + + + +
+
(116)
( ) ( )( ) ( )2 2 2 2,,
3 1 16
8 4 21
g
g
o g h w rm r w h rm r
m p sh b sh p r o g
F e L D D g L D D gP D D m m m F
e
+ = + + + + + +
+
(117)
These torque equations (omitting the torque of the bearings) were plotted in Figure 44 with the empirical data
that they were modified to fit. Based on this modified model the components of the torque and power demands
were as follows:
At the nominal 10m head designed for, the frictional forces on the piston was negligible and therefore
ignored.
The torque of the frictional forces of the rope over the guide was constant, if the empirically determined
corrective coefficient was included for the full 10m head, it accounted for 19% and 39% for the 40mm and
21mm OD rising mains respectively.
The obvious main contribution was that of the of the weight of the water rising to 75% and 52% of the load
for the 40mm and 21mm OD rising mains respectively at the full 10m head.
The theoretical torque of the bearings (which is proportional to head) accounted for the remaining torque
demands, 6% and 9% for the 40mm and 21mm respectively at the full 10m head
7.2.3. Model of Efficiencies
Combining equations 83 and 115 the new modified model predicted the mechanical efficiency to be:
-
32
Figure 44 - Modified predicted and emperically determined torque and eficiency values against head
y y =
0 5
H e a d (m )
Mechanical for 40mm OD Rising Main (Recorded)
Mechanical for 40mm OD Rising Main (Predicted)
Mechanical for 21mm OD Rising Main (Predicted)
Mechanical for 21mm OD Rising Main (Recorded)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 0.5 1 1.5 2 2.5 3
Head (m )
To
rqu
e a
t P
ulley (
Nm
)
0%
10%
20%
30%
40%
50%
0 2 4 6 8 10 12
He ad (m )
Eff
icie
nc
y
( )
( )
( ) ( )
4 42 2 2 2 2
2 2 2 2
2 2
16 2
4 2 1ln ln ln2 2 2
2 1
41
g
g
rm pi
r rm r rm rm pi
w h
pirmrm pi rm pi
rm
m
og w h rm r
r
wsh b rsh p r
p
D DBu D D D D D
gL
DDC D D D D
D
F e L D D gu
e
LD um m m
D
+
+ + =
+ +
+ + + +( )2 2
24
h rm r
og
D Dg F
+
(118)
This modified model is backed by empirical data for the 21mm OD rising main (see Figure 44) and predicted a
mechanical efficiency of 17%. Replacing the null theoretical delivered flow-rate for the 40mm OD rising main
with the empirically determined average of 0.611l/s:
Combining empirical data with equation 83 and 117
( ) ( )
( )
2 2
2 2
0.000611
4
2 11.6
41
24
g
g
w h
m
og w h rm rr
r
p
w h rm rsh b r
sh p r og
p
gL
F e L D D guu
D e
L D DD um m m g F
D
= + + +
+ + + + +
(119)
For the full 10m head and 40mm OD rising main a
44% mechanical efficiency was predicted. The
model attributed the major losses to the weight of
the slip flow and the frictional force over the guide.
The 21mm OD rising main was considerably less efficient than the 40mm OD rising main (see Figure 44). This
low efficiency was attributed to the significant frictional losses detailed above combined with the considerable
un-useful weight of the slip flow (as opposed to the useful force actually lifting the delivered flow). The
lower achieved delivered flow-rates compounded the problem and was caused by the rope being a significant
volume fraction of the rising main.
-
33
The model depicted in Figure 44 predicted that the efficiencies would initially rise sharply, as the constant
guide-friction fell in significance, but would then plateau approaching a limit imposed by the weight of the slip
flow.
8. Conclusions and Future Work In reference to a detailed PDS a rope-pump bolted to either the motor shaft or a simple crank was selected as the
most appropriate system. Detailed CAD drawing of the selected system were generated and used to construct a
physical model of the system. The recorded results were compared to those predicted by a theoretical model and
the model modified accordingly.
8.1. Findings
Based on the empirical data the avera