A
Design Manual
for
Water Wheels
with
details for applications to
pumping
water for village use and
driving
small machinery
WILLIAM G. OVENS
VITA
1600 Wilson
Boulevard, Suite 500
Arlington,
Virgnia 22209 USA
Tel:
703/276-1800 . Fax: 703/243-1865
Internet:
pr-info@vita.org
[C]VITA, Inc. 1975
Reprints:
March 1977
June 1981
January 1989
TABLE
OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
PART ONE: THE WATER WHEEL
I
Introduction
II
Formulation of the Problem
III Design Limitations -
Advantages and Disadvantages
IV
Theoretical Considerations for Design
A.
Stall Torque
B.
Power Output vs. Speed; Required Flow Rates
C.
Bucket Design
D.
Bearing Design
E.
Shafts
F.
Minor Considerations
V
Practical Considerations for Design
A.
Materials
B.
Construction Techniques
C.
Maintenance
PART TWO: APPLICATIONS
I
Water Pumping
A.
Pump Selection Criteria
B.
Attachment to Wheel
C.
Piping
II
Other Applications
APPENDIX I Sample
Calculation
APPENDIX II An Easily Constructed
Piston Pump:
by Richard Burton
BIBLIOGRAPHY
LIST
OF TABLES
Table I Stall Torque
per Foot of Width
Table II Horsepower
output for a Constant Torque
Wheel per RPM
per Foot of Width
Table III Water Power
Input to Wheel per RPM per
Foot of Width
to Maintain Constant Torque (hp.)
Table IV Flow Rate in
Imperial Gallons per RPM
per Foot of
Width of Wheel Required to
Maintain
Constant Torque
Table V Estimated
Maximum Output Horsepower for
Constant Input
Water Flow Rate Condition
Table VI Upper Limits on
Useable Flow Rates for
Various Size
Wheels
Table VII Approximate
Weight Carted by Each Bearing
Table VIII Maximum Bearing
Diameter Required for
Various
Loadings
Table IX Standard Pipe
Sizes for Use as Axles with
Bearing at 12
inches from Wheel Edge
Table X Estimated
Friction Factors
Table XI Peak Pump
Piston Velocities for Pump Rod Attached Directly to a Crank on the Wheel
Table XII Peak Force on
the Pump Rod of a Piston
Pump for Various Bores and Heads
Table XIII Volume of Water
in Various Sized Delivery
Pipes
([ft.sup.3])
Table XIV Inertial Force
per Inch of Stroke for Various
Volumes of
Water at Various Pump Cycle Speeds
Table XV Horsepower
Required for Water Pumping at
Various Flow
Rates and Heads
Table XVI Quantities of
Water Pumped per Stroke for
Various Bore
and Stroke Sizes
LIST
OF FIGURES
Figure 1 Schematic
Side View of Bucket Shape
Figure 2 Schematic View
of Water Distribution on Wheel
Figure 3 Schematic View
of a Slider-Crank Mechanism
Figure 4 Schematic View
of a Trunnion-mounted Pump
and Crank
Figure 5 Schematic View
of a Scotch Yoke Mechanism
Figure 6 Schematic Views
of a Suitable Cam-activated
Pump Rod
PART ONE:
THE WATER WHEEL
I. INTRODUCTION
Supplying power to many
remote locations in the world from central
generators using customary distribution methods is either economically
unfeasible or will be many years in coming.
Power, where desirable, will
therefore need to be generated locally.
Various commercial machinery
is marketed, but the required capital expenditure or maintenance/running
cost is beyond the capability of many potential users.
Some effort has
been expended at the Papua New Guinea University of Technology to devise
low cost means of generating modest amounts of power in remote locations.
This paper reports on one such project involving the development of low
cost machinery to provide mechanical power.
Regardless of the final use to which the power is put the natural sources
of energy which can be utilized are fairly readily categorized.
Among
them:
1.
Falling water
2.
Animals
3.
Sun
4.
Wind
5.
Fossil fuels
6.
Nuclear fuels
7.
Organic waste
Sun, wind and water are free and renewable in the sense that by using
them we do not alter their future usefulness.
From continually operating
cost considerations, a choice from among these is attractive.
From
capital cost consideration hydro-power may be very unattractive.
Sun
and wind have obvious natural limitations based upon local weather
conditions. Furthermore, for
technological and economic reasons, solar
power use is presently limited to applications utilizing the energy
directly as part of a heat cycle.
Animals require specialized care and
continuous food sources.
Conversion of organic waste to useable energy
is being experimented with, with varying success, in several parts of
the world.
Whatever the form of the naturally occurring energy, it may be
transformed,
if necessary, into useable power in a wide variety of ways.
The choice of method depends upon a complex interaction of too many
considerations
to enumerate fully here, but among them are:
1.
the use to which the power will be
put;
2.
the form in which it will be utilized.
This
generally, but
not exclusively, falls into the
broad categories
of mechanical and electrical;
3.
the economic and natural resources
available;
4.
availability of suitable maintenance
facilities;
5.
whether the machinery must be portable
or not.
II. FORMULATION OF THE PROBLEM
In the absence of a specific
request from government or any outside
body, the decision was taken based primarily on the obvious abundance of
available water power to investigate broadly the design possibilities for
low cost machinery to produce small amounts of mechanical power.
One
immediately obvious potential application is the generation of electric
power, but for reasons mentioned under "Other Applications" in
Part Two
this has not been pursued.
However, in many places, villages are
located at some distance from the traditional source of drinking water.
The principal intended use for the power generated by the machine
discussed
in this manual has been the pumping of potable water for distribution
to a village. The project, thus,
has included construction
of a simple pump attachment also.
Several other potential uses are
discussed later.
Limits on the scope of the project were decided based upon numerous
considerations:
1.
Minimum of capital expenditure indicated a device
which could be
constructed locally of inexpensive
materials with no
specialized, expensive components
or machinery
required.
2.
Local construction suggested the desirability of
design details
requiring only simple construction
techniques.
3.
Since the installation was likely to be remote (indicating
a probable
shortage of local skilled tradesmen)
maintenance, if
any, would have to be minimal and
simple.
4.
The device should be such that repair, if any, could
be carried out on-site
with parts and necessary tools
light enough to be
carried easily to the site.
5.
The usual considerations of safety must apply with the
knowledge that the
village children could not/would not
be kept away from the device.
I decided to concentrate on investigating the feasibility of using the
water wheel, it being the device which seemed most likely to optimize
the criteria set out above. There
are other types of machines suitable
for creating mechanical power from hydro sources, but none, known to me,
can be constructed with such simple techniques requiring so low a level
of trade skills as the wooden water wheel.
Water wheels are in use in various parts of the world now.
Many have
been constructed on an ad hoc basis and vary in complexity, efficiency
and ingenuity of design and construction.
The basic device is so simple
that a workable wheel can be constructed by almost anyone who has the
desire to try. However, the
subtleties of design which separate adequate
from inadequate models may escape those without sufficient technical
training. The number of projects
abandoned after a relatively short life
attests to the fact that designers/builders often have more pluck than
skill. It seems desirable to
attack the problem in a systematic fashion
with an objective of establishing a design manual for the selection of
proper sizes required to meet a specific need and to set out design
features based on sound engineering principles.
I offer the following
as an attempt to meet that objective.
The wheel consists of buckets-to hold the water-fixed in a frame and
arranged so that buckets and frame together rotate about a centre axis
which is oriented perpendicular to the inlet water flow.
Traditional
designs employ the undershot, overshot or breast configurations.
In the
undershot wheel, the inlet water flows tangent to the bottom edge of the
wheel. In the overshot wheel, the
water is brought in tangent to the top
edge of the wheel, partially or fully filling the bucket.
It is carried
in the buckets until dumped out somewhat before reaching the lowest point
on the wheel. The breast wheel
has water entering the wheel more or
leas radially, filling the buckets and then again being dumped near the
bottom of the wheel. Typical
efficiency values vary from as low as 15%
for the undershot to well over 50% for the overshot with the breast
wheel in-between.
We shall concentrate on the overshot wheel as being the most likely
choice
to give maximum power output per dollar cost, or per pound of machine, or
per manhour of construction time based upon expected efficiences.
Mitigating
against this choice is the need for a more complex earthworks
and race way with the overshot wheel where the water must be guided in
at a level at least as far above the outlet as the diameter of the
wheel. The undershot wheel, of
course, may be merely set down on top of
the stream with virtually no preparation of raceway necessary.
But in
many streams the rise and fall with heavy local rainfall is spectacular,
so flood protection would be a major consideration for any type of
device.
The simplest flood protection is a channel leading from the river to the
installation, with inlet to the channel controlled to keep flood water
in the main stream. Since a
diversion channel would probably be required
anyway, the odds are very good that a suitable location to employ an
overshot wheel can be found for most installations.
In the event that
the overshot installation is impossible, the undershot wheel straddling
the diversion channel is simple to use.
Another consideration which makes the overshot wheel attractive is the
ease with which it can handle trash in the stream.
First, the water
shoots over the wheel and so trash tends to get flung off into the
tail-race
without catching in a bucket.
Secondly, there are not usually the
tight spaces between race and wheel in which trash can jam.
Somewhat
closer fitting arrangements are required with breast and undershot
wheels to get good efficiency.
III. LIMITATIONS - ADVANTAGES AND
DISADVANTAGES
The wheel is a slow speed
device limited to service roughly between
5 and 30 rpm. Consequently this
limits its usefulness as a power source
for electricity generation or any other high speed operation because of
the step up in speed required.
Although not a great problem from an
engineering viewpoint, adequate gearing or other speed multiplying
devices involve increasing complexities in terms of money, potential
bearing problems, and maintenance.
The slow speed is advantageous when the wheel is utilized for driving
certain types of machinery already in use and currently powered by
hand. Coffee hullers and rice
hullers are two which require only
fractional horse-power, low speed input.
Water pumping can be accomplished
at virtually any speed. Slow
speed output of a wheel cannot of
course, directly power a centrifugal or axial pump.
The positive displacement
"bucket pump" or suction lift pump already in use in various
villages normally operates at well under 100 cycles per minute and can
be adapted for use in conjunction with a wheel at slow speed.
This of
course, has been done for hundreds - maybe thousands - of years
elsewhere.
Devices of this type have relatively low power output capability.
The
power output depends upon the dimensions of the wheel, the speed and
the useable flow rate of water to the wheel.
As an example, a reconstructed
breast wheel installed in a museum in America of 16 ft. outside
diameter and with bucket depth of 12 in. operating at 7 rpm, with
flow rate of 28 cubic feet of water per second had an estimated power
output of 18.5 hp (14 kw) (calculated at an efficiency of 100%).
Actual
output on that wheel has not been measured but would be less than 10 hp
(7.5 kw). A 3 ft. OD, 1 1/2 ft.
vide model constructed by the author is
in the fractional horse-power range.
Already mentioned once, it is worth emphasizing that a useable water
wheel can be built almost anywhere that a stream will allow, with the
crudest of tools and elementary carpentry skills.
IV. THEORETICAL CONSIDERATIONS
A. Stall Torque
The stall torque capacity of
the machine, ignoring the velocity
effect of the water impinging
on the stalled buckets, is easily
calculated by a simple
summation of moments about the shaft due
to the weight of water in each
filled or partially filled bucket.
Obviously this will depend in
part on the amount of spillage
from the bucket which in turn
depends on bucket design. Bucket
configurations used in the 18th and 19th century varied depending
on the skill of the
builder. They were empirically
determined
on the criterion of maximizing
torque by maximizing water retention
in the buckets while
recognizing that optimum design on this
criterion also required
increased construction complexities.
Buckets of shape shown
schematically in a side view, Fig. 1,
dmf1x9.gif (600x600)
were used for overshot and
breast configurations. The straight
sided buckets are less
efficient but simpler to construct. The
width of the bottom of the
bucket was typically 1/4 of the width
of the annulus where that
configuration was chosen. Purely
radial buckets were used in
undershot wheels.
It is convenient to use three
of the wheel's dimensions for
calculation of the torque
capacity of the wheel: the outside
radius, r; the wheel width, w,
i.e., from side to side; and the
annulus width, t, defined as t
= (outside diameter - inside
diameter)/2. See Fig. 1.
The ratio of the annulus
width, t, to the outside radius, r, is
important to wheel design as
there are practical limits to the
useful values which may be
employed. In this paper only ratios
0.05 t/r < 0.25 are
considered. For smaller ratios, the potential
output per foot of diameter of
the wheel is considered too low to
be practical.
For larger values, the buckets become so
deep that
there is insufficient time to
fill each one as it passes under the
race exit.
Also, since the torque and power depend upon
having
the weight of water at the
greatest possible distance from the
wheel axis, increasing annulus
depths increases total wheel weight
faster than it increases power
output. The result is that if more
power is needed it is better
to increase the O.D. than to increase
the annulus width to values
exceeding t/r = 0.25. In this way the
wheel weight and the
structural components to support that weight
remain economically most
advantageous for a given power output.
Historically, wheels have
tended to have t/r values around 0.1 to
0.15.
Upper limits on wheel width
have tended toward approximately 1/2
the O.D. because of structural
problems with wider wheels.
It can be estimated that the
overshot wheels operate with the
equivalent of approximately
1/4 of the buckets full. That is, the
total weight of water doing
useful work on the wheel is 1/4 of
the total that would be
contained in an annular solid of dimensions
the same as the O.D., I.D. and
width of the wheel. The actual
weight distribution of the
water is as shown schematically in
Fig. 2a because of spillage
from the buckets as they approach
dmf2x11.gif (600x600)
the tail race.
If we assume the water is concentrated in
the
annular quadrant shown in Fig. 2b, the stall torque can be
estimated
more easily.
A suitable correction factor could be
applied
to account for actual bucket
design, if that refinement were considered
necessary.
Results for wheels of various
dimensions are given in Table 1.
dmft1120.gif (600x600)
Experience has shown that many
non-technically trained users of
this information will be more
confident of their ability to use
data given in tabular than in
graphical form. Both will be presented
here when appropriate.
B. Power Output
Power output is the product of
the torque on the output shaft and
the rotational speed of the
shaft. On the assumption that there
is sufficient inlet water flow
to keep the buckets full, thereby
keeping the torque constant,
the power output increases linearly
with speed.
In a location where there is virtually an
unlimited
inlet water supply, this
calculation will give an upper limit to
the power output that can be
expected.
The horsepower output per rpm per foot of width is shown in Table II.
dmft2150.gif (600x600)
the Table II entry
appropriate to the size wheel used times the
actual speed in rpm times the
Width Of the wheel in feet.
The water power input is the
maximum power which the wheel could
achieve if it were 100%
efficient. It is calculated as the
product
of the water's specific
weight, the volume flow rate, and head and
is given in Table III for
comparison. This entry is also in
horsepower
dmft3170.gif (600x600)
that required to keep the
buckets full and is given in Table IV.
dmft4190.gif (600x600)
by the bucket wall
thickness. This can be corrected for
later if
desired.
The head is assumed here to be the diameter
of the wheel.
The lower edge of the wheel
is the highest elevation permission for
tailrace water without
interfering with the wheel and is a logical
datum.
Inlet raceways are seldom found with a
significant slope so
that velocity effects of
raceway water are small. It seems
sufficiently
accurate to estimate the
inlet elevation as the top of the
wheel.
Any error thereby introduced will be on the
conservative
side anyway.
Theoretical efficiency values
for the wheel using the assumptions
adopted so far can be found
by taking the ratio of the power output
from Table II and the
corresponding power input of Table III.
These
values, for the water weight
distribution assumed before, are about
50% for the narrow annulus
wheels and drop to just under 45% for
the wider annulus
wheels. As mentioned previously, a well
designed
and constructed wheel will
give efficiencies better than this.
This
comparatively modest value is
primarily the result of not considering
the effect of the water still
in the buckets below the
horizontal centerline.
It reflects the fact that the simplifying
assumption that the buckets
remain full half way down the wheel
and suddenly dump all their
water is not accurate. That inaccuracy
is tolerable because 1) it
makes the analysis so simple
and 2) it gives slightly
conservative figures for power so that
almost every reader will be
assured of getting sufficient power
even from wheels of
relatively amateurish construction.
When the water flow is less
than the required to fill each bucket
completely as may be the case
for a stream of limited size, the
power characteristics are
altered in that the torque now is a
function of speed.
Using the assumption of one annular quadrant
working, but not full, the
volume of water, V, in the quadrant is
V = Q/4N
where
Q = volume flow rate ([ft.sup.3]/min)
N = speed (rpm)
The weight of water in the annular quadrant at any speed is then
pgV where
p = density of
water
g =
gravitational acceleration
With units in feet, pounds, and minutes, the horsepower to be expected
from this annulus working is
hp = 2[pi] NT
--------
33,000
where T = pgV[bar]x =
pgQ[bar]x
---------
4N
[bar]x is the distance to the centroid of the annular quadrant from the
rotation axis. It is equal to
average diameter. [D.sub.av], of the
annulus
divided by [pi].
Therefore
hp =
2[pi]NpgQ[D.sub.av] = pgQ[D.sub.av]
-------------------
-------------
4[pi]Nx33,000
66,000
The power is independent of
the speed. The efficiency is the same
as calculated
previously. It is because the output
power is a
function of the average
diameter, that the efficiency drops off for
wide annulus wheels of a
fixed outside diameter. Potential power
output from a wheel operating
under the conditions of constant flow
may be estimated most easily
by the equation for water input power,
assuming 50% maximum
efficiency and head equal to the outside
diameter.
Power under constant flow
conditions for various diameter wheels
is shown in Table V for
likely attainable flow rates. The
values
dmft5230.gif (600x600)
entries by factors as shown
at the bottom of the table for various
practical t/r values.
The author's prototype with t/r = .17 tested
at approximately 150 gpm,
gave output power of approximately .06 hp
in reasonable agreement with
the values predicted in Table V.
Blank spaces are left where
flow rates are impractical for the
wheel size given.
Upper bounds to practical flow rates for
various
wheel sizes are found by
multiplying the entry from Table 1 by the
practical upper limit of
speed and width for the O.D. and are
shown in Table VI.
Lower bounds are subject to considerably
more
guesswork.
On the assumption that it would be
uneconomical to
construct a wheel of width
less than 1 ft. and to operate it at
less than 25% capacity
(completely arbitrary choice) for the
speeds quoted in Table VI the
useful lower bounds may be estimated.
These are indicated by blank
under the 100 gpm and
200 gpm columns in Table V.
TABLE VI
Upper Limits on Useable Flow Rates for Various Size Wheels in Imperial
Gallons Per Minute (assuming
wheel width = 1/2 (O.D.)
and peripheral velocity is 5 ft/sec.)
Outside Diameter (ft.)
3
4
6 8
10
14 20
Annulus
Width RPM at 5
ft/sec peripheral velocity
+(in.) 32
24
16 12
10
7 5
2
500
625 1000
3
700
900
1400 1900
2500
4
900
1150 1800
2400
8000
6
1650
2600 3500
4500
6000 9500
8
3400
4500 6000
8500
12000
10
5500
7500
10500 15500
12
6500
9000
12500 18500
16
17000
24000
20
20000 30000
24
35000
The upper limit to the speed
at which the wheel will operate depends
primarily upon the rate at which the wheel slings the incoming
water off so that it is not
utilized. This depends primarily
upon the speed and radius of
the wheel and secondarily upon the
bucket configuration and its
relation to the inlet water.
The figures quoted in Table
VI are based on the rule of thumb
peripheral velocity of 5
ft/sec. With smaller wheels this is a
bit high, based on prototype
tests. With the larger wheels the
peripheral velocity may be as
high as 8 ft/sec.
In summary, the type of power
vs. speed curve that one can expect
from a water wheel is as
follows for fixed flow rates: Linearly
increasing from zero speed up
to the speed at which the buckets
can no longer be completely
filled by the prevailing flow, then
constant up to the speed at
which significant amounts of water are
rejected from the wheel by
slinging action, thereafter decreasing
in proportion (roughly) to
the square of the speed.
C. Bucket Design
The optimum bucket design is
taken to be that which produces the
greatest torque on the wheel
shaft. The upper limit to this
condition
is that the buckets fill
completely at the top, carry the full
water weight with no spillage
to the bottom and dump their loads
there.
There is not a practical method of achieving
this maximum.
With fixed buckets, the best
we can do is minimize spillage from
the buckets as they travel
from the top, where they are filled,
to the bottom where they
should be empty (so as to limit losses
incurred by carrying water up
the back side of the wheel).
There are broadly two styles
of bucket as shown in Fig. 1. In the
dmf1x9.gif (600x600)
straight sided bucket the
limits on the angle the bucket makes
with the tangent at the O.D.
or I.D. (See Fig. 1) are from
tangential
(0[degrees]) to radial
(90[degrees]). With tangential buckets,
the filling
process is slow at the top
because of the very shallow angle with
respect to the incoming(nearly
horizontal) water. Furthermore the
emptying process at the
bottom is not complete until after the
bucket passes bottom dead
centre. This carries some water up the
back side and consequently
reduces the efficiency. At the other
extreme, radial buckets are
nearly empty by the time they have gone
1/4 turn from the top because
the bucket wall is then horizontal.
We can estimate the optimum
angle by assuming that the greatest
effect will be due to the
bucket whose weight is acting at the
greatest distance from the
shaft. By drawing buckets of various
angles we can estimate,
graphically, the optimum. While the
tangential bucket carries the
greatest amount of water, its centroid
distance is not a maximum The
maximum occurs at a bucket
angle (to the tangent at the
I.D.) of about 20[degrees]. While the
amount of water still
retained at 90[degrees] after top dead centre by
this bucket shape is about
20% less than for the tangential bucket, the
loss is compensated for in
the early filling and early emptying.
Especially on emptying, the
20[degrees] inclination is a major factor
since the length of the
bucket (distance from I.D. edge to O.D. edge) is
more than 30% shorter than
the tangential bucket. With a
30[degrees]-bucket,
the weight carrying capacity
at 90[degrees] after top dead centre is down
to about 65% of the
tangential, a figure which is so low that it
cannot be compensated for by
the secondary effects on efficiency
such as filling and
emptying. This graphical technique,
while of
no additional value in
designing any individual wheel, also shows
that the assumption of the
distribution of water over an upper
quadrant is a reasonable one
for estimating torque.
I recommend the bucket wall
angle be kept between 200 and 250 to
the I.D. tangent.
The use of flat bottomed
buckets does not significantly change the
water carrying capacity for
wall angles of 20[degrees]. The purpose
is
to decrease the distance the
water must travel to empty the bucket.
Its use is increasingly
beneficial at large t/r ratios but the
builder must accept that the
construction is somewhat more complicated
than that of the straight
sided bucket. Bottom widths should
be approximately 1/4 of the
annulus width, t. This will cut 25%
off the side width with the
attendant saving in travelling distance
to empty the bucket.
The significance of this is that less water
is
carried up the back side of
the wheel. Any water carried up the
back side lowers the
efficiency. I cannot give figures for
the
improvement of efficiency
using flat bottomed buckets but it seems
hard to imagine as much as
ten percentage points.
Historically, bucket shapes
have varied considerably. They were,
as far as I can determine,
chosen emperically. (In a historical
sense this is a euphemism for
"arbitrarily" or "by educated guesswork").
By the time engineers, rather
than carpenter-craftsmen,
were considering the problem
the water wheel's usefulness was
already on the decline).
Even in relatively recent manuals for
construction, circa 1850,
while wheels were still in general use
in the U.S., bucket side
angles of 45[degrees] were recommended - a choice
which can easily be shown to
be less efficient than smaller angles.
The 20[degrees] - 25[degrees]
figure is, however, in close agreement with the
design of two wheels that I
know are still in use in the U.S.
The number of buckets to use
depends upon the volume consumed by
the bucket wall
material. The ideal wheel has closely
spaced
buckets of very thin wall
thickness. A reasonable figure to design
by is that not over 10% of
annular volume should be consumed in
bucket material.
Typical values for the size wheels discussed
here
would be 25 - 30 - 1/4 in.
thick buckets on a 3 foot wheel and
50 - 1-1/4 in. thick buckets
on a 14 foot wheel.
D. Bearing Design
The wheel itself has only one
rubbing or sliding part subject to
wear, viz.
the bearings upon which the axle is
supported. Standard
bearing design is covered in
almost any machine design text. In
the manufacture of such a device as is discussed here, the value
of such
standard" bearings is
questionable. Fully weather-proofed
ball or roller bearings are
too expensive and complicated to satisfy
the initial criteria.
Bronze bushings with suitable
shaft material would be satisfactory
but lubrication and
replacement both present problems. The
use of
wooden bearings is, I think,
the best alternative for several reasons:
1.
Simplicity of manufacture with local skills.
2.
Availability of replacement parts.
3.
Negligible cost.
Wooden bearings are used
commercially for such applications as washing
machine wringer bearings
under conditions simulating those proposed for
the wheel.
Rock maple, lignum vitae, and various
species of oak are
used commercially, but when
these are not native to the country of
intended use, substitutes may
be found. Among woods with fairly
widespread distribution,
others which may reasonably be expected to be
satisfactory are beech and
red mangrove. Forestry departments,
when
they exist in a country are
generally in a position to make useful
suggestions.
In the absence of any
specific knowledge, the general rule is "the
harder, the better".
An estimate of allowable
loading based on experience with commercially
available wooden bearings
would be around 75 psi (for oak) to 150 psi
(for lignum vitae) for
orientations with the sliding surface parallel
to the grain and about 150 to
300 psi respectively for end grain use.
If the wood used has strength
and density properties comparable to
those mentioned above, it is
likely that safe loading would be about
100 psi parallel to the grain
and 200-250 in end grain usage. It
remains to be seen what the
wear resistance at these pressures will
be, but structurally the
figures given can be used with confidence.
Length to diameter ratios of
bearings in this application would
reasonably be expected to be
about unity and on that basis the
sizes of the bearings can be
estimated for wheels operating at
maximum output.
An allowance for the weight of the wheel
itself
is made on the basis that the
volume of wood required is approximately
equal to the volume of water
carried at stall and that the specific
gravity of wood operating
constantly in water is about unity.
Table VII shows the
approximate weight on each bearing per foot of
width of wheel.
Total weight carried on each bearing is then
the
product of the Table entry
and the width of the wheel in feet.
This
of course assumes that the
wheel is simply supported at each end of
the shaft and does not allow
for additional loads imposed by the
attached machinery.
It is important that significant loads due
to
the Table VII values for the
purposes of determining bearing size
from Table VIII for the side
of the wheel where the machinery is
attached.
In this event the bearings will apparently
need to be of
different sizes.
In practice, unless the indicated sizes are
very
different, we usually make
both the size indicated by the larger load.
Thus one is really longer
than it needs to be.
Bearing diameters required to
support the various loads are given in
Table VIII calculated on the
basis of 100 psi in parallel useage and
200 psi for end grain useage
and L/D = 1. Values are given to
20,000 lb. to allow for the
largest reasonable bearing loads.
TABLE VII
Approximate Weight Carried by Each Bearing Excluding Loads Due To
Attached Machinery
(per foot of width of the wheel) (lb.)
Outside Diameter (ft.)
3 4
6
8 10
14
20
+(in.)
2
24
32 50
3
35
47 70
95
120
4
44
60 89
125
160
6
86
140 185
235
335 470
8
180
240 305
440
675
10
290
370
530 765
12
330
445 635
920
16
820 1215
20
1020 1500
24
1760
TABLE VIII
Minimum Bearing Diameter
Required for Various Loadings (in.)
Load (lb.)
100
200
500 ]000
2000
5000 10000
20000
Parallel Useage
1
1-1/2 2-1/4 3-1/4 4-1/2
7
10 14
End Grain Useage
1/2
1 1-3/4 2-1/4
3-1/4
5 7
10
These bearings are assumed to
be steel on wood. In the likely event
that, especially in larger
sizes, the bearing is considerably larger
than the required shaft size,
a "built up and banded" bearing may be
used. A wooden cylinder is
built onto the shaft at the bearing location
such that the cylinder O.D.
is the necessary size. Then steel bands
are bent and fastened to the
cylinder. The criterion for design in
this case is that the product
of the diameter and the total width (sum
of the individual widths) of
the bands equals or exceeds the square
of the entry in Table VIII
for the corresponding load and grain
orientations.
If it is possible to arrange
for and be certain of, suitable maintenance,
a steel shaft in bronze
bushings mounted in commercial
plummer blocks (available
from hardward suppliers) is probably the
best choice. Proper alignment
may be a minor problem but is usually
fairly easy to overcome. This
choice involves additional initial
expense and is justified only
if maintenance can be guaranteed
regularly and frequently.
E. Shafts
Shafting may be wooden or
steel. The diameter is of course dependent
upon which material is used
and the dimensions of the wheel. Minimum
permissible shaft diameters
d, may be estimated from the equation
for stress for solid metal
shafting
[d.sup.3] = 16 [square
root][M.sup.2] + [T.sup.2]
-------------------------------------
[pi]S
In this equation M is the
maximum bending moment occuring where
the wheel sidewall attaches to the shaft. It can be estimated as
the product of the bearing
load (entry in Table VII for the appropriate
wheel) and the distance from
the wheel side wall to the
centre of the bearing. In the
interest of keeping the shaft as
small as possible, it is
therefore desirable to locate the bearings
as close to the side of the
wheel as possible. (Note that in most
cases, it is not critical to
include the additional machine load
on the bearing, discussed in
connection with the use of Table VIII.
It must be included only when
the external machine load times the
distance along the shaft from
the point of application of the load
is larger than the bearing
load from Table VII times the distance
along the shaft from the
bearing to the point where the wheel is
attached.)
T is the torque acting on the
shaft and a conservative estimate
is found from Table I. S is
the allowable shear stress of the metal.
dmft1120.gif (600x600)
(13,000 is used in the
example in Appendix 1.)
For solid wooden shafts two
equations are used and the larger diameter
of the two results is chosen
as the diameter of the shaft.
[d.sup.3] = 16T
----
[pi]S
[d.sup.3] = 32M
----
[pi]B
where S, T and M have the
same meaning as before. However, the value
of S is typically 150 to 300
psi for hardwoods. B is the allowable
bending stress and has a
value of about 1500 psi for typical hardwoods.
If wood is used it must be
sound and free from longitudinal cracks.
For hollow shafting like a
pipe, the equation to determine the outside
diameter is:
[d.sup.3] = 16[square
root][M.sup.2] + [T.sup.2]
-------------------------------------
[pi]S(1 - [k.sup.4])
where K = Ratio of inside to
outside diameter.
The values of O.D. and I.D.
are standardized for pipes. For bearing
loads tabulated in Table
VIII, on the assumption that the centre of
the bearing is 1 foot from
the edge of the wheel, the standard pipe
sizes shown in Table IX
should be satisfactory. Table IX automatically
allows for torque that would
be reasonable to expect from a wheel of
such a size that the bearing
load would be given in Table VIII.
The values are approximate
only since exact values cannot be given
until all the details
concerning the loads due to the attached pump
or machine are known. The
values given should serve as a guide only
and the final decision should
be checked against the equation to be
sure. When making substitutions,
in assembly, of one pipe size for
another, it is permissable to
use larger pipe than shown in Table IX
but not smaller pipe.
TABLE IX
Minimum Standard Pipe Sizes
for Use as Axles with Bearings at 12
inches
from Wheel Edge
Bearing load (lb)
100
200 500
1000
2000 5000
10000
Pipe Diameter (in)
1" 1 1/2"
2 1/2"
3" 4"
6"
8"
Comparing these figures with
the required bearing diameters of Table VIII,
it is obvious that when using
pipe or solid steel shaft, the
bearing will need to be of
the build up type when using wooden
bearings. An alternative is
to use a shaft whose size is selected
according to the needs of the
bearing size. It will be much stronger
(and heavier) than necessary
but may save some work. With wooden
shafts, the required shaft
diameter will usually exceed the required
bearing diameter and then one
has the choice of reducing the shaft
diameter at the bearing
location (but only there) or of using larger
bearings. In either case the
shaft must be banded with steel, sleeved
with a piece of pipe or given
some similar protection against wear
in the bearing.
F. Minor Considerations
We have considered all the
major theoretical aspects of selection of
sizes etc. to meet specific
requirements. All have been based on an
assumed efficiency of 50% - a
figure which is readily achievable in
practice with an overshot
wheel. There is one minor consideration
over which the design/builder
has control which may affect the
effiency slightly. The
raceway exit should put water onto the wheel
slightly before top dead
centre. The exact location is a function of
1.
flow rate and raceway inclination which
affect
the inlet water
velocity; and
2.
the bucket sidewall angle and peripheral
velocity
which affects how
smoothly the inlet water comes
onto the wheel.
Exact calculations hardly
seem justifiable for a machine which by
its very nature is as crude
and (relatively) inefficient as this.
Let it be sufficient that the
designer-builder get the water in
approximately tangent to, and
at the top edge of, the wheel.
V. PRACTICAL CONSIDERATIONS
A. Materials
Most wheels are wood, of
course, though they need not be. Among
the considerations for
selection of the proper material are the
ease of working, cost,
availability and durability. The average
carpenter can make a proper
choice on all these except perhaps the
latter. Forestry departments
in many countries can provide this
information on potentially
useful species. Others which would
probably be suitable are
mentioned in the section on bearing design.
Builders of water wheels may
naturally consider a "marine" plywood
as a likely material. It is
convenient to work with but the quality
varies widely around the world.
Because even the best grades have
a doubtful durability when
operating continuously in water unless
painted, plywood should be
chosen only when it can be well cared for
or when a relatively short
life is anticipated
Regarding the framework to
mount the wheel on, bamboo might seem a
logical choice in many
countries but the durability is such that
it probably would require
more long term care and replacement than
other materials. The species
listed for the bearings in section
IV D are all fairly durable
under constantly wet conditions and
should be the first to be
considered.
B. Construction Techniques
Any person sufficiently
skilled to build a water wheel will probably
also be sufficiently knowledgeable
to work out most of the construction
details. This manual is
intended to give the engineering groundwork
necessary to select the
proper overall size of wheel to meet a given
need and to make sure that
prevailing water supplies are, in fact,
adequate. However, a few
general suggestions may help the reader
avoid some pitfalls.
Attachment of the wheel sides
to the shaft, whether the sides are
spoken or solid, can be
accomplished in many ways. If a steel shaft
is used, a thin flange plate can be welded to the shaft (if such
facilities are available) and
this greatly facilitates the attachment.
With a solid side plate there
is no further problem but if
the spokes are used, the
bending in the spokes at the flange must
not be so great as to break
the spokes. The spokes should be
attached to the flange with
two or more bolts and the distance
required between the bolt
holes to support bending varies with wheel
diameter and the rigidity of
the spoke/wheel joint. For a flexible
joint the required a distance
would be approximately 1/10 to 1/12
of the outside diameter of
the wheel. For example, on a 12 foot
wheel, when using radial
spokes attached to a flange by 2 bolts
and to the wheel side plate (annular ring) by one, the flange
bolts should be about a foot
apart on each spoke.
Alternatively if the spokes
are quite rigid and firmly attached to
annular ring of the wheel as
with 2 or more bolts, the bolt hole
separation can be reduced to
1/20 of the diameter of the wheel at
the flange.
A simple spoke arrangement to
use is pairs of spokes, (one spoke
of each pair on each side of
the shaft) crossing at right angles
to make a shape like the
tic-tac-toe or noughts and crosses symbol.
The wheel axis runs through
the centre square and the extremities
of the lines are attached to
the wheel annulus.
Any glue used should be
highest quality waterproof glue for obvious
reasons. Resorcinol glue is probably the best choice.
Bucket attachment to the side
wall may be made by either grooving
the side wall to receive the
bucket edge or by attaching strips to
the inside of the side wall
to fasten the buckets to. There is an
advantage to the annulus
shape of side wall in that the inside of
the bucket is accessible from
the I.D. This makes closing off the
inside of the bucket simpler
because the necessary pieces can be
inserted through the I.D.
With solid sidewalls, the buckets must
be made complete and
non-leaking before the sidewall is attached.
This is by no means
impossible but may be more difficult.
If a solid sidewall is used,
holes should be drilled adjacent to
the bucket bottom into the
space between the bucket and the haft
to let any leakage water out.
A solid side wall would not commonly
be used. Spokes offer several
advantages.
Numerous books are available
to give helpful hints on various
construction techniques for the truly amateur builder.
C. Maintenance
The wood used may be painted
or varnished for a protective coating.
This will obviously extend
the life of the wheel. Periodic repainting,
if desired, can be carried
out. The decision on painting
must be made on purely
economic grounds. If a very durable wood has
been used initially, painting
is a luxury. If a somewhat less durable
species is used, painting is
probably cheaper and easier than early
replacement or repair of the wheel.
The only major maintenance
problem is in bearings. Generous allowances
have been made in the figures
in Table VIII but the bearing
will still ear. This will
drop the wheel from its original position.
Shimming under the bearing
block will compensate for this. Bearing
replacement, when the block
is completely worn through is a simple
matter.
Lubrication is totally
unnecessary with lignum vitae or commercially
processed maple, if
available. With the other species, we can not make
such a flat statement.
Generally speaking the bearing should be made
from the hardest wood
available and lubricated as needed. Oils and
grease in small amounts will
probably do no harm and may slow the wear
rate. Pig grease and tallow
would certainly be harmless and might help.
PART TWO:
APPLICATIONS
I. WATER PUMPING
A. Pump Selection
The only type of pump which is
reasonable to use at the slow speed
of the wheel is a positive
displacement pump. They are called by
various names such as bucket
pump, lift pump, piston pump, windmill
pump and occasionally even
simply by brand name such as "Rocket"
pump.
Numerous models are available commercially and vary in cost
from a few dollars for small
capacity pumps to several hundred for
high capacity, high head,
durable, well manufactured units. Units
can be manufactured at low cost
in the simplest of workshops.
Details are given in Appendix
II.
Such pumps may vary in bore
size, stroke length and head capacity.
There is a practical limit to
the speed at which they can operate.
This is usually above the
frequency of the fastest of wheels. A
frequency of speed multiplier
such as a multi-lobed cam or a gear
set may be used, but these more
complicated pumps and mechanisms,
while increasing the efficiency
of the pumping process, contravene
the criteria of Section II,
Part One for simplicity and will not
be discussed.
We will discuss only very simple pumps.
Even with simple single or
double acting pumps there are certain
problems.
one single acting pump attached to the wheel
will cause
speed surges on the wheel
because of the fact that actual pumping
takes place only half the
time. The other half is spent filling
the cylinder.
During this filling stage considerably less
wheel
torque is required than when
actually pumping. The speed surge
can be partially overcome by
using
1. two single acting pumps
180[degrees] out of phase so that one
of the pumps is always
doing useful work;
2. a double acting pump
which has the same effect as 1.
but is built in one
unit; or
3. best of all two double
acting pumps 90[degrees] out of phase.
Such use of multiple simple
pumps will also improve the overall
efficiency of the system.
(In general one unit can be attached
easily to a crank at each end
of the wheel shaft).
There are pressure variations
in the delivery line which depend
on several factors.
As long as the peak pressures do not exceed
the capacity of the pump and
related mechanism, nor stall the
wheel, such variations will
cause no harm. The pressure peaks
can be damped with an air
chamber in the delivery line or smoothed
by using two or more simple
pumps as mentioned in the preceeding
paragraph.
The possibilities are so numerous and the
details
sufficiently complex that they
cannot all be included here. A
pump expert or pump design
manual should be consulted if the design
ideas given here seem
insufficient for the user's needs.
In general the pressure peak
will be a function of the peak piston
velocity, the pump bore size,
the delivery pipe size, the length
of the delivery pipe and the
type of pipe used. When speaking of
pump performance and design
requirements, the term "head" is
encountered often.
It is a means for visualizing the fluid
pressures
involved in the pump or
attached pipes. It means the height
of water in a vertical pipe
necessary to produce, at the bottom
of the pipe, the pressure being
referred to. The pressure is an
actual system will not, in
general, be produced just by a static
column of water but it will be
the same as if it were. It's
just a handy shortcut often
used by fluids engineers. The head
The head required at the pump
outlet will be made up of two main
components:
1. the actual change in
elevation to the delivery pipe
exit, i.e. the
(vertical) height of the hill; and
2. friction loss in the
pipe which is given by the
equation:
L V
friction loss = f - -
D 2g
where f = friction
factor obtainable from handbooks or
Table X
L = length of pipe
D = inside diameter of
pipe
V = velocity of water in
the pipe
g = gravitational
acceleration
(Note: Units for dimensions
must be consistent. See Appendix I
for an example of the use of
this equation).
TABLE X
Estimated Friction
Factors for Cool Water
Water
Velocity
(ft/sec.)
1
5
10
Old Iron Pipe
.045
.040 .038
New Iron Pipe
.030
.023 .021
Plastic Pipe
.025
.017 .015
It is evident that this becomes
a major factor in very long pipes,
in small diameter pipes, or
with high velocities. The water
velocity
in the delivery pipe is a
function of the peak pump piston
velocity and the ratio of the
pump bore size and the delivery pipe
size.
Peak piston velocity for pumps attached directly to the
wheel is given in Table XI for
various strokes and wheel speeds.
From Table XI, the delivery
line velocities can be estimated
simply by multiplying the Table
XI entry by the ratio of the pump
bore area and the delivery pipe
area. That is, piston velocity
times piston area = water
velocity in delivery pipe times pipe bore
area.
As a rule of thumb, this
resulting delivery pipe velocity should
be a maximum of 10 ft/sec. in
short runs, and even smaller for
very long pipes.
The peak head required of the pump will be
the
sum of the two different heads
mentioned, i.e., elevation change
plus friction loss head.
The bore size (piston area) and
peak head occurring during pumping
will determine the force
required at the pump rod since force on an
area is the product of the area
and the pressure acting on that
area.
Figures for force at the rod are given in Table XII.
No
allowance is made for rod
diameter so the figures given are conservative.
Bore sizes quoted are commercially
available.
TABLE XI
Peak Pump Piston Velocity (ft/see) for a Pump Rod Attached Directly to a
Crank on the Wheel
Wheel Speed Stroke
(in.)
(R.P.M.)
2 1/4
4
6 8
10
12
5
0.048 0.087
0.129
0.172
0.216 0.260
6
.059 .104
.156
.208
.259 .310
8
.078 .138
.207
.276
.345 .414
10
.097
.173
.259 .345
.432
.518
12
.117 .208
.312
.416
.520 .624
15
.147 .260
.390
.520
.650 .780
20
.195 .345
.518
.690
.865 1.04
TABLE XII
Peak Force on the Pump Rod of a Piston Pump Required for Various Bores
and Heads (lb.)
Peak Head (ft.)
change in elevation and friction loss
Pump Bore (in.) 50
100
200 300
400
500
1 1/4
30
60 110
370
220 280
1 1/2
40
80 160
240
320 400
1 3/4
60
110 220
320
430 540
2
70
140 270
420
560
700
2 1/2
110
220 440
660
880 1100
3 1/4
185
370 740
1120
1480 1850
4 1/4
315
630 1260
1890
2520 3150
These figures are required to
design such parts as clevis pins
(if used) and to determine
that, if the pump rod is attached directly
to the wheel, that the crank
arm length times the entry in Table XII
does not exceed the torque
capacity of the wheel as given by
Table I.
Of course, if levers or other
torque/force multiplying devices are
used, appropriate calculations
at the wheel can be made. The force
at the pump rod still remains
as given in Table XII. The velocity
given in Table XI must be
adjusted for the change in crank arrangement.
Additionally, if the line is
very large so that a large mass of water
must be accelerated on each
stroke, the inertial forces can become
greater than the pressure
forces. The inertial forces can be
estimated with the aid of
Tables XIII and XIV.
TABLE XIII
Volume of fluid in
various sized delivery pipes ([ft.sup.3])
Pipe
length (ft.)
Nominal pipe size
50
100 200
500
1000
1"
.3 .6
1.2
3 6
2"
1.16
2.32 4.65
11.6
23.2
3"
2.46
4.91 9.82
24.6
49.1
4"
4.38
8.78 17.50
43.8
87.5
TABLE XIV
Inertial force (lb.) per inch
of stroke for various volumes of fluid at various pump cycles speeds
Pump Cycles per
Minute
Volume of Fluid in delivery
pipe([ft.sup.3])
.5
1
2 5
10
50
100
5
.133
.266 .533
1.33
2.66 13.3
26.6
10
.577
1.14 2.29
5.77
11.4 57.7
114
15
1.20
2.40 4.80
12.0
24.0 120
240
20
2.14
4.27
8.33 21.4
42.7
214 427
25
3.31
6.61 13.2
33.1
66.1 331
661
30
4.78
9.65 19.1
47.8
96.5 478
965
This inertial force is at its
peak just as the piston starts its
pumping stroke.
At this time the friction loss is zero
because
the delivery pipe velocity is
zero. Hence the total rod force at
the start of the stroke ill be
equal to the force due to the
static head plus the inertial
force. It should be compared with
the rod force when the friction
loss is a maximum and the components
designed to withstand the
larger of the two.
We can calculate the power
required to accomplish pumping under
various conditions of head,
flow rate and pump type. These figures
are given in Table XV for
steady flow and are adjusted for unsteady
flow explained below.
This is the theoretical minimum
power input required to the pump
under steady conditions.
Under the unsteady conditions
of a piston pump, to estimate the
water wheel power capacity
required, multiply the table entry by
2 1/2 for one single acting
pump, by 2 for one double acting pump
or two single acting pumps
180[degrees] apart or by 1.5 for 2 double acting
pumps 90[degrees] apart.
This will give an estimate of the size of
wheel
and flow rate required to the
wheel.
As mentioned near the beginning
of this section, there will be
speed fluctuations in the wheel
which may be pronounced in smaller
wheels working near their
capacity. This is no particular
disadvantage
so long as the stall torque
capacity of the wheel exceeds
the minimum torque necessary to
keep the pump moving. The magnitude
of the fluctuations decreases
with double acting or multiple
pumps installations and where the mass of the wheel is such that
a flywheel action begins to
take place.
TABLE XV
Horsepower Required for Water
Pumping at Various Flow Rates and Heads (both assumed steady)
Total Head (ft.)
Flow Rate
(imp.gal/hr.)
50
100 200
300
400 500
5
0.00125
0.0025
0.0050 0.0070
0.01
0.0125
10
.0025
.0050
.01 .015
.02
.025
25
.00625
.0125
.025 .0375
.05
.0625
50
.0125
.025
.05 .075
.1
.125
100
.25
.50 .1
.15
.2 .250
150
.0375
.0750
.15 .225
.3
.375
200
.05
.1 .2
.3
.4 .500
250
.0625
.125
.25 .375
.5
.625
300
.075
.15
.3 .45
.6
.75
500
.125
.25
.5 .75
1.0
1.25
1000
.25
.5 1.0
1.5
2.0 2.5
"See text for correction factors
for various types of pump sets."
The volume pumped per stroke
varies slightly with the design of
the pump and with the bore and
stroke sizes. One commercial
manufacturer quotes figures
which can be taken as representative.
These are given in Table XVI.
B. Method of attachment to
wheel
In activating any piston pump,
it is done ideally, such that
straightline motion of the
piston rod is achieved. Any bending
in the rod puts undue side
loads on the discharge head seal and
on the piston bucket.
Straightline motion mechanisms are described
and discussed in textbooks, so
I will not endeavor to
give details of the common
mechanisms. The books seldom mention
however, the practical problems
which arise when trying to use
such mechanisms.
Nor do they usually compare advantages and
disadvantages.
I will mention some possible
mechanisms along with
the advantages and potential
problems.
A slider and crank mechanism
(See Fig. 3) is attractive as a simple
dmf3x53.gif (600x600)
device with the advantage of
requiring no special techniques to
prevent bending moments on the
pump plunger. Stroke is easily
adjustable
by attaching the crank pin to
the wheel shaft via a flange
plate with holes drilled at
various distances from the rotation axis,
through which the crank pin can
be fixed. Unless a double acting
pump is used, the pumping
stroke and return stroke will have different
forces on the crank pin
resulting in non-uniform wheel rotational
speed (unless compensated for
by other means - such as attaching
single acting pumps operating
180[degrees] out of phase). This
non-uniform
motion can be alleviated to an
extent by attaching the slider
(pump axis) offset from the
wheel axis. It then becomes a form of
quick return mechanism.
This, however, increases the side load on
the slider during the return
stroke, which necessitates moving the
slider bearings apart
(increasing the slider length) to maintain
the same slider bearing
pressure as with the symmetrical arrangement
if bearing pressure and the
resulting frictional drag on the slider
become large enough to cause a
problem. Lubrication of the slider
bearing presents a
problem. Although precautions can limit
somewhat
the exposure to water in the
bearing, it is unlikely that the
bearing can be completely
protected. Pressure grease fittings
using a suitably wash-resistant
grease might prove suitable.
Packing box style lubrication
with oily felt or rags could also
be successful.
Both methods rely on periodic attention,
which could be
of an intolerable
frequency. There are also the crank pin
and clevis
pin at the slider to be
lubricated. Finally, alignment is a
potentially
tricky problem because of the
narrow tolerance allowable on
parallelism of the wheel shaft
and crank pin and on perpendicularity
of the plane of the slider
crank mechanism with the wheel shaft.
One major advantage compared
with the next method discussed is that
since the pump body can be
fixed if the alignment is sufficiently
accurate, the connection with
the distribution pipe can be rigid.
TABLE XVI
Quantities of Water Pumped per
Stroke for Single Acting Pumps of Various Bore and Stroke Sizes
(Imperial Gallons)
Stroke (in.)
Bore (in.) 2 1/4
4
6 8
10
12
1 1/4
.009
.016 .023
.032
.040 .049
1 1/2
.013
.023 .035
.045
.057 .069
2
.023
.040 .062
.082
.102 .122
2 1/2
.035
.064 .095
.127
.159 .191
3
.052
.092 .139
.184
.230 .278
3 1/2
.070
.125 .187
.248
.312 .276
4
.092
.163 .245
.227
.410 .489
5
.143
.255 .382
.510
.638 .765
A second method of attachment
is to pivot the pump body about an
axis parallel to the wheel
shaft (as on trunnions), attach the
pump rod end to the same kind
of crank pin as before and let the
pump oscillate side to side as
the piston goes up and down. (See
Fig. 4).
This eases the difficulty of the alignment
problem involving
dmf4x56.gif (600x600)
the plane of the crank
mechanism previously discussed but
introduces new
complications. The pump rod is
subjected to side
loads.
This is ordinarily intolerable at both the
gland and the
bucket but fortunately is
easily overcome by a simple frame
attached to the pump with
sliding bearing surrounding the crank
pin which the pump rod end (at
the crank pin) then slides in. The
bearings absorb all the side
loads required to cause the oscillation,
leaving the pump rod loaded
linearly only. Side loads on
these slider bearings would be
smaller than the side loads on the
slider in the slider crank
mounting so that the sliding bearing
problems with this technique
are somewhat simpler. A serious
objection
to this mounting method is the
necessity for a flexible
connection from the pump to the
distribution pipe. If the reader
intends to build his own pump,
which would be likely if considering
this particular arrangement,
plan to have the outlet of the
pump colinear with the trunnion
axis. In this way a simple seal
to allow the pump exit pipe to
oscillate in the delivery pipe will
suffice.
This method of flexible connection will
probably be the
most durable.
The scotch yoke mechanism (See
Fig. 5) is simple and direct but may
dmf5x57.gif (600x600)
require more sophisticated
machining than available equipment will
allow.
Furthermore, there is the potential danger
of excessive
wear and short life if the
lubrication is insufficient. This is
not
generally a suitable mechanism
for unattended use in harsh conditions.
A cam activated pump rod is
an attractive alternative. It
eliminates the need for any
linkage, simplifying the alignment
problem and eliminating some
parts. Side loads on a properly
designed profile would be
very small and a sliding bearing on
the outboard end of the pump
rod would easily absorb it. A
suitable cam profile is given
schemetically in Fig. 6. Force for
dmf6x59.gif (600x600)
the return stroke can easily
be supplied by a properly weighted
pump rod and the simplest
location for such weight would be
immediately above the
follower plate. Solid mounting of the
pump
in this case allows rigid
supply piping to be attached directly
to the pump.
A pump bought ready made with
a handle can be attached quite simply
by a rod suitably aligned
between a crank on the wheel and the free
end of the pump handle.
Then force and velocity calculations must
be modified.
Various straight line motion
linkages are easily constructed. They
have the advantage of
simplicity and durability even under harsh
working conditions.
Many such linkages are discussed in books on
Theory of Machines and
Machine Design.
One simple technique to
achieve straight line motion seldom seen
in texts on machine design is
to run a cable over a pulley such
that the end of the cable
attached to the pump is colinear with
the pump rod.
The other end can be attached to the wheel
crank
and the cable provides
sufficient flexibility that no solid linkage
is needed.
An alternative to this approach is to link
the wheel
crank to a sector of a pulley
sheave in such a way that the sheave
oscillates as the crank
rotates. With the cable wrapped far
enough
around the sector so that the
cable always remains tangent to the
sector and fixed there, the
free end of the cable can be attached
colinear with the pump rod to
provide straight line motion. This
is the mechanism used on oil
drilling rigs.
The cable, as a part of the
drive mechanism, can be made very long
in order to drive pumps
located at a considerable distance from
the wheel itself.
Such a technique provides the means to
power,
for instance, a shallow bore
pump in the middle of a village using
power generated at a stream
some distance away.
C. Piping
For any water distribution
system where the water must be transported
to a higher elevation, piping
is usually required. There
are alternatives such as
buckets on an endless belt, etc., but that
is outside the scope of this
manual.
The choice will probably fall
between polythene and galvanized
iron pipe.
There are advantages and disadvantages to
both. I
shall endeavor to give some
helpful information to aid the designer
in making the best choice.
Polythene pipe is available
in long (now around 200 meter) lengths
so numbers of couplings and
joints are greatly reduced compared to
the iron pipe which comes in
short lengths (21 1/2 ft typically).
It is flexible (softer,
weaker and more elastic in strict engineering
terminology) and for this
reason is more susceptable to damage
from bush knives, rocks, pig
hooves, etc. Its strength is limited
such that it is rated to
support at best 300 foot normal working
heads at standard
conditions. The strength is strongly
temperature
dependent however, and at
120[degrees] F head capacity is down to
185 ft maximum.
It is not fire resistant.
Consequently in open
country it would probably
need to be buried. If the local soil
is very rocky, the burying
process must be done with great care
to keep the pipe from
suffering rock (penetration) damage.
Sand
is usually used as a bed and
cover.
Iron pipe can generally
simply be laid on the ground with rock
piles to support it through
low spots. It will support more than
1000 ft heads with plenty of
safety margin. For heads to get
that high, the system
required will be more sophisticated than
can be made by the techniques
detailed in this manual.
Prices for the two types are
competitive in the higher strength
grades of polythene but for
low pressure systems, polythene may
be substantially cheaper.
Polythene has a smoother bore
so that friction losses are less than
with iron pipe, although this
would not likely be a significant
factor.
It becomes more important in long gravity
feed systems.
Weight of a given length is
vastly different. 100 ft of high
strength 2" polythene
weighs 60 lb while 100 ft 2" standard iron
pipe weighs 357 lb.
Therefore, long distance transport by hand
to
very remote areas might
influence the decision for polythene even
in spite of its other
shortcomings.
II. OTHER APPLICATIONS
While water pumping is an
obvious use for the water wheel, other
machinery can be adapted to
use the mechanical power output of the
wheel.
It is not the intention of this section to
attempt to
enumerate all the possible
applications. Rather, I include this
section to offset any impression
that may have been given by the
preceeding section that water
pumping is the most important, or
perhaps only use to which the
wheel may be put.
Generation of electricity is
a possibility which will probably
spring to the minds of most
people reading this manual. There
are wheel driven electric
generators in operation in Papua New
Guinea today but the number
of attempts and failures testify to
the fact that it is not a
simple, cheap task to make a successful
rig. The principal
difficulties are the speed step-up required
for generators and speed
regulation. Low voltage D.C. generation
using readily available parts
(old auto generators or alternators)
avoids the speed regulation
problem. Simple starter-motor-pinion/
flywheel-ring-gear sets could
be adequate for speed step-up at a
reasonable cost.
Typical ring gear sets have a lower limit of
10
diametral pitch size teeth
which gives a power rating of 10 R.P.M.
of about 1/2 h.p.
It is, therefore, marginal to expect to
produce
continuous output from a 12
volt automobile generator at, say, 60
amps for long periods of time
without gear problems. The small
amount of power generated,
the need for 12 volt bulbs, resistance
losses in long distribution
systems and other problems also mitigate
against this being a useful
bolt-on accessory. Electricity
generation
is better left to the higher
speed devices which are more amenable
to speed regulation such as
the Banki Turbine of a centrifugal
pump being forced to run as a
turbine.
Attachment directly to other
mechanical machinery can be accomplished
by a variety of coupling
devices described in various
machine design books.
Two circumstances are likely to occur:
1.
the machine to be driven will be located
some
distance from the
wheel; and
2.
the input shaft of the machine will not
easily
be aligned with the
wheel shaft.
Alignment difficulties are
overcome simply and cheaply with old
automobile drive shafts and
their attached universal joints.
Note that the use of one
universal joint will not give constant
speed on both sides.
For a constant input speed, the output is
alternately faster and slower
than the input depending upon the
angle between the two
shafts. The speed variations are small
and
will generally not be of any
consequence. If the speed variations
cannot be tolerated, either a
special constant velocity joint (as
from the front wheel drive
automobile) or two ordinary U joints
must be used, each to
compensate for the non-uniform motion of the
other.
Flexible shafts are
commercially available but are of limited
torque carrying capacity.
Solid shafts can transmit
torque over considerable distance but
require bearings for support
and may therefore be expensive.
Virtually any stationary
machine which is currently hand-powered
could be run by water wheel
power. The means to accomplish the
attachment would vary from
machine to machine of course, but only
in the case of where the
wheel and the machine are separated by long
distances should there be any
significant problem.
APPENDIX I
Sample
Calculation for Wheel-pump set
The following is an example of the use of this manual to make decisions
relating to water wheel for use in water pumping.
The decisions made
must be consistent with the bounds placed upon the system by the
village's
needs (how much power is required) and the geography and size of the
supply stream (how much power we can expect to get from the wheel).
If
the power required is greater than the power that can be generated by
the wheel, then the system cannot work.
This example is taken from
calculations made for Ilauru village, approximately 15 miles south of
Wau, New Guinea. One of the
possible locations for a wheel is in a stream
about 350 feet below the level of the village.
The hill is quite steep
and would require about 750 feet of pipe.
There is a place in the stream
where the water level drops quite rapidly through a vertical distance
of 8 or 10 ft. The stream is
about 10 ft. wide, averages 6 or 9 inches
depth and flows about between 1 and 2 ft. per second (estimated by
measuring
the time for a leaf to travel a fixed distance).
That description
establishes the conditions to determine the maximum wheel size.
The village has about 300 people.
Each person now consumes less than
2 gallons of water per day in the village according to a rough estimate.
If the water were pumped into the village, experience in other countries
shows that the consumption would increase.
A minimum of 10 gallons per
day per person is sometimes quoted as a minimum viable scheme.
Let us
calculate for twice that to allow for expansion of population or of
consumption.
1.
Total water requirement in gallons per hour
20 gal/person-day
x
300 people x
day/24 hr
= 250 gal/hour
assuming storage
facilities at the village to allow larger
draw at peak hours.
2.
Power required to meet this pumping rate from Table XV.
250 gal/hour at approx.
400 ft. head (350 actual ft. rise +
some losses as yet uncalculated) requires about 1/2 h.p.
under
steady conditions.
3.
Depending on the type of pump arrangement used, the wheel will
need to be designed for
2 1/2 times that for a single acting pump,
2 times that for double acting pump or 1 1/2 times that for
2
double acting pump.
Assuming the simplest case of 1 single
acting pump we need a
wheel of 1 1/4 h.p. potential.
4.
Can we get that much power from a water wheel under the stated
conditions at the
stream? The largest diameter possible is
limited by the drop in
the stream in a useable distance -- about
8 feet.
An 8 ft. wheel will operate at about 12 rpm
or less
(Table VI).
The stream has a flow rate of at least
10 ft x 1/2 ft
x 1 ft = 5 [ft.sup.3]
----- ---------
sec sec
or
5 [ft.sup.3]
x 6 1/4 gal x 60 sec = 1800 gal
---------- ----------
------
---------
--------
sec [ft./sup.3]
min
min
At 1800 gal/min we should
be able to produce 2 h.p. at least
from an 8 ft. wheel
(Table V) or slightly less depending upon
the exact t/r values
finally chosen.
Therefore we conclude
that the job, in theory, is possible.
Had the flow rate been,
for example, only 500 gallons per
minute, the task of
pumping 250 gal per hour to the village
would probably have been
impossible.
5.
At an estimated 12 rpm and 4 ft. width (maximum usually used
is half the diameter) we
can estimate the annulus width necessary
(Table II).
1 1/4 h.p. needed
------------------
=
0.025 h.p. per rpm per ft of width
12 rpm x 4 ft wide
In the entry under 8 ft.
diameter wheels we see that all annulus
widths listed will
provide at least that much power. We
now know we can make the
wheel less than 4 ft. wide if desired
and the annulus width
can be between 3 in. and 12 in.
It is now completely
established that an 8 ft. diameter water
wheel in this location
will do the job required.
6.
If the wheel operates at 12 rpm and the pump is directly
coupled so that there is
one stroke per rpm with no added
leverage (for instance,
as with the wire connection suggested
in Part Two, Section
IB), there will be one stroke per revolution.
To accomplish 250 gal/hr
we need:
250 gal
hr
min
--- x ------ x
---------- = .35 gal/stroke
hr
60 min
12 strokes
From Table XVI that
means we need 3 1/2 pump with 12" stroke
or 4" pump with
9" stroke etc.
7.
If we limit the velocity in the pipe to 10 ft/sec then the
pipe size with the 3
1/2" pump (chosen because it is cheaper
than the 4" pump)
is related to the peak piston velocity and
the pump size.
From Table XI the peak piston velocity at
12" stroke 12 rpm
is .624 ft/sec. The delivery pipe cross
section area must be
approximately
.624 x 11 [(3
1/2).sup.2] 1
--------------- x -- = Pipe area
= .64 [in.sup.2]
4
10
This would require a
nominal 1" diameter pipe.
8.
The pipe would need to be galvanized iron to withstand the
pressure
of heads exceeding 350
ft. If a nominal 1" pipe is used,
the actual peak velocity
is about 7 ft/sec.
The friction head loss
would be (Table X)
friction loss = 0.022 x
750 [7.sup.2]
---- x --------- = 150 ft
1/12 2 x 32.2
Thus the total peak head
causing forces on the pump rod
would be 350 (elevation)
+ 150 (loss) = 500 ft.
Commercial 31/2 m. pumps
are fitted with 2 in. pipe outlet
holes and if 2 in. pipe
is used the loss is much less
because the velocity is
less and the diameter is greater.
friction loss =
0.028 x 750 [2.sup.2]
---- x --------- = 8 ft
2/12 2 x 32.2
The saving is obviously
substantial but the cost of doubling
the pipe size may be
unattractive.
9.
Assuming we use the 1" pipe we find the required pump rod
force from Table XII is
about 1850 lb. For a 12" stroke a
crank length of 6"
is required and so the peak torque on
the machine is 925 ft/lb.
From Table 1 we see that
this is well within the capacity
of the wheel if it is 4
ft. wide.
10.
To allow for reasonable future expansion of needs without
adding unnecessary
weight to the wheel I would select a 4"
annulus.
Having done that, the bearing loads are
(Table VII)
about 500 lb. each.
Assuming the bearings can be located
fairly close to the
wheel, say 6" away, the solid steel
shaft size required is
found from:
[d.sup.3] = 16[square root][(6 x 500).sup.-2] + [(925 x
12).sup.2]
-------------------------------------------------------
[pi] (13,000)
d = 1.65 in
Any solid steel shaft larger than this will be satisfactory.
APPENDIX II
An Easily
Constructed Piston Pump
dmfspx71.gif (600x600)
by R. Burton
This pump was designed by P. Brown (of the Mechanical Engineering
Workshop
at the Papua New Guinea University of Technology) with a view to
manufacture in Papua New Guinea.
Consequently the pump can be built up
using a minimum of workshop equipment.
Most parts are standard pipe
fittings available at any plumbing suppliers.
To avoid having to bore and hone a pump cylinder, a length of copper
pipe is used. Provided care is
taken to select an undamaged length and
to see that the length is not damaged during construction this system
has proved quite satisfactory.
As can be seen from the cross-sectional diagram, the ends of the pump
body consist of copper pipe reducers silver soldered onto the pump
cylinder. This does make
disassembly of the pump difficult, but avoids
the use of a lathe.
If a lathe is available, a screwed end could be silver soldered to the
upper end of the pump to allow for simple disassembly.
The piston of the pump consists of a 1/2" thick P.V.C. flange with
holes
drilled through it (see diagram).
A leather bucket is attached above
the piston and together with the holes serves as a non-return valve.
In this type of pump the bucket must be made of fairly soft leather,
a commercial leather bucket is not suitable.
Bright steel bar is
used as the drive rod and has to be thread cut at its ends using a die.
A galvanized nipple is silver soldered to the top copper reducer of the
pump to allow the discharge pipe to be attached.
An `O' ring seal of the type used to join P.V.C. pipe is used as a
seal for the foot valve. This seal does not require any fixing since
it push fits into the lower copper pipe reducer. A 1/2" screwed
flange
with a plug in its centre forms the plate for the foot valve. This plate
must be restrained from rising up the bore of the pump by three brass
pegs fitted in through the side wall of the pump above the valve plate.
These pegs must be silver soldered in to prevent leakage or movement.
A parts list for a 4" bore x 9" stroke pump is set out below
together
with a tool list.
Parts
1 only 12" x
4" dia. copper tube
2 only 4" to 1
1/2" copper tube reducers
1 only 1 1/2"
galvanized nipple
1 only 1/2"
screwed flange
1 only 1/2"
plug
1 only 1/2"
P.V.C. flange
1 only Rubber `O'
ring 4" dia.
1 only piece of 4
1/2" dia. leather
1 only 15" x
1/2" dia. bright steel bar
1/8" dia.
brazing rod
Tools
Handi gas kit
Silver solder
Hand drill
1/2" Whitworth
die
1/2" Whitworth
tap
Hacksaw
Hammer
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