Alan E. Belcher's 1972 Coil Pump

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Copyright © 1995 American Society of Civil Engineers. Reprinted from "Revenues Lost to Fish Passage" (Proceedings "Waterpower '95", American Society of Civil Engineers, San Francisco 1995).

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Recovery of Revenues Lost to Fish Passage
Alan E. Belcher
70 South Main Street #2, Waterbury, Vermont 05676, U.S.A.

Reprinted from WATERPOWER'95
Proceedings of the International Conference on Hydropower
Published by ASCE
Held July 25 - 28, 1995, San Francisco, CA

(This paper was one of 12 nominated for the "Best of
Waterpower '95" award, from more than 280 papers presented.)

Table of Contents


Introduces a fundamentally new type of hydraulic engine/pump set which forms the core of a system to recover energy usually expended in fish passage. An historical background is presented. Equations are developed from those describing two types of manometer. Principles of operation and salient features are explained.


Operation of fish passage systems at hydroelectric plants is becoming increasingly onerous in terms of lost power generation. Increases of regulatory mandated instream flows are turning once profitable hydropower sites into economic liabilities. This is particularly evident when older plants seek relicensing. All too often their efforts to improve capacity through technical upgrades are defeated by these stringent requirements.

The manometric engine/pump set offers an elegant solution by providing a reliable means for generating power from instream flows while ensuring the safe passage of fish and other riverine fauna. The system's inherently large size is more than offset by its many advantages. Having only one moving part, the machine is the very essence of simplicity. Its extended life-cycle and low maintenance are therefore assured. From the standpoint of fish passage the system provides a physically clear and unobstructed path from intake to discharge, the water flow being controlled by a series of traveling U-tube manometers. At the only point where physical impact with fish could occur, the highest linear velocity can be reduced to a mere 1.2 m/sec or so. This technology could do much to alleviate the tensions surrounding fish mortality at hydropower sites.

Note: Permission to reproduce text and illustrations in paragraphs "Background" through "Basic Principles of Operation" is kindly granted by "The Northern Engineer", School of Engineering, University of Alaska Fairbanks.


The earliest literature referring to the simple manometric pump, described as a screw or spiral pump, appears in "The Cyclopaedia" (Reese 1820) and "A Descriptive and Historical Account of Hydraulic and Other Machines for Raising Water" (Ewbank 1849). Both references attribute the invention of this pump circa 1746 to Andrew Wirtz, a pewterer of Zurich.

In 1972 Alan E. Belcher invented a similar pump which applied the same principles of operation. Neither Belcher - nor, for that matter, the United Kingdom Patent Office - discovered the evidence of prior art and U.K. Patent 1427723 was subsequently granted in 1976. Belcher did not learn of the existence of prior art until December 1985 after exchanging correspondence with Alan Stuckey, a retired researcher formerly with the University of Salford and co-author of the paper "The Stream-powered Manometric Pump" (Stuckey, Wilson 1980). An unpublished paper by Belcher, circulated to selected individuals in early 1973, described the principles of operation of the hydrostatic pump, as it was known at that time. This document inspired a significant portion of a dissertation "The Hydrostatic Pump and Other Water-lifting Devices in the Context of the Intermediate Technology Approach" (Ohlemutz 1975) submitted by Dr. Rudolf E. Ohlemutz towards his doctoral degree in engineering. It was published in May, 1975. The same document by Belcher served as a basis for the paper "The Stream-powered Manometric Pump" (Stuckey, Wilson 1980). In 1979 Dr. Peter R. Morgan invented a pump closely resembling the original Wirtz pump and published his findings under the title "A New Water Pump: Spiral Tube" (Morgan 1979). Dr. Morgan had no knowledge of the prior inventions of Wirtz and Belcher and, as mentioned in his first publication, his "searches through the relevant literature failed to reveal a similar arrangement."

From the published literature examined to date it appears that Belcher, realizing the pump's potential for handling large quantities of fluid, has been the only researcher to develop the use of helical conduits of rectangular cross-section in place of the more commonly used tubes or pipes. However, this is not a new concept having been suggested first in the original literature, and later applied by Dr. Ohlemutz. Belcher also pursued theories and assumptions supporting the presence of torque which, by laws of physics, had to be produced by the head of water being pumped.

In 1974 Belcher, with the help of Dr. Alan Mayne, discovered that the cross-sectional area of two independent coils of different diameter could be precisely matched by a simple geometric formula, thus proving the feasibility of the manometric engine. When Belcher was working on the development of mathematical equations that would accurately predict the torque resulting from a given head and helical coil configuration, evidence came to light of the ring balance manometer, a device used for measuring small differential pressures - "Engineering Measurements" (Collet, Pope 1983). The equations associated with this instrument gave Belcher the sought after mathematical proof as well as the means for computing torque in relation to discharge head or pressure. The results of the final equations correlate closely and consistently with standard turbine and pump formulas.

A United States patent for the Manometric Engine was issued to Alan Belcher in 1980.

The U-Tube Manometer

The U-tube manometer is a basic instrument for measuring pressure - "Mechanical Engineers' Handbook - Engineering Measurements" (Marks 1951). In its most common form it consists of a transparent tube formed into a U and partially filled with a sealing liquid, usually water or mercury (Fig. 1A):

U-Tube Manometer

To measure the pressure of a fluid it is necessary to know the specific weight of the sealing liquid. One of the vertical limbs of the U-tube is then connected to the fluid to be measured, while the other remains open to the atmosphere. Any pressure difference between the fluid and the local atmospheric pressure will cause the sealing liquid to be displaced away from the source of the highest pressure until hydrostatic equilibrium is reached. The pressure sustaining the displacement is the product of the difference in level of the sealing liquid in each limb of the U-tube (the hydrostatic column or head) and the specific weight of the sealing liquid. This is represented by the following equation where y symbolizes the specific weight of the sealing liquid and h is the vertical distance between the levels of sealing liquid in the two limbs of the U-tube, then p is the pressure:

p = yh (1)

If both limbs of the U-tube are connected to fluids the instrument will indicate the pressure difference existing between the two fluids. If two or more U-tubes are connected in series (Fig. 1B), and providing that the communicating fluid between each is of less specific weight than the sealing liquid, then a pressure applied across the group of U-tubes will equal the algebraic sum of the hydrostatic columns or heads in each of the U-tubes multiplied by the specific weight of the sealing liquid "Mechanics, Fluids" (Streeter 1987). Equation 1 can be expanded as follows:

p = yh1 + yh2 + yh3+ ....... + yhn (2)

or substituting from equation 1:

p = p1 + p2 + p3 + ....... + pn (3)

Another important point is that the quantity of sealing liquid does not influence the pressure measured - "The Measurement of Pressure - Precision Manometers" (author unknown). The only requirement is that there be enough liquid to maintain a seal at the bottom of the U under the maximum pressure anticipated without overflow occurring from either vertical limb. However, the U-tube manometer need not follow the usual pattern of having two vertical limbs; the tube can also be formed into a ring or annulus, but it will still obey the laws of hydrostatics as described above.

The Ring Balance Manometer

This instrument is used for measuring small differential pressures. Although somewhat obscure in this country it is better known in Europe and, judging from available literature, it was probably developed in Germany at the beginning of this century.

Ring Balance Manometer

The instrument is essentially a variant of the U-tube manometer in which the U-tube is formed into a ring, partitioned at the top and having a flexible hermetic connection at each side of the seal (Fig. 2). As in the basic manometer, the tube is partially filled with a sealing liquid of known specific weight. However, the annular tube is pivoted at its center so it is free to rotate through a vertical plane. A weight of known mass is attached to the tube or its supporting frame at a point diametrically opposed to the partition. When a pressure difference is applied across the annular tube, the sealing liquid will be displaced away from the source of highest pressure, just as in a conventional U-tube manometer. However, the mass of the displaced liquid will also produce a turning moment, causing the annular tube to rotate about its pivot. This, in turn, moves the weight off the vertical line of the pivot to produce an opposing turning moment, until a point is reached where both moments balance. The pressure applied then becomes a function of the degree of rotation and can be read directly from an appropriate scale.

In the following equations the pressure p is found from equations 1, 2 and 3 above. In the equations below p1 represents the high pressure, p2 the low pressure, A the cross-sectional area of the tube, r1 the mean radius of the ring, m the mass attached to the bottom of the ring, r2 the radius of the point of application of the mass,  the angle of rotation, and g is the acceleration constant of gravity. The rotating moment is:

rotating moment = (p1 - p2)Ar1 (4)

and restoring moment is:

restoring moment = mgr2 sin  (5)


(p1 - p2)Ar1 = mgr2 sin  (6)


p1 - p2 =  sin  (7)

It is evident from the foregoing that the differential pressure applied to the ring balance is proportional to the angle of rotation, i.e. the angle of rotation is a measure of the pressure difference across the instrument. As in the case of the basic U-tube manometer, the quantity of sealing liquid has no effect upon the turning moment produced. This fact is particularly important when considering the operation of either the manometric engine or pump. It is also important to realize that the turning moment depends exclusively on the pressure difference displacing the sealing liquid to one side of the pivot, while the product of this pressure difference and the surface area of the partition makes absolutely no contribution to the turning moment. These two fundamental facts, though perhaps obscure and confusing, are key concepts that must be clearly understood and grasped before one can begin to comprehend the underlying principles of the manometric pump and the manometric engine.

Basic Principle of Operation

The manometric pump and the manometric engine combine the basic principles of the multiple U-tube manometer and those underlying the ring balance manometer to create, in effect, a multiple ring balance manometer. In turn, this can be thought of as being superimposed on the principle of the archimedean screw. Since the engine and the pump are structurally the same, only the latter will be described. The basic manometric pump consists of a helical conduit of rectangular cross-section or a cylindrically wound hose (Fig. 3):

One end of the conduit is connected, via a header or radial pipe, to a discharge pipe coincident with the axis of rotation of the cylindrical coil. The opposite end of the coil is open to the atmosphere. An optional rotary joint is provided to allow the cylindrical coil to rotate independently of the discharge pipe. However, if the cylindrical coil and discharge pipe are inclined the latter can rotate together with the coil, and the rotary joint can be eliminated.

The cylindrical coil is immersed in water to a depth of from 30 to 70 percent of its diameter, in a horizontal position or inclined at up to 45 degrees of horizontal. In the latter case it is only the first turn of the coil - the one having the end open to the atmosphere - that must be immersed to the required depth. Whether the remainder of the coil becomes completely immersed or rises above the surface of the water, is immaterial to the operation of the pump. As the cylindrical coil is rotated, water flows by gravity into the open end of the conduit as soon as this submerges. Further rotation causes the open end to emerge from the water, trapping water within the conduit. Still further rotation, provided this is in the appropriate direction, repeats the process and a segment of water remains trapped within each successive turn of the helical conduit. This creates, in effect, a system of series-connected U-tube manometers capable of opposing a pressure or head equal to the algebraic sum of the hydrostatic columns produced by the displacement of water within each turn of the cylindrical coil. Equations 1 through 3 describe the hydrostatic processes involved. The maximum head that can be achieved is determined approximately by the internal diameter of the cylindrical coil multiplied by the number of turns in the coil, multiplied by the cosine of the angle of inclination. Continued rotation of the cylindrical coil causes alternate segments of water and air to be forced from the last helix turn, through the header or radial pipe, and into the discharge pipe. At this point the successive segments of air and water can no longer act as U-tube manometers, but each time an effective manometer is lost as it moves into the discharge pipe, a new manometer is formed in the first turn of the helical coil. This action maintains in existence a constant number of U-tube manometers.

Since the water in each turn is displaced away from the source of pressure there is therefore a mass of water permanently displaced to one side of the axis of rotation, producing a turning moment under the effect of gravity. In the case of the pump this turning moment constitutes the mechanical load of the pump, while in the case of the engine it is this moment that produces rotative movement.

Computation of Torque and Power

The equations for solving torque and power are derived from equations 1 and 4. Torque, or moment of a force is the product of the force and the perpendicular distance of the force from the particular point. Choosing F to represent the force, and r the distance, then T becomes the torque:

T = Fr (8)

This must also hold true for equation 4 where the product of the pressure difference (p1 - p2) and the cross-sectional area A and the mean radius of the ring r2 gives rotating moment. What might not be so clear is the substitution of force F for the pressure difference (p1 - p2), since there is no obvious mechanically displaceable surface for the pressure to act upon in a traditional manner. Turning briefly to equation 7, and assuming r1 to be equal to r2 and sin to be 1, then this equation could be simplified as follows:

p1 - p2 =   (9)


(p1 - p2)A = mg (10)

This proves that the product of the pressure difference p1 - p2 by the cross-sectional area A is, in fact, a force acting in a vertical direction. It therefore becomes possible to substitute, in equation 4, the terms of specific weight y and of vertical distance h of equation 1, and T then becomes the rotating moment or torque:

T = yhAr1 (11)

and, if N is made to represent revolutions per minute and T torque in kg-m, then the resulting power in metric horsepower is:

2 NT
HP =   (12)

The coil systems in manometric pumps and engines invariably consist of several turns of conduit. The situation is addressed in part by equations 2 and 3 but, in addition to variations of head, the cross-sectional area also changes at each turn. These factors mean that the validity of equation 11 is restricted to a single turn of coil, whereas equation 12, on the other hand, can solve for multiple turns, providing that T represents the algebraic sum of the torques developed at each individual turn in the group.

Manometric Fish Passage System

A typical arrangement for a manometric fish passage system is illustrated in Fig. 4:

This is a somewhat simplified line drawing and is not exactly in proportion. The engine section extracts power from the fish passage stream while the pump section, when present, provides usable energy in the form of high pressure water to drive a hydro turbine, or industrial quality compressed air which can be used directly without further conversion. The concentric helices—two for the engine and two or four for the pump section—are an integral part of the structure. Their purpose is to provide a helical conduit of rectangular cross-section. The whole structure rotates about its horizontal axis while partly submerged in water.

The path taken by fish migrating downstream is shown by the arrowed broken line, while the path for those migrating upstream is shown by the arrowed solid line. Note that the pump section can constitute an entirely separate hydraulic system to which the fish have no access. The upstream migration will probably require some form of attractant system since the manometric engine does not produce water turbulence of its own accord.

The hydraulic principles of the engine are a little more challenging. Starting from the high pressure header 'C', there are two streams entering this part of the engine. The drive stream coming in from the penstock 'A' via the rotary joint, consisting solely of water, combines with the discharge 'D' from the compressor helix. The latter discharge consists of approximately one part water to one part compressed air. The addition of the drive water changes the ratio to approximately two parts water to one part compressed air, which is the ratio of the two fluids as they enter the power helix. As they progress along the this helix the air expands and, at the point of discharge at atmospheric pressure at 'B', the ratio will once again be one part water to one part air. It was stated earlier that the quantity of liquid in each annulus had no effect upon torque, and a close analysis of equations 1 through 7 bears this out since there is no term in any of these to describe the sealing liquid as a discrete entity. However, the cross-sectional area, determined by the total amount of fluid contained within each turn of helix, does influence the foregoing equations. The torque produced by the power helix is therefore greater than that of the compressor helix only by the amount of the drive water added at the high pressure header. If the compressor helix were designed to pass the same amount of air and water as the power helix, the torques would balance out and there would be no turning moment.

The foregoing facts are of critical importance to any manometric fish passage system since they allow full control over the flow rate through the system by simply varying the ratio between the compressor helix and the power helix. If the objective were to provide fish passage with minimum loss of water, or favor upstream migration, then the system would be designed to produce only enough moment to turn itself. In such cases flow rates through the engine would be at a minimum, probably not exceeding 1 m/sec, and it is unlikely that there would be much interest in recovering the small amount of energy so expended. The pump section could possibly be eliminated entirely. At the other end of the scale a manometric system could be designed to extract as much energy as possible with only the downstream migration being catered for. Some large scale applications in this category are currently undergoing initial evaluation, and results thus far are very encouraging indeed.

An alternative strategy would be to throttle back the high pressure discharge from the pump to a point where the manometric engine would almost stall. This would significantly reduce flow velocities through the engine, thus permitting upstream fish migration. Although under these circumstances the flow of high pressure water would probably be too low to run the impulse turbine efficiently, the compressed air source would still be available.

Computer Software

Specially designed computer programs are essential for arriving at the proper ratios between power and compressor helices, or pump and extractor helices. Such programs have been developed far enough to be useful in general evaluation tasks, but they do need some more refinement. These programs produce optimized designs of manometric engine/pump sets for any application, including fish passage. Working from only three dimensionless parameters input by the operator the program can produce all the data for a machine correctly sized and optimized for the application in hand. Shop drawings and bills of material can also be produced. Despite the fact that this software is still in its final stages of development it has nonetheless proven invaluable in modeling and testing manometric engines and pumps on a "what if" basis.


Although there are still some areas requiring further investigation, it is most unlikely that any serious flaws will be uncovered. There can be little doubt that the proof of this technology has progressed to the point where half-scale demonstration units can be contemplated with utmost confidence. For the owners and operators of hydropower sites this holds out the hope that large instream flows and massive releases at dams will no longer be a threat to their operations. The response by the hydropower industry, environmentalist movement, and regulatory bodies alike will determine just how long it will take for this simple and elegant technology to become reality.


(author unknown), "The Measurement of Pressure - Precision Manometers".

Collett, C. V. and A. D. Pope. 1983. "Engineering Measurements", Pitman, pp. 269.

Ewbank, Thomas. 1849. "A Description and Historical Account of Hydraulic and Other Machines for Raising Water", New York City.

Marks, Lionel S. 1951. "Mechanical Engineers' Handbook - Engineering Measurements". 5th Ed. McGraw-Hill Book Company, pp. 2068 - 2069.

Morgan, Peter R. 1979. "A New Water Pump: Spiral Tube", The Zimbabwe Rhodesia Science News. 13(18):179-180.

Ohlemutz, Rudolf E. 1975. "The Hydrostatic Pump and Other Water-lifting Devices in the Context of the Intermediate Technology Approach", Dissertation, University of California, Berkley.

Reese, A., et. al., "The Cyclopaedia", Vol. XXXIII (Text), Vol. V (Plates), First American Edition, 1819 - 1820, Boston Public Library (Special Collection).

Streeter, V. L. "Mechanics, Fluid", Encyclopedia Britannica, 15th Ed., Vol. 23, pp. 865 - 866.

Stuckey, Alan T. and E. M. Wilson. 1980. "The Stream-powered Manometric Pump", Proceedings of the Institute of Civil Engineers Conference on Appropriate Technology in Civil Engineering, London, pp. 105 - 108.


Alan Belcher


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