# Ram Pump Calculations

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Further losses occur in the distribution and use of the electricity.

### 8.7 The hydraulic ram pump

This mechanical hydro-power device is well established for domestic and farm water pumping at remote sites, where there is a steady flow of water at a low level. The momentum of the stream flow is used to pump some of the water to a considerably higher level. For example, a stream falling 2 m below can be made to pump 10% of its flow to a height 12 m above. This is clearly a useful way of filling a header tank for piped water, especially in rural areas. It is an interesting device, perhaps surprising in its effectiveness and certainly intriguing for student practical study.

Figure 8.9 shows the general layout of a pumping system using a hydraulic ram. The water supply flows down a strong, inclined pipe called the 'drive pipe'. The potential energy MgH of the supply water is first converted into kinetic energy and subsequently into potential energy mgh. The kinetic energy is obtained by a mass of water M falling through a head H, and out through the impulse valve V^. Operation is as follows:

1 The speed of flow increases under the influence of the supply head so a significant dynamic pressure term arises for the flow through the valve (see Bernoulli's equation (2.2)).

2 The static pressure acting on the underside of the impulse valve overcomes the weight of the valve, so it closes rapidly.

3 Consequently the water at the bottom becomes compressed by the force of the water still coming down the pipe.

4 The pressure in the supply pipe rises rapidly, forcing open the delivery valve Vd, and discharging a mass of water m into the delivery section.

5 The air in the air chamber is compressed by the incoming water, but its compressibility cushions the pressure rise in the delivery pipe.

Figure 8.9 General layout of a hydraulic ram pumping system. After Jeffrey et al.

Figure 8.9 General layout of a hydraulic ram pumping system. After Jeffrey et al.

6 The combined pressure of air and water forces the mass m up the delivery pipe.

7 As soon as the momentum of the supply column is exhausted the delivery valve closes, and the water contained in the drive pipe recoils towards the supply.

8 This recoil removes the pressure acting on the underside of the impulse valve, which thereupon falls and again allows the escape of water.

9 Simultaneously, the recoil causes the small air charging valve to open, admitting a small amount of air into the impact chamber of the ram. This air is carried along with the water into the air chamber to compensate for that absorbed by the water.

10 The whole cycle repeats indefinitely at a rate which is usually set to be about 1 Hz.

A theory for calculating all these quantities is given by Krol (1951), which uses only one main empirical parameter, the drag coefficient of the impulse valve. The efficiency of the device over a period equals mh/MH. Very solid and reliable rams are available commercially. Their efficiency is about 60%.

It is also possible to build a ram (of slightly reduced performance) from commercial high pressure pipe fittings (Inverson 1978, Jeffrey et al. 1992).

### 8.8 Social and environmental aspects

Hydro-power is a mature technology in wide use in many countries of the world: it produces about 20% of the world's electric power. In at least twenty countries, including Brazil and Norway, hydro-power accounts for over 90% of the total electricity supply. Hydroelectric systems are long-lasting with relatively low maintenance requirements: many systems, both large and small, have been in continuous use for over fifty years and a few early installations still function after a hundred years. Their relatively large initial capital cost has been long since written off, so that the 'levelised' cost of power produced from them is much less than from non-renewable sources which require expenditure on fuel and more frequent replacement of plant. If the external costs are internalised (see Chapter 17), the non-renewable sources become even more expensive. For hydro plant with ample supply of water, the flow can be controlled to produce either base-load or rapidly peaking power as demanded; if the water is limited, then sale of electricity at peak demand is easy and most profitable. Nevertheless, the initial capital cost of hydro power is always relatively large, so it has been observed that 'all power producers wish they had invested in hydro-power twenty years ago, but unfortunately can't afford to do so now - and they said the same twenty years ago!'

The complications of hydro-power systems arise mostly from associated dams and reservoirs, particularly on the large-scale projects. Most rivers, including large rivers with continental-scale catchments, such as the Nile, the Zambesi and the Yangtze, have large seasonal flows making floods a major characteristic. Therefore most large dams (i.e. those >15m high) are built for more than one purpose, apart from the significant aim of electricity generation, e.g. water storage for potable supply and irrigation, controlling river flow and mitigating floods, road crossings, leisure activities and fisheries. The electricity provides power for industry and services, and hence economic development. For although social and economic development requires much more than just power and water, such projects appeal to politicians and financiers seeking a path to national development that is centralised and thus conceptually and administratively 'simple'. But as the World Commission on Dams (2000) pointed out, the enormous investments and widespread impacts of hydropower have made large dams, both those in place and those on the drawing board, one of the most hotly contested issues in sustainable development. Countering the benefits of large hydro referred to above are adverse impacts; examples are debt burden (dams are often the largest single investment project in a country!), cost over-runs, displacement and impoverishment of people, destruction of important ecosystems and fishery resources, and the inequitable sharing of costs and benefits. For example, over one million people were displaced by the construction of the Three Gorges dam in China, which has a planned capacity of over 17 000 MW; yet these displaced people may never consider they are, on balance, beneficiaries of the increased power capacity and industrialisation. Some dams have been built on notoriously silt-laden rivers, resulting in the depletion of reservoir volume predictable to all except the constructors and the proponents.

Hydro-power, like all renewable energy sources, mitigates emissions of the greenhouse gas CO2 by displacing fossil fuel that would otherwise have been used. However, in some dam projects, in an effort to save construction time and cost, rotting vegetation (mostly trees) have been left in place as dam fills up, which results in significant emissions of methane, another greenhouse gas.

Such considerations have led to an almost complete cessation of dambuilding in many industrialised countries, where the technically most attractive sites were developed decades ago. Indeed in the USA, dams have been decommissioned to allow increased 'environmental flow' through downstream ecosystems. However, in many countries, hydroelectric capacity has been increased by adding turbine generators to water supply reservoirs and, for older hydropower stations, installing additional turbines and/or replacing old turbines by more efficient or larger capacity modern plant. This has positive environmental impact, with no new negative impact, and is an example of using an otherwise 'wasted' flow of energy (cf. Section 1.4). Likewise, the installation of small 'run-of-river' hydroelectric systems, with only very small dams, is generally considered a positive development; the output of such systems in China is greater than the total hydro-power capacity of most other countries.

Problems

8.1 Use an atlas to estimate the hydro-potential of your country or state, as follows:

a Call the place in question, X. What is the lowest altitude in X? What area of X lies more than 300 m above the lowest level? How much rain falls per year on this high part of X? What would be the potential energy per year given up by this mass of water if it all ran down to the lowest level? Express this in megawatts. b Refine this power estimate by allowing for the following: (i) not all the rain that falls appears as surface run-off; (ii) not all the run-off appears in streams that are worth damming; (iii) if the descent is at too shallow a slope, piping difficulties limit the available head. c If a hydroelectric station has in fact been installed at X, compare your answer with the installed capacity of X, and comment on any large differences.

8.2 The flow over a U-weir can be idealised into the form shown in Figure 8.10. In region 1, before the weir, the stream velocity u1 is uniform with depth. In region 2, after the weir, the stream velocity increases with depth h in the water.

a Use Bernoulli's theorem to show that for the streamline passing over the weir at a depth h below the surface, uh = (2g)1/2 (h + u2/2g)1/2

Hints: Assume that ph in the water = atmospheric pressure, since this is the pressure above and below the water. Assume also that u1 is small enough that p1 is hydrostatic.

b Hence show that the discharge over the idealised weir is

Qth = (8g/9)1/2LH3/2 c By experiment, the actual discharge is found to be

Qexp = Cw Qth where Cw ^ 0.6. (The precise value of Cw varies with H/L and L/b.) Explain why Cw < 1. d Calculate Qexp for the case L = 0.3 m,L = 1m,b = 4m,H = 0.2m. Calculate also u1 and justify the assumptions about u1 used in (a) and (b).

8.3 Verify that f defined by (8.18) is dimensionless. What are the advantages of presenting performance data for turbines in dimensionless form?

Figure 8.10 A U-weir. (a) Front elevation. (b) Side elevation of idealised flow (uh is the speed of water over the weir where the pressure is ph.)

8.4 A propeller turbine has shape number f = 4 and produces 100 kW (mechanical) at a working head of 6m . Its efficiency is about 70%. Calculate a The flow rate b The angular speed of the shaft c The gear ratio required if the shaft is to drive a four-pole alternator to produce a steady 50 Hz.

8.5 A Pelton wheel cup is so shaped that the exit flow makes an angle 9 with the incident jet, as seen in the cup frame. As in Figure 8.4, uc is the tangential velocity of the cup, measured in the laboratory frame. The energy lost by friction between the water and the cup can be measured by a loss coefficient k such that u?i = U2(1 + k)

Show that the power transferred is cos 9

Derive the mechanical efficiency ym. What is the reduction in efficiency from the ideal when 9 = 7°,k = 0.1? What is the angle of deflection seen in the laboratory frame?

8.6 A Pelton wheel is to be installed in a site with H = 20m,Qmin = 0.05 m3 s—1.

a Neglecting friction, find (i) the jet velocity (ii) the maximum power available (iii) the radius of the nozzles (assuming there are two nozzles).

b Assuming that the wheel has shape number

where P1 is the power per nozzle, find (iv) the number of cups (v) the diameter of the wheel (vi) the angular speed of the wheel in operation.

c If the main pipe (the penstock) had a length of 100 m, how would your answers to (a) and (b) be modified by fluid friction using: (vii) PVC pipe with a diameter of 15 cm? (viii) Common plastic hosepipe with a diameter of 5 cm? In each case determine the Reynolds number in the pipe.

Bibliography

### General articles and books on hydro-power

Gulliver, J.S. and Arndt, R.E. (1991) Hydropower Engineering Handbook, McGraw Hill. {Professional level, but readable. Includes substantial chapters on preliminary studies, small dams, turbines, economic analysis. {Chapter on environment has strong slant towards US issues and regulations.}

Ramage, J. (2004, 2nd edn) Hydroelectricity, Chapter 5 of Boyle, G. (ed.) Renewable Energy: Power for a Sustainable Future, Oxford UP. {Non-technical survey, with many photos and illustrations.}

### Mechanics of turbines

Francis, J.R. (1974, 4th edn) A Textbook of Fluid Mechanics, Edward Arnold, London. {Has a clear chapter on hydraulic machinery, with thorough physics but not too much technical detail.}

Massey, B. and Ward-Smith, J. (1998, 7th edn) Mechanics of Fluids, Nelson Thomes, London. {Longer account of turbomachinery than Francis, but still at student level.}

Turton, R.K. (1984) Principles of Turbomachinery, E. and F.N. Spon, London. {Stresses technical details.}

Small scale (mini) hydropower (~!00kW)

Cotillon, J. (1979) Micro-power: An old idea for a new problem, Water Power and

Dam Construction, January. {Part of a special issue on mini-hydro.} Francis, E.E. (1981) Small scale hydro electric developments in England and Wales,

Proc. Conf. Future Energy Concepts, IEE, London. Khennas, S. and Barnett, A. (2000) Best Practices for Sustainable Development of Micro Hydro Power in Developing Countries, ITDG, London. {Available on web at <www.microhydropower.net>; see also (much shorter) ITDG technical brief on micro-hydro power at < www.itdg.org>.} Leckie, J., Masters, G., Whitehouse, H. and Young, L. (1976) Other Homes and Garbage, Sierra Club, San Francisco. {Another book from the 1970s, with a good discussion of energy principles; the chapter on hydro-power is particularly good on measurement techniques for small installations.} McGuigan, D. (1978) Harnessing Water Power for Home Energy, Garden Way, Vermont {A useful guide for householders with technical aptitude in remote areas.}

Moniton, L., Le Nir, M. and Roux, J. (1984) Micro Hydroelectric Power Stations,

Wiley. {Translation of a French book of 1981.} Water Power and Dam Construction (1990) Micro Hydro: Current Practice and

Future Development, Scottish Seminar - special issue of journal. US Dept. of Energy (1988) Small-scale Hydropower Systems, NCIS Washington DC. {Non-technical account with many good line drawings.}

### Hydraulic ram

Inverson, A.R. (1978) Hydraulic Ram Pump, Volunteers in Technical Assistance, Maryland, USA, Technical Bulletin no. 32. Construction plans of the ram itself.

Jeffrey, T.D., Thomas, T.H., Smith, A.V., Glover, P.B., and Fountain, P.D. (1992) Hydraulic Ram Pumps: A Guide to Ram Pump Water Supply Systems, ITDG Publishing, UK. {See also ITDG Technical brief 'hydraulic ram pumps', online at <www.itdg.org> .}

Krol, J. (1951) The automatic hydraulic ram, Proc. Inst. Mech. Eng., 165, 53-65. {Mathematical theory and some supporting experiments. Clumsy writing makes the paper look harder than it is.}

### Institutional and environmental issues

International Energy Agency (1993) Hydropower, Energy and the Environment {Conference proceedings, but with useful overview. Focuses on implications of upgrades to existing facilities.}

World Commission on Dams (2000) Dams and Development: A New Framework for Decision Making (at www.dams.org). {The Commission was set up by the World Bank and the International Union for the Conservation of Nature to review the effectiveness of large dams in fostering economic and social development and to develop new criteria for assessing proposals for such dams.}

Moreira, J.R. and Poole, A.D. (1993) Hydropower and its constraints, in T.Johansson etal. (eds) Renewable Energy: Sources for Fuels and Electricity, Earthscan, London (pp. 71-119). {Good survey of global issues and potential, with focus on social and environmental constraints, and case studies from Brazil.}

### Journals and websites

Water Power and Dam Construction, monthly, Quadrant House, Sutton, UK. {General journal including production information, conference reports, articles, etc.}

<www.microhydropower.net> Portal with downloadable books and papers and an online discussion forum.}

World Energy Council (2001) Survey of energy resources 2001 (chapter on hydropower), available on web at <www.worldenergy.org/wec-geis/publications/ reports/ser/hydro/hydro.asp>. {Data on installed capacity and technical potential for numerous countries, compiled by utilities and energy agencies; publication covers other energy resources as well, including fossil and even OTEC.}

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### Responses

• liviano beneventi
How to calculate the weight ram pump?
2 years ago
• Hallie
How to calculate numbr of pumps required to move a ram?
7 months ago