1. Introduction1. Introduction2.1 Flow and Pressure3. Suction and Lifting of Water
2.2 Centrifugal Pumps
2.3 Axial Flow Pumps
2.4 Mixed Flow Pumps
2.5 Piston Pumps
2.6 Helical Rotor Pumps & Other Positive Displacement Pumps
2.7 Other types of pumps4. Energy Required for Pumping
4.1 How Big to Make the Motor or Engine5. Pipeline Design
4.2 Unit Cost of Energy
4.3 Cost to Pump a Unit of Water5.1 Pump Pressure6. Layout and Plan what You are Going to Do
5.2 Pipeline Pressure
5.3 Air in Pipelines
5.4 Water Hammer
To keep this discussion a bit simpler, it is only about pumping water. Even so, if you are going to effectively and practically deal with pumps and pumping, you will need to measure distances and heights. Although this article does not deal with measure of these directly, there are other articles here that might assist you.
2.1 Flow and Pressure3. Suction and Lifting of WaterEach type is suited to a particular type of job, characterised principally by the flow required and the pressure the liquid needs when it gets to where it is to be used.
When talking about pumps the pressure is measured as the height of water which would be supported by the pressure of the pump. It is called head. So a pump that is putting out 55 metres head, would support a column of water 55m above the pump spindle.
In Australia flow is usually measured in Litres per second (L/s) or in cubic metres per second. There are 1000L in a m3, but unless pumping water for a city or a large irrigation farm on the plains or a power station, the larger unit will probably not be required. In fact, I am going to refer to flow as it is in L/s from now on.
Centrifugal pumps work because a rotating impeller flings water from a centre entry point to the outside of the rotating part. A casing is used to collect and direct water tangentially away from the impeller. Centrifugal pumps:
... are used to provide high pressures with relatively low flows, ... can suck water (ie. there is a negative pressure on the inlet side of the pump), at least when they are operated in their mid-speed range, ... are used for sprinkler irrigation.
Axial flow pumps usually consist of a propeller-like impeller inside a casing with directs the water at right angles to the impeller. Axial flow pumps:
- are used to lift large flows through relatively small changes in level,
- nearly always have to be submerged well beneath the water surface to operate and definitely cannot suck water,
- have a rotating part that look like a ship's propeller.
These are pumps which have some characteristics of axial flow pumps and some characteristics of centrifugal pumps. They are used principally for lifting water out of rivers for storage or for flood irrigation, but I am sure there are other uses, too. Their suction characteristics are better than axial flow pumps but not as good as centrifugal pumps.
Piston pumps were used for lifting stock water from a low creek to high pasture, and you can still find them in apparently original installations doing this duty more than half a century later. But they are not without their problems. Water is pushed by pistons out of each cylinder and valves prevent water from returning into the cylinder from the discharge pipeline. The flow of water is therefore in a pulses as the pump operate and there is a continual surging in the pipeline. To try and smooth this out and increase the life of the pipelines, there are always air chambers on both side of the pump, which must be kept filled with air and correctly adjusted. Piston pumps are quite efficient, but require a large starting torque to get the pistons going, which is not easy to do with either a diesel or a squirrel cage electric motor.
Piston pumps will generally lift water further than most other pumps.
2.6 Helical Rotor Pumps & Other Positive Displacement Pumps
A helical rotor is a shaped rod of steel which is rotated in a rubber stator which has the effect of making a chamber of liquid pass from one end of the pump to the other. The pulsing is smaller than for a piston pump, but might still be significant.
Helical rotor pumps will lift water well, when new. Wear is an issue with them. However, they have a couple of niches for which almost no other pumps are suitable. For example, it is possible to use helical rotor pumps with electric motors and solar cells.
There are some other types of pumps, like diaphragm pumps, which also market niches. Diaphragm pumps are used in non-foaming applications, like lifting the contents of grease traps. Air pumps are used for lifting water out of bores and effectively just provide air to push the water up while the air is expelled - it is quite literally blown out of the hole. There are other types of pumps, too and some adaptions of the principles already outlined. Jet-pumps pass some of the discharged water from a centrifugal pump back down a bore to use in a shaped nozzle to lift water and increase the suction lift of the pumping system.
The hydraulic ram requires some special mention, because its power source is the water. In 25years' of practice I have only seen one of these that worked and it made such a loud noise that it could be heard a kilometre away, like a repetitive and rapid stockwhip. But the idea is cute because the power for the lifting of water is the flow of some of the water which passes to waste. The principle of the pump is that there is a surge or waterhammer effect that pushes water up the hill when a valve closes. The valve is made to close as a cycle by a clever arrangement that runs some water to waste. I have a practical book that gives some advice about how to make one, although I have not seen one made to the precise instructions obviously.
For an excellent detailed explanation, with diagrams, see the Centre of Alternative Technology site, and for more information the Ram Company site.
People of my acquaintance and association installed some hand operated village water supply pumps in PNG in the 1980s. The pumps were made up entirely from PVC fittings and pipes and for a valve had a brass washer seat and a glass marble. There is an important photo on my wall which shows one of these contraptions with some black feet on the edge of the photo. The concrete surround is self-servingly inscribed by those white fellas who put it in and on the other side by the people whose feet can be seen. The second inscription is more insightful. It says, "God I givim, tankyu long God Triwan". Those who wrote the first white fellas' message, and those of us on whose behalf they wrote it, will probably never write such a presumptuous message again. Pumps can be an important lesson in a much broader area than just physics.
Water is never really sucked by a pump, the atmospheric pressure lifts the water, so the pressure of the atmosphere is important to estimating what each pump will do.
The general equation is:
| L = Pa - Pv - Hfs - NPSH | where: L is the allowable lift in metres, Pa is atmospheric pressure in metres, Pv is the saturation vapour pressure at the temperature of the water in metres, Hfs is the loss of pressure in the suction main of the pump in metres, NPSH is the net positive suction head of the pump in metres. |
NPSH is a measured quantity for the pump. It is affected by the rotation speed of the pump among other things, but is usually published in pump curves at standard speeds.
If you make the approximation that Ps - Pv is about 9.5m and the loss in the suction main is usually about 1m, even if the NPSH is small the maximum lift is theoretically about 8.5m. In practice the maximum lift you can expect from a positive displacement pump is about 8m, from a centrifugal pump is about 6m, and from a mixed flow pump about 4m. Axial flow pumps generally require that the impellers of the pump be below the level of the surface of the liquid (as sort of negative lift, if you like).
Ian Jamie published an equation for atmospheric pressure on this list some time ago and there are other published methods of getting at each of the quantities in the equation.
4. Energy Required for Pumping
4.1 How Big to Make the Motor or Engine
I am ducking the issue of pump speed, as I think it is just too complicated for a simple discussion like this one, but common pump speeds are:
Generally, the faster a pump is turning, the
worse it is at sucking water, but the more efficient it gets.
Of course, there is no such thing as a free
lunch, so energy is required for pumping. You can calculate how much
energy is required if you know the pressure of the pump that is required and
the flow of water it will deliver at this pressure. The power required
for pumping is then:
| Pn = Q
x P / eff |
where: Pn is the net power in kW, Q is the flow in cubic metres per second, P is the pressure in kilopascals, eff is the efficiency of the pump at that pressure and flow as a representative fraction. |
It turns out that there is an simpler formula,
which is widely used:
| Pn = q x H / e | where: q is the flow in litres per second, H is the head (ie. pressure) in metres of water, e is the efficiency of the pump at that pressure and flow as a percentage. |
This will give an estimate of how much energy an electric motor or a diesel would be required to deliver to the pump at its shaft. Of course, there are some losses in transmission of power. Typically, close coupled electric pumps have a transmission efficiency of about 90%. Shafts and gearboxes have varying efficiencies and, of course, the more complicated the arrangement, the more energy is lost in transmission, but for simple arrangements, if there is no other information, assume an efficiency of 85%. The efficiency of belt drives varies with the belts, but assume about an 80% efficiency if there is no other information.
If you are using a diesel engine, you will need to derate its performance for age and wear, and for altitude and humidity. There are tables for this, but if you have no information and you not on the top of Mt Kosciuszko, allow 75% of the power shown in the manufacturer's performance chart. BTW, petrol engines are much worse.
You should always check that the engine develops the required power at the revolutions per second that you require it for the pump. It is no use having a belt drive so that you can run the motor at 1800rpm, but it does not develop the power you need at the pump until the motor is revving 2400rpm, you would get there, the motor will overload, get hot and eventually fail. If in doubt mail or ring up a supplier or a consultant to have a look at it for you.
If you are using electricity to power a pump, and it is on a tariff that is for simple use per kilowatt-hour, then you can estimate the cost of energy required at the pump shaft fairly simply by asking the electricity supplier how much it costs. It is more complicated for large pumps which are sometimes on demand tariffs and I don't propose to look at these.
If you are providing your own energy to the pump with a diesel engine, the engineer will operate with a particular fuel consumption. If you have no idea how much fuel it will use, assume it will use about 0.32kilograms per kilowatt hour. Diesel usually has a specific gravity of about 0.86 at the soft of temperatures common in Australia, so you can convert the weight to volume of fuel, which is how it is normally bought.
If you are calculating the cost of energy, don't forget to allow for the cost of extending electrical power to the site and providing a track to get equipment (and fuel, if required) in and out.
The cost of photovoltaic cells and storage batteries generally exceeds the cost of power extension by a significant margin, but for small pumps lifting water to storage from isolated places, it might be worthwhile. I will post separately on the costs of these, or you could contact BP Solar.
4.3 Cost to Pump a Unit of Water
You can use the same approach to estimate
how much it costs to pump water per unit volume:
| C = 2.778 x H x c / E | where: C is the cost of pumping water in dollars per megalitre, c is the cost of energy per kilowatt hour, E is the efficiency of pumping in percentage. |
If you are running a travelling irrigator expect costs of $40/ML, but if you are just lifting water into a channel, costs might only be $2.50/ML.
Of course, this is just the energy cost. You will need to estimate maintenance costs and eventually replacement costs. Naturally, this depends on the use you make of the equipment. If you are using a diesel engine, costs for maintenance are likely to be significantly more than for an electric motor.
The pressure that a pump is required to overcome is made up of a couple of major components: the lift or static head, the friction loss with the walls of the pipe, and the pressure that water is required to have when it gets there. There are some other quantities, but these are the main ones.
First you need to select the pump discharge that is required. This depends on the application and might need you to count the number of sprinklers or something similar that must be supplied at any one time.
To estimate the lift, you need to use a level or acquire a map that can give you an estimate of the lift from the water surface at the lower level to the water surface at the upper level.
To estimate the friction loss, you need the
length and diameter of the pipe. In the general case, estimating friction
loss is quite complicated, but for most of the situations in common use
you can use Manning's equation:
| f = n 2 x v 2
/ R1.333 |
where: f is the unit friction loss (m/m), n is Manning's roughness (Most of the common pipe material are reasonably smooth, so if there is no other information, assume n = 0.012), R is the hydraulic radius (m), which for a round pipe is a quarter of the diameter. |
So in most cases:
| f = 14 820 000 x Q 2 / d 5.333 | where: Q is the discharge in litres per second, d is the diameter in millimetres. |
You then multiply the unit friction loss by the length of the pipe, to get a figure for pressure loss.
You need to allow a little for the pressure loss that occurs through valves and fittings, including those on the suction side of the pump.
If you need to operate some machinery at the end of the pipeline there will need to be the operating pressure for this too.
Add all this up and than add 5% for good measure. At the flow you have assumed this is the pressure required to be delivered at the pump.
Pipe materials generally come in a number of grades to cope with the various pressures that might be experienced in practice. Obviously, no one selects a pipe grade higher than they need, because of the additional expense. Sometimes, pipe grades vary over the length of the pipeline.
Air in pipelines prevents them working properly. It gathers at high points, and is generally expelled by automatic airvalves placed there for the purpose. Air valves are also required to let air in if there is a negative pressure for some reason, like the pipeline is drained or water hammer occurs. It is quite possible to pipelines to be sucked flat by negative pressure, which generally breaks them.
Long pipelines or those with pulsating flow will suffer from a pressure surge phenomenon which occurs most noticeably when the pump starts or stops. It can break long pipelines and means that you need to allow for additional pressure in the pipeline. An increase of 20% would be a good allowance, if there is no other information.
6. Layout and Plan What You are Going to Do
I find that pumping problems are much easier
if I draw the situation on a scale plan in some detail. You will need
a large piece of paper to do this and it will take some time, but it invariably
leads to a better result.
