GB2504736A

GB2504736A - Apparatus and method for determining the flow rate of a pump

Info

Publication number: GB2504736A
Application number: GB201214176A
Authority: GB
Inventors: Thomas Paul Clifford
Original assignee: RIVENTA Ltd
Current assignee: RIVENTA Ltd
Priority date: 2012-08-08
Filing date: 2012-08-08
Publication date: 2014-02-12
Anticipated expiration: 2032-08-08
Also published as: GB201214176D0; GB2504736B

Abstract

Apparatus and method for determining the flow rate output by each operational pump in a multiple parallel pumping system. The method comprises: measuring a flow rate of the combined fluid flow at a location downstream of the parallel arranged pumps 13; determining an average pump head for the operational pumps with a pressure sensor 14, 15, 16, wherein the pump head is assumed to be the same for each operational pump; determining a relationship between the pump head and flow rate for each pump based upon the measured combined flow rate and average pump head data, and based upon the assumption that the measured combined flow rate is equal to the sum of the individual flow rates for each operational pump; and using the determined relationships between pump head and flow rate to calculate the flow rate for each operational pump.

Description

Pumping System

FIELD OF THE INVENTION

The present invention relates to a multiple parallel pumping system, and in particular relates to apparatus and methods for determining the flow rate output by the individual pumps of the pumping system.

BACKGROUND OF THE INVENTION

In sewage pumping stations, and other pumping systems for pumping water or other media, it is conventional to provide a plurality of pumps arranged in parallel. The pumps each feed from a suction tank, well, inline or the like and output to a discharge tank, supply line or the like. One or more of the plurality of pumps may be operational at any instance, and each pump may be operated at a constant or variable rate -typically by varying the pump rotational speed. During periods of low demand only one or two of the pumps may be operational, whereas during peak demand several, or possibly all, of the pumps maybe operational.

A key metric for the pumping station is the total flow rate output by the multiple parallel pumps. This is usually measured by means of a flow meter disposed at a downstream location from the pumps for measuring the combined flow of all operational pumps. The total flow rate output by the multiple parallel pumps, together with a measurement of the pumps' head, may be used to monitor the operational conditions of the pumping station as a whole. It can be used to determine problems such as a main burst or other leak discharging polluted fluid to the environment generally finding its way into a water course, a full blockage of the main or a gradual build up, e.g. sedimentation, constricting the main. Such problems increase pumping costs and reduce the maximum output of the station under storm or emergency occasions. The maximum output needs to meet with obligations to environment authorities.

Whilst the total flow rate is important, it is also desirable to know the contribution made by each pump individually. For example, to detect problems at an individual

I

pump (rather than system) level, certain pump performance parameters, such as pump head. electncal power, pump efficiency and flow rate. may be required. From these the hydraulic performance of the pump can be determined. Pump problems may include a reduction in pump efficiency through damage (e.g. a piece of wood passing S through the pump), an air lock on start up meaning the pump does not self prime and therefore fails to pump or may damage itself, impeller and casing ragging (collection of sanitary material reducing the through area) in sewage applications, etc. If the flow rate, pump head and (electrical) power consumption of each pump is known then it becomes possible to calculate the hydraulic pumping efficiency of each pump. Observed over time the pump efficiency can be used to assess maintenance requirements on a predictive basis before part degradation or failure requires that pump to be taken off line, thus avoiding unscheduled maintenance through prior warning and/or costly and inefficient time-based maintenance.

It is in theory possible to measure the flow rate of each pump of a multiple paralld pumping system directly. However, it would be very costly to install flow meters on every pump and analyse the pumps individually. Furthermore it will often not be technically possible to install a flow meter for measuring the flow rate of each pump.

This may be due to space constraints. Also, to obtain an accurate flow rate measurement using conventional magnetic or ultrasonic flow meters, for example, the flow rate should be measured in a region of fully developed flow, which typically only occurs in a relatively long, straight length of pipe. The lines leading from the individual pumps are rarely suitable for the flow velocity profile to fully develop and so flow meters are not instailed here as they would provide inaccurate readings.

SUMMARY OF THE INVENTION

A first aspect of the invention provides a method for determining the flow rate output by each operational pump of a plurality of pumps in a multiple parallel pumping system. the method comprising: measuring a flow rate of the combined fluid flow at a location downstream of the parallel ammged pumps; determining an average pump head for the operational pumps, wherein the pump head is assumed to be the same for each operational pump; determining a relationship between the pump head and flow rate for each pump based upon the measured combined flow rate and average pump head data, and based upon the assumption that the measured combined flow rate is equal to the sum of the individual flow rates for each operational pump; and using the determined relationships between pump head and flow rate to calculate the flow rate for each operational pump.

A second aspect of the invention provides apparatus for determining the flow rate output by each operational pump of a plurality of pumps in a muhiple parallel pumping system, the apparatus comprising: first input means for receiving an average pump head for the operational pumps, wherein the pump head is assumed to be the same for each operational pump; second input means for receiving a measured flow rate of the combined fluid flow at a ocation downstream of the parallel alTanged pumps; and an algorithm for calcu'ating the flow rate for each operational pump by: determining a rdationship between the pump head and flow rate for each pump based upon the measured combined flow rate and average pump head data, and based upon the assumption that the measured combined flow rate at the downstream location is equal to the sum of the individual flow rates for each operational pump, and using the determined relationships between pump head and flow rate to calculate the flow rate for each operational pump.

The invention essentially divides the combined flow rate from a plurality of operational pumps into the contributing component of each pump. The invention requires knowledge of which pump(s) are operational, and this may be derived from e.g. pressure transducers in each parallel path of the system, or power meters associated with each pump, etc. The invention may be applied to any pumping system, regardless of pump type and pumped media. In particular. though not exclusively, this invention has application in a sewage pumping station. This has a major environmental benefit as the invention may help ensure continued uninterrupted operation of the pumping station, thereby avoiding the discharge of sewage into water courses. The environmental consequences that may otherwise ensue typically carry significant financial implications for the utility company by way of fines, as well as damage to corporate image, etc. Any problems may be predicted and maintenance scheduled for noirnal working hours and avoiding bad weather or storm times.

The method may further comprise measuring a power consumption of one or more, or all, of the operational pumps. Typically this would be by measurement of electrical power consumption for an electro-mechanical pump.

The method may further comprise calculating a total "wire to water" efficiency of one or more of the operationa' pumps. The efficiency of one or more of the plurality of pumps may be monitored over time. Generally the efficiency of the pump motor does not change with time, therefore for a known motor efficiency or known motor efficiency relationship it is possible to compute the hydraulic (pump) efficiency which does change appreciably with time, use and/or wear.

A drop in pump efficiency for a particular pump may be indicative of the start of component degradation, prompting a prediction of when a maintenance activity will need to be carried out. Predictive maintenance is far more efficient that traditional fixed or reactive maintenance leading to reduced costs and avoiding unnecessary downtime of the pump.

Alternatively the drop in efficiency may be indicative of damage to an interna' component after the pump has passed foreign matter or that the impeller, casing or other internal parts have become restricted with a collection of sanitary material (in the sewage industry). An air lock can be detected by the relationship between power and flow rate. A constriction, or blockage affecting that pump, or a leak affecting that individual pump main can be detected by that pump's individual operating point, on its pump performance graph. being outside a normal range. The ability to single out the affected pump enaNes the operator to bring on line another of the pumps to take over whilst the affected pump is investigated and brought back to full operation, thereby ensuring continued full operation of the pumping system. Detecting a leak or burst in the common discharge main can be detected by the station operating point (combination of aH pumps) being outside a normal range.

Any one or more of the plurality of pumps may be operational at any given time.

Typically at least two of the pumps will be operational. It will be appreciated that the problem of ascertaining the respective contribution of the pumps to the total flow rate is trivial when only a single pump is operational.

The method may further comprise periodically re-determining the relationship between the pump head and flow rate for each pump.

The step of determining the relationship between the pump head and flow rate for each pump may include: describing a set of pump operating scenarios, wherein in each scenario one or more of the pumps is operational, and each pump is operational for at least one different scenario in the set; operating the pumps according to the set of pumping scenarios; determining the average pump head of the operational pumps and measuring the combined flow rate at the downstream location for each scenario; and computing the relationship between the pump head and flow rate for each pump.

These scenarios will typically occur during the normal course of operation of the pumping system as operation of the pumps will generally be cycled according to a rotation scheme coded into a controller of the system. This will typically rotate the pumps for even usage so there should be no need to intervene to force particular pump combinations to obtain the critical minimum combinations required to determine the relationship between the pump head and flow rate for each pump.

The set of pumping scenarios may be conducted at an approximately constant average pump head.

The set of pumping scenarios may be repeated, with each set of scenarios being conducted at a different average pump head. Collecting pump head and combined flow rate data across a range of pump heads enables the pump head vs. flow rate relationship for each individual pump to be determined across the range of operating conditions. However, if the pump head cannot be varied, for any reason, then the pump head vs. flow rate relationship for each individual pump will be a single data point, which is not problematic as the relationship will still be valid for the single pump head operating condition.

The number of pumping scenarios in each set of scenarios may be equal to or greater than the number of pumps in the system.

The method may further comprise, for each scenario, determining an tith order polynomial that approximates to the relationship between the measured combined flow rate at the downstream location and the average pump head.

The order n of the polynomial may be selected as the lowest order that sufficiently accurately approximates to the relationship, e.g. by a regression test.

The method may further comprise, for each scenario in which a plurality of pumps are operational. defining expressions for the flow rate of each individual pump as a function of the measured combined flow rate at the downstream location for that combination of operational pumps.

The method may further comprise defining an nth order polynomial with unknown coefficients that describes the relationship between the flow rate and the pump head for each pump. The order ii of the relationship for each pump can be derived from the combined flow vs. head relationship.

The method may use the assumptions that: i) the pump head is the same for each pump; and ii) the measured combined flow rate at the downstream location is equal to the sum of the individual flow rates for each pump, to solve for the previously unknown coefficients of the nth order polynomial for each pump as a function of the average pump head and downstream combined flow rate.

The step of solving the polynomials preferably includes applying matrix algebra, but may include any algebraic, analytical, numerical or iterative mathematical methods, such as neural networks or genetic algorithms.

The step of determining the average pump head may include: determining the pressure (static) head and elevation head on either side of the operational pump(s); using either an initial value of the flow rate, or the calculated flow rate, to determine the velocity head of the operational pump(s); and wherein the average pump head is the averaged sum of the pressure head differential, elevation head differential and velocity head differential for the operational pump(s).

The pressure head may be measured directly from pressure transducers upstream and downstream of each pump. The elevation head may be determined from known elevations of the pressure transducers. The velocity head is a function of the flow rate through each pump. As the flow rate is not directly measured it may be initially estimated (or assumed zero). The pump head is the sum of the pressure head differential, the elevation head differential and the velocity head differential across the pump, and in a multiple parallel pump configuration the pump head of all operational pumps will be the same. Therefore the average pump head is suitable for all operational pumps.

Based upon this initial, assumed value of the pump head, the pump head vs. flow rate relationship for each operational pump can be determined by the method of this invention, and so the flow rate through each operational pump can be calculated.

Whilst the calculated flow rate will initially include an error it has been found that by updating the velocity head based upon the calculated flow rate and re-sohing to update the pump head vs. flow rate relationship for each operational pump, the calculation quickly converges.

The pressure transducers may be disposed upstream of the respective pump, e.g. within each pump main, and downstream of the pumps, e.g. in a common discharge main.

The apparatus may include input means for receiving static pressure data at a known elevation on either side of the operational pump(s).

In a further aspect, the invention provides a pumping system comprising: a plurality of parallel arranged pumps; a flow meter disposed at a location downstream of the parallel alTanged pumps for measuring a flow rate of the combined fluid flow, and apparatus for determining the flow rate output by each operational pump of the plurality of pumps. according to the second aspect of the invention.

In the pumping system there are no flow meters for measuring the flow rate of each pump individually. The downstream flow meter may be the sole flow meter in the system, or there may be a plurality of downstream flow meters to provide an average reading.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described with reference to the accompanying drawings, in which: Figure 1 illustrates schematically a multiple parallel pumping system in accordance with an embodiment of the invention.

DETAILED DESCRIPTION OF EMBODIMENT(S)

Figure 1 illustrates an embodiment of the invention in which a pumping system 1 comprises a suction tank, well, or inline, 2, leading via inlet main 3 aiid common inlet manifold to a multiple parallel pump arrangement 4. The mifitiple parallel pump arrangement 4 leads via common outlet manifold and outlet main S to a discharge tank, or inline, 6 in the direction of fluid flow.

The multiple parallel pump arnmgement 4 in this example includes three pumps 7, 8, 9. Each pump 7, 8,9 has a respective main 10, 11, 12 arranged in parallel between the inlet main 3 and the discharge main 5.

A flow meter 13 is disposed in the discharge main 5 at the exit from the common outlet manifold. The flow meter 13 is disposed at a location conducive to a reliable measurement of the combined fluid flow downstream of the multiple parallel pumps.

The flow meter 13 is therefore disposed at a location where the combined flow is substantially developed. i.e. the velocity profile is substantially invariant in the flow direction, in a relativdy long, straight length of the discharge main 5.

The pumping system 1 includes only a single flow meter 13 for measuring the combined flow from one or more of the pumps 7. 8, 9 when operating, and there are no flow meters associated with the individual pumps 7. 8, 9.

A pressure transducer 14, 15. 16 is disposed in each respective pump main 10, 11, 12 for measuring the static pressure of the fluid at the respective pump inlet. A further pressure transducer 17 is disposed in the outlet main 5 adjacent the flow meter 13 for measuring the static pressure of the fluid at the exit from the common discharge manifold. The pressure transducers are of conventional type and are commonly available. In an alternative alTangement, pressure transducers maybe provided in each respective pump main 10, 11, 12, one on the suction side and one on the discharge side of each pump. This would enhance the accuracy of the pressure measurement as the measurement locations are closer to the respective pumps, and do not include any losses between the pump outlet and the measurement location. In a further alternative anangement, pressure transducers may be provided one in the inlet main on the common suction side and one in the outlet main on the common discharge side.

Monitoring apparatus 18 receives inputs from each of the pressure transducers 14, 15, 16 & 17, the combined flow rate meter 13, and each of the pumps 7. 8, 9. The monitoring apparatus includes an algorithm for dividing the combined flow rate observed by flow meter 13 into the individual components of flow rate being output by each operating pump. The algorithm is capable of dividing the combined flow rate without making any major assumptions that would either invalidate the downstream

conclusions or significantly impair them.

The algorithm uses the flow meter 13 output which, due to its installation in a technically advantageous location (straight length of pipe) as per design of the system, ensures that the combined flow rate value that is being divided up is generally of good accuracy.

If there is an inherent error in the combined flow rate reading then this is shared amongst all pumps and so the relative comparison between them is fair. Also the error will always be present in the combined flow rate reading and so degradation of pump performance with time can be detected as it is the relative difference between values over time that is observed.

The algorithm will now be described in detail. The algorithm requires. as inputs.

knowledge of which of the pumps 7. 8, 9 are operational at a given instance, the combined flow rate value output by the flow meter 13, and the "head" of the pumps 7,

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The "head" is a measure of the total energy in the Kincompressible) fluid expressed as the height of an equivalent static column of that fluid. The (total) head comprises three components: the "dynamic" or velocity head associated with movement of the fluid; the "static" or pressure head associated with the static pressure in the fluid; and the "potential" or elevation head associated with the height of the fluid relative to some datum. The total head, or simply "head", is the sum of the velocity head, the pressure head and the elevation head. Here, the "pump head" is the differential total head across each pump, i.e. the difference in total head on either side of the pump. In a multiple parallel pump arrangement the pump head is validly assumed to be the same for each operational pump since each pump has identical conditions at the inlet and outlet manifolds.

In the pumping system shown in Figure i the pressure transducers 14, iS, 16 and 17 are operable to measure the static pressure on either side of each pump 7, 8. 9. The locations of those pressure transducers 14, 15, 16 and 17 in space are also known.

hence it is a straightforward matter to determine the pressure head and the elevation head of each pump.

The vdocity head is a function of the flow velocity, v, vA2/2g). As there are no flow meters associated with each respective pump, only the single downstream flow meter 13. the flow rate (and therefore the flow velocity) through each pump is not directly measurable.

As mentioned above the algorithm is capable of dividing the combined flow rate measured by flow meter 13 into the constituent components output by each of the operating pumps 7, 8, 9. However, to do this the algorithm requires knowledge of the pump head, which is a function of the flow rate through each pump. Therefore, an initial assumption of the pump head must be made based upon an assumed value of the flow rate through each pump. This can be set as any value, including zero. By iteration the pump head can be accurately determined. Since the pump head is the same for all operating pumps the head recorded can be the average for all the pumps or recorded for all individual pumps and averaged.

From the pump head and combined flow rate data recorded, a relationship between the pump head and combined flow rate can be determined by the algorithm. For example.

polynomial regression and equation fit tests (such as R2) can be used to determine the lowest order polynomial that accurately fits the data. This will typically be a second order equation but may be third or forth order for example.

So the equation of the pump head (y) v combined flow rate (x) for a given combination of operating pumps can then be determined with all coefficients known.

For example for pumps 1 and 2: y12 = a12(x12)2 + b12x12 + c12 Using the same order ii polynomial as for the combined flow, the pump head (y) v flow rate (x) for each individual pump can be defined with unknown coefficients that must be solved by the algorithm. For example. for pump 1: yi = ai)2 + b1x1 + ci To solve for the unknown coefficients in the pump head (y) v flow rate (x) for each individual pump, a minimum number of expressions for the combined flow will be required. In the exemplary three pump arrangement of Figure 1, three expressions of pump head (y) v combined flow rate (i.e. data for three different pumping scenarios) is required. For example, these data may be obtained by operating pumps l&2, then pumps 2&3, and then pumps 1&3. Alternatively, the three expressions could be obtained by operating pump 1 then pumps l&2 then pumps i&3, etc. Various pumping scenarios are envisaged to provide at least the minimum data required to solve the head v flow rate expressions for each pump. The minimum data requires a set of pumping scenarios in which in each scenario one or more of the pumps is operational, and each pump is operational for at least one different scenario in the set.

In the following worked example, head and combined flow rate data is obtained for the following pump combinations: 1&2, l&3. 2&3.

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With values for the coefficients a1, a2. a3. b1... c3 substituted back into equations (7)- (9) the head (y) v flow rate (x) expressions for each individual pump can be determined. For a given head the flow rate contribution of each operating pump can therefore be determined.

As mentioned previously, the algorithm is initially run based upon an initial value (e.g. zero) for the flow rate through the pump to ca'culate the pump head. This will produce an error but by recalculating the flow rate based upon the solved coefficients for the head y) v flow rate tx) expressions for each individual pump and iterating a few times the error diminishes quickly.

Although the invention has been described above with reference to one or more preferred embodiments, it will be appreciated that various changes or modifications may be made without departing from the scope of the invention as defined in the appended claims. For example, the pumps may be variable speed pumps and the algorithm may then make use of the "affinity laws" to express the relationship between variables involved in pump performance. Also, the number of pumps in the multiple parallel arrangement may be increased or decreased to any number.

Claims

Claims 1. A method for determining the tiow rate output by each operational pump of a plurality of pumps in a multiple parallel pumping system. the method comprising: measuring a flow rate of the combined fluid flow at a location downstream of the parallel arranged pumps; determining an average pump head for the operational pumps, wherein the pump head is assumed to be the same for each operational pump; determining a relationship between the pump head and flow rate for each pump based upon the measured combined flow rate and average pump head data, and based upon the assumption that the measured combined flow rate is equal to the sum of the individual flow rates for each operational pump; and using the determined relationships between pump head and flow rate to calculate the flow rate for each operational pump.
2. A method according to claim 1, further comprising measuring a power consumption of one or more of the operational pumps.
3. A method according to claim I or claim 2, further comprising calculating a total efficiency of one or more of the operational pumps.
4. A method according to claim 3, further comprising monitoring the total efficiency of one or more of the plurality of pumps over time.
5. A method according to any preceding claim, wherein any one or more of the plurality of pumps is operational at a given time.
6. A method according to any preceding claim, further comprising periodically re-determining the relationship between the pump head and flow rate for each pump.
7. A method according to any preceding claim, wherein the step of determining the relationship between the pump head and flow rate for each pump includes: describing a set of pump operating scenarios, wherein in each scenario one or more of the pumps is operationa', and each pump is operational for at least one different scenario in the set; operating the pumps according to the set of pumping scenarios; determining the average pump head of the operational pumps and measuring the combined flow rate at the downstream location for each scenario; and computing the relationship between the pump head and flow rate for each pump.
8. A method according to claim 7, wherein the set of pumping scenarios is conducted at an approximately constant average pump head.
9. A method according to claim 8, where the set of pumping scenarios is repeated, with each set of scenanos being conducted at a different average pump head.
lO. A method according to any of claims 7 to 9, wherein the number of pumping scenarios in each set of scenarios is equal to or greater than the number of pumps in the system.
11. A method according to any of claims 7 to 10, further comprising, for each scenano, determining an iith order polynomial that approximates to the relationship between the measured combined flow rate at the downstream location and the average pump head.
12. A method according to claim II, wherein the order n of the polynomial is selected as the lowest order that sufficiently accurately approximates to the relationship.
13. A method according to any of claims 7 to 12, further comprising, for each scenario in which a plurality of pumps are operational, defining expressions for the flow rate of each individual pump as a function of the measured combined flow rate at the downstream location for that combination of operational pumps.
14. A method according to any of claims 7 to 13, further comprising defining an nth order polynomial with unknown coefficients that describes the relationship between the flow rate and the pump head for each pump.
15. A method according to claim 14, further comprising using the assumptions that: i) the pump head is the same for each pump; and ii) the measured combined flow rate at the downstream location is equal to the sum of the individual flow rates for each pump, to solve for the previously unknown coefficients of the eith order polynomial for each pump as a function of the average pump head and downstream combined flow rate.
16. A method according to claim 15, wherein the step of solving the polynomials includes applying matrix algebra.
17. A method according to daim 15, wherein the step of solving the p&ynomials indudes numerical or iterative mathematical methods.
18. A method according to any preceding claim, wherein the step of determining the average pump head includes: determining the pressure head and elevation head on either side of the operational pump(s); using either an initial value of the flow rate, or the calculated flow rate, to determine the velocity head of the operational pump(s); and wherein the average pump head is the averaged sum of the pressure head differential, elevation head differential and velocity head differential for the operational pump(s).
19. A method according to any preceding claim, where in the pumping system is a sewage pumping station.
20. Apparatus for determining the flow rate output by each operational pump of a plurality of pumps in a multiple parallel pumping system, the apparatus comprising: first input means for receiving an average pump head for the operational pumps. wherein the pump head is assumed to be the same for each operational pump; second input means for receiving a measured flow rate of the combined fluid flow at a location downstream of the parallel arranged pumps; and an algorithm for calculating the flow rate for each operational pump by: determining a relationship between the pump head and flow rate for each pump based upon the measured combined flow rate and average pump head data, and based upon the assumption that the measured combined flow rate at the downstream location is equal to the sum of the individual flow rates for each operational pump, and using the determined relationships between pump head and flow rate to calculate the flow rate for each operational pump.2k Apparatus according to claim 20, further comprising: third input means for receiving static pressure data at a known elevation on either side of the operational pump(s); and wherein the algorithm is further configured to: determine the pressure head and elevation head on either side of the operational pump(s) based upon the static pressure and elevation data; determine the velocity head of the operational pump(s) based upon either an initial value of the flow rate, or the calculated flow rate, for each pump; and calculate the average pump head of the operational pump(s) by averaging the sum of the pressure head differential, elevation head differential and velocity head differential for each operational pump.22. A pumping system comprising: a plurality of parallel alTanged pumps; a flow meter disposed at a location downstream of the parallel alTanged pumps for measuring a flow rate of the combined fluid flow, and apparatus according to claim 20 or claim 2i.23. A pumping system according to claim 22, wherein there are no flow meters for measuring the flow rate of each pump individually.24. A pumping system according to claim 22 or 23, wherein the downstream flow meter is the sole flow meter in the system.25. A pumping system according to any of claims 22 to 24, further comprising a pressure transducer at a known elevation on either side of each pump.26. A pumping system according to claim 25, wherein a common pressure transducer is disposed downstream of the parallel ananged pumps. and respective pressure transducers are disposed upstream of the parallel arranged pumps.27. A sewage pumping station including the apparatus of claim 20 or 21, or the pumping system of any of claims 22 to 26.Amendments to the claims have been filed as follows Claims 1. A method for determining the flow rate output by each operational pump of a plurality of pumps in a multiple parallel pumping system. the method comprising: S measuring a flow rate of the combined fluid flow at a location downstream of the parallel arranged pumps; determining an average pump head for the operational pumps, wherein the pump head is assumed to be the same for each operational pump; determining a relationship between the pump head and flow rate for each pump based upon the measured combined flow rate and average pump head data, and based upon the assumption that the measured combined flow rate is equal to Cv) the sum of the individual flow rates for each operational pump; using the determined relationships between pump head and flow rate to o calculate the flow rate for each operational pump, wherein the step of determining the relationship between the pump head and flow rate for each pump includes: describing a set of pump operating scenarios, wherein in each scenario one or more of the pumps is operational, and each pump is operational for at least one different scenario in the set, and in at least one of the scenarios a plurality of the pumps is operational; operating the pumps according to the set of pumping scenarios; determining the average pump head of the operational pumps and measuring the combined flow rate at the downstream location for each scenario; and computing the relationship between the pump head and flow rate for each pump.2. A method according to claim 1, further comprising measuring a power consumption of one or more of the operational pumps.3. A method according to claim I or claim 2, further comprising calculating a total efficiency of one or more of the operational pumps.4. A method according to claim 3. further comprising monitoring the total efficiency of one or more of the plurality of pumps over time.5. A method according to any preceding claim, wherein any two or more of the plurality of pumps is operational at a given time.6. A method according to any preceding claim, further comprising periodically re-determining the rdationship between the pump head and flow rate for each pump.C') 7. A method according to any preceding claim, wherein the set of pumping scenarios is conducted at an approximately constant average pump head. Co0 8. A method according to claim 7, where the set of pumping scenarios is repeated, with each set of scenarios being conducted at a different average C'\i pump head.9. A method according to any of claims 6 to 8, wherein the number of pumping scenarios in each set of scenanos is equal to or greater than the number of pumps in the system.10. A method according to any of claims 6 to 9, further comprising, for each scenario, determining an th order polynomial that approximates to the relationship between the measured combined flow rate at the downstream location and the average pump head.11. A method according to claim 10, wherein the order n of the polynomial is selected as the lowest order that sufficiently accurately approximates to the relationship.12. A method according to any preceding claim, further comprising, for each scenario in which a plurality of pumps are operational, defining expressions for the flow rate of each individua' pump as a function of the measured combined flow rate at the downstream location for that combination of operational pumps.13. A method according to any preceding claim, further comprising defining an nth order polynomial with unknown coefficients that describes the relationship between the flow rate and the pump head for each pump.14. A method according to claim 13, further comprising using the assumptions that: i) the pump head is the same for each pump; and CD ii) the measured combined flow rate at the downstream location is equal to the sum of the individual flow rates for each pump.to solve for the previously unknown coefficients of the eith order polynomial for each pump as a function of the average pump head and downstream combined flow rate.15. A method according to claim 14, wherein the step of solving the polynomials includes applying matrix algebra.16. A method according to claim 14, wherein the step of solving the polynomials includes numerical or iterative mathematical methods.17. A method according to any preceding claim, wherein the step of determining the average pump head includes: determining the pressure head and elevation head on either side of the operational pump(s); using either an initial value of the flow rate, or the calculated flow rate, to determine the velocity head of the operational pump(s); and wherein the average pump head is the averaged sum of the pressure head differential, elevation head differential and velocity head differential for the operational pump(s).18. A method according to any preceding claim, where in the pumping system is a sewage pumping station.19. Apparatus for determining the flow rate output by each operational pump of a plurality of pumps in a multiple parallel pumping system, the apparatus comprising: first input means for receiving an average pump head for the operational pumps, wherein the pump head is assumed to be the same for each operational pump; C') second input means for receiving a measured flow rate of the combined fluid flow at a location downstream of the parallel arranged pumps; and an algorithm for calculating the flow rate for each operational pump by: determining a relationship between the pump head and flow rate for each C'\i pump based upon the measured combined flow rate and average pump head data, and based upon the assumption that the measured combined flow rate at the downstream location is equal to the sum of the individual flow rates for each operational pump, and using the determined relationships between pump head and flow rate to calculate the flow rate for each operational pump, wherein the step of determining the relationship between the pump head and flow rate for each pump includes: describing a set of pump operating scenarios, wherein in each scenario one or more of the pumps is operational, and each pump is operational for at least one different scenario in the set, and in at least one of the scenarios a plurality of the pumps is operational; operating the pumps according to the set of pumping scenarios; determining the average pump head of the operational pumps and measuring the combined flow rate at the downseam location for each scenario; and computing the relationship between the pump head and flow rate for each pump.20. Apparatus according to claim 19, further comprising: third input means for receiving static pressure data at a known elevation on either side of the operational pump(s); and wherein the algorithm is further configured to: c) determine the pressure head and elevation head on either side of the operational pump(s) based upon the static pressure and elevation data; o determine the velocity head of the operational pump(s) based upon either an initial value of the flow rate, or the calculated flow rate, for each pump; and calculate the average pump head of the operational pump(s) by averaging the sum of the pressure head differential, elevation head differential and velocity head differential for each operational pump.
21. A pumping system comprising: a plurality of parallel arranged pumps; a flow meter disposed at a location downstream of the parallel arranged pumps for measuring a flow rate of the combined fluid flow, and apparatus according to claim 19 or claim 20.
22. A pumping system according to claim 21, wherein there are no flow meters for measuring the flow rate of each pump individually.
23. A pumping system according to claim 21 or 22, wherein the downstream flow meter is the sole flow meter in the system.
24. A pumping system according to any of claims 21 to 23, further comprising a pressure transducer at a known elevation on either side of each pump.
25. A pumping system according to claim 24, wherein a common pressure transducer is disposed downstream of the parallel arranged pumps. and respective pressure transducers are disposed upstream of the parallel arranged pumps.
26. A sewage pumping station including the apparatus of claim 19 or 20, or the pumping system of any of claims 21 to 25. C') aD