WO2018069539A1

WO2018069539A1 - Methods and devices for the determination of the flow speed of a liquid in a free-surface flow

Info

Publication number: WO2018069539A1
Application number: PCT/EP2017/076262
Authority: WO
Inventors: Michel VERBANCK; Nicolas DE VILLE DE GOYET; Dragana PETROVIC
Original assignee: Université Libre de Bruxelles
Priority date: 2016-10-13
Filing date: 2017-10-13
Publication date: 2018-04-19

Abstract

The present invention relates to methods for determining the flow speed of a liquid, wherein said methods comprise the steps of measuring a flow-speed dependent absolute or relative pressure at a depth L in said liquid, measuring the depth L, and calculating the flow speed of the liquid as a function of these variables.

Description

METHODS AND DEVICES FOR THE DETERMINATION OF THE FLOW

SPEED OF A LIQUID IN A FREE-SURFACE FLOW

Field of the invention

The present invention relates to methods for the quantification of the flow speed of a liquid in a free-surface flow. The invention also relates to a kit and an apparatus for the quantification of the flow speed of a liquid in a free-surface flow.

Description of prior art

There are many instances in which the quantification of the flow speed of a liquid is key to the solution of the considered engineering problem (Hirsch R.M. & Costa J.E. - 2004: U.S. Stream Flow Measurement and Data Dissemination Improve. Eos. 8(20): 197).

When the liquid is for example water flowing in a river bed, a collector or a sewer, flow speed information in such free-surface flow conditions may be essential for flow discharge determination, and as such for different aspects of water and environmental management: water budget calculation and flood forecasting and protection, engineering designs (dams, bridges, reservoirs, overflows structures, etc), water resources planning and protection (Morgenschweis G. - 2010: Hydrometrie: Theorie und Praxis der Durchflussmessung in offenen Gerinnen VDI-Buch, ISBN 978-3-642-05389-4. Springer-Verlag Berlin Heidelberg. 582). An exemplary application addressed here is the continuous monitoring of flow discharge based on the specific collection of a flow speed signal characterizing the free-surface flow section being instrumented.

As it is often highlighted in the field of free-surface flow hydrometry, there are many local circumstances preventing to extract a representative flow rate information (Q) from the simple monitoring of water depth (H): backwater influence, poor stability of the Q-H rating curve due to scouring-deposition effects, changes in hydraulic roughness, complex cross-section geometry, etc. Continuous water depth monitoring nowadays is a well-solved problem but, in the circumstances listed above, trying to infer continuous discharge information out of it is generally doomed to fail, and is preventing the setting-up and implementation of modern water management options (Morgenschweis 2010). As an example, for the planning and dimensioning of further extensions or modifications of the urban water infrastructure, a very important problem is the dimensioning (and retrofitting) of sewer networks for proper management of the 'Combined Sewage Overflows' (CSO). Sewer overflow results in the uncontrolled bypass of waste water treatment plants and consecutive river pollution. Building a CSO management plan supposes that one knows sufficiently well, year in year out, which storm outlet is working at what time and how many m³ of discharge it is releasing into the fluvial environment.

In many cities, especially with older and incompletely chartered sewer networks, this data is largely lacking. The present invention would provide, at affordable costs, relevant data for the understanding of CSO behavior and subsequent planning of infrastructure changes.

In general terms, an estimation of discharge using indirectly measured flow speed would have valuable advantages, but data must be collected in a standardized way, with a known accuracy, and continuously in time (Hirsch & Costa, 2004). Presently there exist costly, non-contact, alternative solutions to traditional flow speed measurements (Morgenschweis, 2010) such as, for instance, expensive radar current meter sensing devices and video imagery techniques.

The German patent application DE19806316 discloses a device and a method for determining the flow speed in sewers (not in open channels in general). The method comprises the measurement of hydrodynamic pressure and hydrostatic pressure. The water level is not measured independently. The hydrodynamic pressure is compensated with the hydrostatic pressure for determining the flow speed.

Summary of the invention

It is an object of the invention to provide methods that indirectly and more precisely determine the flow speed of a liquid in a free-surface flow, for a long time survey, and/or in a more economical way, and/or for a wider variety of environmental conditions.

The invention is defined by the independent claims. The dependent claims define advantageous embodiments.

According to a first aspect, the invention concerns methods for measuring a flow speed of a liquid.

According to a first embodiment, there is provided a method for determining a flow speed of a liquid in a free-surface flow, the method comprising the steps of: a) Measuring environmental variables comprising:

- a flow speed dependent absolute pressure p_a at a depth L in said liquid,

- the depth L at which the absolute pressure p_a is measured, b) calculating the flow speed U of the liquid from the following equation:

wherein

L/ is the flow speed of the liquid;

o is a numerical pre-factor;

g is the gravitational acceleration;

p is the density of the liquid;

Po is the air pressure above the liquid. According to a second embodiment, there is provided a method for determining a flow speed of a liquid in a free-surface flow, the method comprising the steps of:

a') Measuring environmental variables comprising:

- a flow speed dependent relative pressure p_r at a depth L in said liquid,

- the depth L at which the relative pressure p_r is measured,

b') calculating the flow speed U of the liquid from the following equation:

wherein

U \s the flow speed of the liquid;

a is a numerical pre-factor;

g is the gravitational acceleration;

is the density of the liquid.

Each of these two embodiments of the method is based on similo-static pressure measurements, a concept where a pressure sensor, such as a hydrostatic liquid sensor for example, is forced to work in a dynamic regime, and is under the influence of hydrodynamic effects. This results in a drop of the pressure measured by the pressure sensor compared to hydrostatic conditions, which is proportional to the flow speed (the Bernoulli effect). In other words, in dynamic conditions (presence of not-negligible flow speed) the liquid level measured by the pressure sensor will therefore underestimate the correct liquid level. The difference between the correct liquid level (measured separately by another sensor) and the one measured with the immerged pressure sensor is proportional to the flow speed.

The method of the invention is suitable for different flow conditions (e.g. for both subcritical and supercritical flows), with reduced costs, provides richer information (not only speed, but also water level). Moreover, the method is easy to implement in collectors, sewers and rivers. The actual measurement of the liquid level (indirect measurement) is one of the major differences between the present invention and the prior art. The present method does not need to comprise the measurement of hydrostatic pressure as in DE1 980631 6. Consequently, the present method is more reliable in any condition, and in any environment.

With a method of the present invention, records of the flow speed may be obtained. The method allows the records of the flow speed in the whole depth of a liquid using only a single pressure sensor in the liquid.

In the method of the first embodiment, the air pressure p₀ may be a constant value such as the standard atmospheric pressure for example (101 325 Pa) or it may be a measured pressure. Preferably, step a) of the method according to the invention further comprises the step of measuring the air pressure p₀ above the liquid, in which case it is the value of said measured pressure p₀ which is used in the equation of step b) of the method. Measuring the air pressure above the liquid and using the measured value for calculating the flow speed will result in a more accurate determination of the flow speed, particularly when the liquid is flowing in closed volumes such as in conduits for instance.

The value of the numerical pre-factor a may for example be a constant value established by experiments and of which concrete examples will be given in the detailed description of embodiments of the invention. Whatever the embodiment, the value of the numerical pre-factor a is however preferably made dependent on a temperature 7^~of the liquid. Preferably, the numerical pre- factor a is a polynomial function of the temperature T. More preferably, the numerical pre-factor a is calculated according to the following equation :

a = 0.0025 T³ - 0.0950 T² + 1.1123 T - 1.9000 , wherein 7^" is expressed in °C. The density p of the liquid may be a standard density which is for example a value taken up from a known table for the concerned liquid and at a normal temperature such as 1 5 °C for example. Preferably, the density is made dependent on the temperature of the liquid. More preferably, the density of the liquid p is calculated according to the following equation:

wherein,

p(T₀) is a reference density of said liquid at a known temperature T₀, yS is the volumetric thermic expansion coefficient of the liquid,

7^~ is the temperature of the liquid,

Making the numerical pre-factor a and/or the density p of the liquid dependent on the temperature of the liquid allows to compensate for viscous stresses, and/or to account for heat conduction influence, and/or to indirectly compensate for residual turbulence effects, and hence to obtain a more accurate value of the flow speed.

Preferably, step a) of a method according to the invention further comprises measuring the temperature 7^~ of the liquid, preferentially at a location where the flow speed dependent pressure p_a or p_r is measured, and using the value of the measured temperature to calculate the numerical pre-factor a and/or the density p of the liquid when they are chosen to be temperature-dependent.

According to a second aspect of the invention, a kit of parts for the determination of a flow speed of a liquid in a free-surface flow is provided, said kit comprising:

- a pressure sensor configured to measure a flow-speed dependent absolute or relative pressure p_a or p_r at a depth L in the liquid,

- a liquid-depth probe configured to measure the depth L,

- a software which, when executed, gathers data provided by the pressure sensor and by the liquid-depth probe, and performs a method as described hereinabove to calculate the flow speed U of the liquid in function of the said data. Preferably, the kit further comprises a temperature sensor able to measure a temperature 7^~ of the liquid, preferentially at a location where the pressure p_a or p_r is measured, and the software, when executed, gathers data provided by the pressure sensor, by the liquid-depth probe, and by the temperature sensor, and performs a method as described hereinabove to calculate the flow speed U of the liquid in function of the said data.

In case the pressure sensor is able to measure a flow-speed dependent absolute pressure p_a, the kit preferably further comprises an air pressure sensor configured to measure an air pressure p₀ above the liquid, and the software, when executed, gathers data provided by the pressure sensor, by the liquid- depth probe, by the air pressure sensor, and by the temperature sensor when present, and performs a method as described hereinabove to calculate the flow speed U of the liquid in function of the said data.

According to a third aspect of the invention, there is provided an apparatus for the determination of a flow speed of a liquid in a free-surface flow, said apparatus comprising:

- a pressure sensor disposed in the liquid at a depth L, and configured to measure a flow-speed dependent absolute or relative pressure p_a or p_r at the depth L;

- a liquid-depth probe configured to measure the depth L;

- a data management system operatively connected to the pressure sensor, and the liquid-depth probe; and

- a software which, when executed, gathers data provided by the pressure sensor, and the liquid-depth probe, and performs a method as described hereinabove to calculate the flow speed U of the liquid in function of the said data. Preferably, the apparatus comprises a temperature sensor able to measure a temperature 7^~ of the liquid, preferentially at a location where the pressure p_a or p_r is measured, the data management system is further operatively connected to the temperature sensor, and the software, when executed, gathers data provided by the pressure sensor, the liquid-depth probe, and the temperature sensor and performs a method as described hereinabove to calculate the flow speed U of the liquid in function of the said data. Preferably, when the pressure sensor is configured to measure a flow-speed dependent absolute pressure p_a, the apparatus further comprises an air pressure sensor to measure an air pressure p₀ above the liquid, the data management system is further operatively connected to the air pressure sensor, and the software, when executed, gathers data provided by the pressure sensor, the liquid-depth probe, the air pressure sensor, and the temperature sensor when present, and performs a method as described hereinabove to calculate the flow speed U of the liquid in function of the said data.

Short description of the drawings

These and further aspects of the invention will be explained in greater detail by way of examples and with reference to the accompanying drawings in which:

Fig.1 shows the dependency of the pre-factor a on the liquid temperature T; Fig.2 illustrates the results of a method according to the invention in a test flume;

Fig.3 illustrates the flow speed measurement with an electromagnetic current meter vs. the flow speed measurement with a method according to the invention;

Fig.4 illustrates the performance of a method according to the invention when the method is applied to a combined sewer overflow event;

Fig.5 illustrates the performance of a method according to the invention when the flow speed of the liquid is high;

Fig.6 is a schematic view of a system for determining the flow speed of a liquid in a free-surface flow according to one embodiment of the invention.

Fig.7 is a schematic representation of a pressure sensor configured to measure a flow-speed dependent pressure, and disposed in the liquid. The drawings of the figures are neither drawn to scale nor proportioned. Generally, similar or identical components are denoted by the same reference numerals in the figures.

Detailed description of embodiments of the invention

A first method according to the invention for determining a flow speed of a liquid in a free-surface flow comprises the steps of:

a) Measuring environmental variables comprising:

- a flow speed dependent absolute pressure p_a at a depth L in said liquid,

- the depth L at which the absolute pressure p_a is measured, b) calculating the flow speed U of the liquid from the following equation (I):

wherein

U \s the flow speed of the liquid;

o is a numerical pre-factor;

g is the gravitational acceleration;

p is the density of the liquid;

Po is the air pressure above the liquid.

Alternatively, a second method for determining a flow speed of a liquid in a free- surface flow comprises the steps of:

a') Measuring environmental variables comprising:

- a flow speed dependent relative pressure p_r at a depth L in said liquid,

- the depth L at which the relative pressure p_r is measured,

b') calculating the flow speed U of the liquid from the following equation ( ):

wherein

L/ is the flow speed of the liquid;

a is a numerical pre-factor;

g is the gravitational acceleration;

p is the density of the liquid.

The liquid may for example be water, oil or derivatives thereof, chemicals, beverages, etc.

A free-surface flow, sometimes also called open-channel flow, is the gravity driven flow of a fluid under a free surface, typically water flowing under air in the atmosphere such as in a river, an irrigation channel or a sewer.

The methods may be used in wide range of flow conditions such as for example subcritical and supercritical flow conditions (with respect to the value of the Froude number). The flow speed which can be determined with this method can be as low as 0.2 m/s, depending on the accuracy of the pressure sensor and the general flow conditions. There is basically no upper limit to the speed that can be determined by the methods.

The methods comprise the measurement of a flow speed dependent pressure (p_a or p_r) at a depth L in the liquid. This pressure can be measured anywhere in the liquid column. Preferably, this pressure is measured in the lower 30% of the maximum height of the liquid relatively to its bottom, and in a more preferred embodiment, in the lower 20% of the maximum height of the liquid relatively to its bottom. This pressure is for example measured with a pressure sensor. The pressure sensor can be any type of known pressure sensors having preferably an accuracy better than 0.2% at full scale. Preferably, the pressure sensor is of the capacitive or piezo-resistive type. The terms absolute pressure and relative pressure (sometimes called gauge pressure) and corresponding sensors are well known in the art.

The term "Flow speed dependent pressure" is self-explanatory in the sense that it concerns a pressure which depends on the flow speed of the liquid at the location where the said pressure is measured.

The flow speed dependent absolute pressure p_a or flow speed dependent relative pressure p_r, is therefore the pressure measured by a pressure sensor immersed in the flowing liquid and arranged in such a way that it is under the influence of the dynamic effects of the movement of the liquid in and/or round the sensor. It should furthermore be understood that the methods according to the invention do not rely on a differential pressure measurement, such as the one implemented in Pitot tubes (R G Fulstom - Review of the Pitot Tube - Transactions of the ASME, 1956) and Irwin probes (Irwin, H. P. A. (1981 ) - A simple omnidirectional sensor for wind-tunnel studies of pedestrian-level winds. Journal of wind engineering and industrial aerodynamics, 7(3), 219-239). In Pitot tubes, Irwin probes and equivalent speed-determining devices, the derivation of the fluid speed from pressure actually requires the knowledge of a pressure difference (e.g. measurement of the pressures at two separate points within the fluid). It is useful to stress that the methods according to the present invention are not differential-pressure methods. Within the fluid they rely on only one pressure value measured at one given point. It is the independently measured water depth L (a length, in meters) which provides the key secondary information allowing, by the logic of the equation according to the invention, to obtain the value of the fluid speed and, ultimately, of the uni-dimensional flow- forming velocity. According to the methods of the invention, only a single pressure measurement is needed and such method is easier to implement and more convenient since only one pressure sensor fitted into the system to be monitored is needed, instead of having two. Having only one immersed sensor naturally reduces the risks of failures (i.e. two sensors would double that risk).

To this end, the pressure sensor (4) is disposed in the liquid so that it is influenced by at least the dynamic effects of the liquid on the sensor. An exemplary arrangement is illustrated on Fig.7 where one can see a pressure sensor (4) whose active part (4a) (the part which is mobile under the effect of pressure applied to it) will be under influence of dynamic effects of the liquid. It will be obvious that many other configurations are possible. The method also comprises the measurement of the depth L at which the pressure p_a or p_r is measured. In other words, the depth L is thus the (instant) height of the liquid column above the location where the pressure p_a or p_r is measured. The top of the depth L is thus formed by the free-surface, namely where there is the interface between the flowing liquid and the ambient atmosphere. The inventions presented, respectively, by Wargo 2009 and Klosinsky 2010 cannot be compared to the present invention as the flows they consider do not present such an air-liquid interface. The depth L in their case is thus inexistent. Being inexistent, it cannot be measured. The L signal being inexistent, it cannot be used by them as an input to calculate the fluid speed. Also, Wargo 2009 and Klosinsky 2010 use the fluid temperature as an input but the fact that the depth L does not exist in the systems they consider demonstrates that the speed-determination methods that they are, respectively, proposing are inherently different from the one proposed by the present invention. The depth L may be measured with a depth sensor placed inside the liquid or outside the liquid, preferably at a level above the level at which the pressure is measured. Care must of course be taken that the measurement of the depth L is not affected by hydrodynamic effects in case the depth sensor is placed inside the liquid. Preferably, the depth L is measured by a limnimeter not affected by hydrodynamic effects, such as for example a radar or an ultrasonic- based device. Preferably the limnimeter is disposed at the vertical of the location where the flow speed dependent pressure p_a or p_r is measured (i.e. in the air headspace).

The method of the present invention is based on the Bernoulli effect. What is known as the Bernoulli effect is a drop of the local fluid pressure as a function of the corresponding increase of flow speed in the considered streamline. As shown in the example of Fig.7, the pressure sensor (4) placed in the liquid creates a significant obstacle to the flow. There is thus local steric hindrance while continuity should be maintained (in case of an incompressible liquid). This means that, comparatively to the undisturbed flow speed field (which is approaching the pressure sensor), there is a spatial acceleration of the streamlines which are coming in the immediate vicinity of the pressure sensor. The implication of this dominant Bernoulli effect is thus that, comparatively to what the pressure sensor should deliver as fluid pressure, any further increase of the approaching flow speed will mark itself as a further deficit in the recorded pressure signal. According to the first embodiment of the method, equation (I) requires the value of the air pressure p₀ above the liquid. The air pressure p₀ may be a constant value such as the standard atmospheric pressure for example (101325 Pa) or it may be a measured pressure. Preferably, the method according to the invention further comprises the step of measuring the air pressure p₀ above the liquid, in which case it is said measured pressure p₀ which is inserted into the equation (I) during step b) of the method. Measuring the air pressure above the liquid and using this measured value for calculating the flow speed will result in a more accurate determination of the flow speed, particularly when the liquid is flowing in a collector or a sewer for instance. Alternatively, the air pressure p₀ above the liquid is not measured, nor inserted into the equation, in the second embodiment of the method wherein only the flow speed dependent relative pressure p_r is measured and needed for calculating the flow speed according to the equation ( ). To produce an accurate and representative flow speed record, it is important to appreciate the de-facto value of the pre-factor a in the equation (I) or ( ). Bernoulli's approach relies (notably) on two simplifying assumptions. Firstly, that the fluid behaves as if it was ideal and could be considered inviscid. But viscous stresses are known to be present in the case of a real fluid (Batchelor G.K. - 1967: An introduction to fluid dynamics, CUP New York, 615p). The second assumption inherent in Bernoulli's approach of the energy budget in a considered material element following the streamline is that heat conduction by the fluid is negligible. In a preferred embodiment of the invention, the pre-factor a is dependent on the temperature 7^~of the liquid. Heat-conductive properties of a liquid in the immediate proximity of an electrically-wired sensor could indeed be not negligible. In brief there are thus three reasons explaining why the method benefits from a pre-factor a being dependent from the liquid temperature T, and preferentially from a measured liquid temperature 7^":

1 °) compensating for viscous stresses,

2°) accounting for heat conduction influence,

3°) indirect compensation for residual turbulence effects. These fluid dynamics processes are complex and the validity of the equations used in step b) or b') under variable thermic environments has been explored experimentally. Fig. 1 is a demonstration that a temperature effect is present, significant and reproducible. The horizontal axis represents the temperature of the liquid (here water) in °C, whereas the vertical axis represents the (dimensionless) pre-factor a. The pre-factor a, once calibrated, may be introduced into the equations (I) or ( ). In a preferred embodiment of the invention, the pre-factor a is a polynomial function of the temperature T. The polynomial function may be derived from experimental data. Preferably, the pre- factor a is calculated using the following equation (II), in which the temperature T is preferentially the measured temperature of the liquid and is expressed in degrees Celsius: a = 0.0025 T³ - 0.0950 T² + 1.1123 T - 1.9000 (II) Alternatively, the pre-factor a may be a constant value such as for example any value illustrated on Fig. 1 . Preferentially, a has a value comprised between 1 ,8 and 2,8. More preferentially, a equals 1 ,9.

In a preferred embodiment, the method also comprises the measurement of the temperature 7^~of the liquid. Any known temperature sensor can be used for this purpose, such as for example a thermistor or a thermocouple immersed in the liquid. The temperature sensor may be placed at any distance from the pressure sensor. Preferably, the temperature sensor and the pressure sensor are located close to each other so that the temperature sensor will measure the temperature of the liquid close to or at the location where the flow speed dependent pressure p_a or p_r is measured. The distance between the temperature sensor and the location where the flow speed dependent pressure p_a or p_r is measured, is for example preferably smaller than 50 cm, more preferably smaller than 20 cm, even more preferably less than 10 cm. In a preferred and/or complementary embodiment, the temperature T is measured in the lower 30% of the maximum height of the liquid relatively to its bottom, and in a more preferred embodiment, in the lower 20% of the maximum height of the liquid relatively to its bottom.

The liquid density p is the normal density of the liquid. It can be given a value at a temperature of 20 °C for instance, whatever the actual temperature T of the liquid. In a preferred embodiment of the method, the liquid density p is temperature dependent. In order to improve the accuracy, the method of the invention preferably comprises a step of calculating the liquid density at the temperature T of the liquid, according to following equation (III):

p = -2222- („,)

1+β(Τ-Τ₀) wherein,

p(T) is the density, preferentially expressed in kg/m³, of said liquid at the temperature Γ,

p(T0) is a reference density, preferentially expressed in kg/m³, of said liquid at a known temperature T₀,

β is the volumetric thermic expansion coefficient of the liquid, preferentially expressed in °C^"1 ,

7^~ is the measured temperature of the liquid, preferentially expressed in °C, r₀ is the temperature at which the reference density of the liquid is known, expressed in °C. T₀ may be any temperature, provided p{T0) is known.

β is temperature dependent, β may be determined by an experimental determination using a known method, β may alternatively be found in reference chemical property tables known in the art.

5 Alternatively, β may be calculated by an equation allowing a better accuracy of the β value.

When the liquid is water, β may for example be calculated using the following equation (IV):

i o /J = 1(T⁶ (-62.67914 + 15.84576Γ - 0.Π758Γ²) ₍iv)

Wherein 7^~is the measured temperature of the liquid, expressed in °C.

For example, when the liquid is water and the temperature of the liquid T = 15 20 °C,

β will be equal to 0.000207 °C^"1.

In equations I, II, III and IV, the temperature T is preferably the temperature of the liquid at or close to the location where the flow speed dependent absolute 20 pressure p_a or flow speed dependent relative pressure p_r of the liquid is measured. The term "close to" is to be understood as "at less than 50 cm from", preferably as "at less than 20 cm from", even more preferably as "at less than 10 cm from".

25 The time resolution between two consecutive sets of measurements of the environmental variables may be very short. To avoid inaccurate determination of the flow speed, any of the aforementioned environmental variables (L, T, p_a, p_r, po) may be measured over a period of time suitable for integration, i.e. a time-integration period. The time-integration period is preferably larger than 0.5

30 seconds, more preferably larger than 10 seconds. Alternatively, the time- integration period is larger than 1 minute. The value of any environmental variable inserted in the equation (I) may for example be an average of the values of said environmental variable as measured over one of the said time- integration periods.

The invention also concerns a kit of parts (1 ) for the determination of a flow speed of a liquid (2) in a free-surface flow, said kit of parts comprising:

- a pressure sensor (4) configured to measure a flow-speed dependent absolute or relative pressure p_a or p_r at a depth L in the liquid (2),

- a liquid-depth probe (6) configured to measure the depth L,

- a software which, when executed, gathers data provided by the pressure sensor and by the liquid-depth probe, and performs any one of the methods as described hereinabove to calculate the flow speed U of the liquid in function of the said data. Preferably, and when the pressure sensor is configured to measure a flow- speed dependent absolute p_a, the kit further comprises an air pressure sensor (7) to measure an air pressure p₀ above the liquid, and the software, when executed, gathers data provided by the pressure sensor (4), the liquid-depth probe (6), and the air pressure sensor (7), and performs the method as described hereinabove to calculate the flow speed U of the liquid in function of the said data.

Preferably, the kit further comprises a temperature sensor (5) configured to measure the temperature 7^~ of the liquid (2), and the software, when executed, gathers data provided by the temperature sensor (5), and performs the method as described hereinabove to calculate the flow speed U of the liquid in function of the said data.

Preferably, the pressure sensor (4) and the temperature sensor (5) are disposed at the same depth, more preferably close to each other. The distance between the temperature sensor (5) and the pressure sensor (4), is for example preferably smaller than 50 cm, more preferably smaller than 20 cm, even more preferably less than 10 cm. More preferably, the pressure sensor and the temperature sensor are provided within one single measuring device. The pressure sensor (4) and/or temperature sensor (5) and/or measuring device may comprise means for grounding (9) them. Said means for grounding (9) ensure the positional stability of the sensors or measuring device in the liquid (2). The pressure p₀ above the liquid may optionally be measured with for example a barometer (7). The measurement of the liquid depth may for example be performed with a radar or an ultrasonic probe (6). The pressure sensor (4), the temperature sensor (5), the liquid depth-probe (6) and the optional barometer (7) are preferably connected to and/or communicate with a data management system (8). The data management system (8) may contain a data logger and/or a data transmission unit and/or a data processing unit. The invention also concerns an apparatus for the determination of a flow speed of a liquid in a free-surface flow, comprising:

- a pressure sensor (4) disposed in the liquid at a depth L, and configured to measure a flow-speed dependent absolute or relative pressure p_a or p_r at the depth L;

- a liquid-depth probe (6) able to measure the depth L;

- a data management system operatively connected to the pressure sensor (4), and the liquid-depth probe (6); and

- a software which, when executed, gathers data provided by the pressure sensor, and the liquid-depth probe, and performs any one of the methods as described hereinabove to calculate the flow speed U of the liquid in function of the said data.

Preferably, and when the pressure sensor is configured to measure a flow- speed dependent absolute p_a, the apparatus further comprises an air pressure sensor (7) to measure an air pressure p₀ above the liquid, the data management system (8) is further operatively connected to the air pressure sensor (7), and the software, when executed, gathers data provided by the pressure sensor (4), the liquid-depth probe (6), and the air pressure sensor (7), and performs the method as described hereinabove to calculate the flow speed U of the liquid in function of the said data.

Preferably, the apparatus further comprises a temperature sensor (5) configured to measure a temperature T of the liquid, the data management system (8) is further operatively connected to the temperature sensor (5), and the software, when executed, gathers data provided by the pressure sensor (4), the liquid-depth probe (6), the temperature sensor (5), and the air pressure sensor (7) when present, and performs the method as described hereinabove to calculate the flow speed U of the liquid in function of the said data.

Working examples

The present method for the flow speed determination was tested in controlled laboratory conditions, in an irrigation channel and applied on existing combined sewer overflow data, the liquid under test being water.

Flume tests

A series of tests were performed in a controlled lab conditions, in a rectangular hydraulic test flume (10 m x 0,5 m x 0,6 m) in which the discharge can be precisely increased from 15 l/s up to 83 l/s. Two different types of pressure sensors, piezo-resistive and capacitive, were deployed in the flume. Externally, water level is monitored and crosschecked by a radar limnimeter and two ultrasonic limnimeters. In addition, a limnimetric scale is installed on the lateral wall of the flume for visual validation of the water level variation throughout the experiments. These devices provide an accurate measurement of the water level in hydrostatic conditions with an error no greater than a few millimetres.

The tests were conducted as follows. The water level was slowly increased to keep conditions as hydrostatic as possible. Once the water height was high enough, the end gate of the flume was opened to increase the flow speed. The speed was measured in different ways. Three techniques were used depending on the flow conditions: - The surface speed was measured with the transit time of a floating object along a known distance.

- The discharge in the flume can be precisely calculated due to a fixed- geometry rectangular weir. As there is no downstream influence, each water level over the weir can be associated to a unique discharge. The water level was measured with an ultrasonic limnimeter placed above a weir. The average speed can therefore be calculated with the water level.

- For high speeds, a propeller-type current meter was used. The speed was increased step by step by decreasing the water level with the same pumped discharge (by manipulation of the flume end-gate). When the maximum speed was reached with a single pump, a second pump was switched on to increase the discharge up to 83 l/s which allowed to increase the water level with the same speed. The maximum flow speed obtained in the channel was 0.91 m/s. If the section was reduced, then the flow speed could locally be increased up to 2m/s.

Fig. 2 illustrates the performance of the method of the present invention in a test flume using a capacitive type of absolute pressure sensor. The horizontal axis represents a reference flow speed in m/s (cross-section averaged), whereas the vertical axis represents the flow speed in m/s as determined by the method according to the invention. It is shown that the method can be satisfactorily applied for a large range of flow speed. A flow speed higher than 1 m/s shown in Fig. 2 actually correspond to supercritical flow conditions (Fr>1 ). The same performances were obtained using a piezo-resistive type of absolute pressure sensor.

Irrigation channel

The present method was also tested in an irrigation channel, 20 m wide, working at maximal discharge of 40 m³/s controlled by a 6.25m wide sector valve at its entry. A maximum water depth in the channel was 3.5m. The section was irregular with sandy soil at the centre of the flow and rougher particles on the side of the channel. The water temperature was stable during tests (around 29 °C). Although the channel water was turbid, suspended sediment density however was not high enough to affect the flow speed measurements. A radar limnimeter was installed under the bridge crossing the channel. For reference measurements, an electromagnetic current meter with integrated pressure sensor was installed at 0.7m from the bottom. A high sensitive pressure sensor with an integrated temperature sensor was fixed to the current meter pole. A barometer was hanged on the bridge to perform a measurement of the atmospheric pressure. Additionally, a scale was fixed on the lateral wall of a centrally-located longitudinal overflow weir and it was used as the water level reference for all the other sensors.

The various water level measurements allowed us to cross-validate the measurement and to calibrate all sensors that needed to be calibrated on-site.

The maximum flow speed recorded was 1 .5 m/s at the 5 out of 6 valve opening scale and the average speed when the first wave had passed was around 1 m/s. As illustration, measurement results during one testing day are shown in Figure 3, wherein one can see the speed measured with the electromagnetic current meter (reference speed) vs the speed computed by the method of the present invention (observed speed).

The initial water level with the valve closed was 0.95 m and it was stable for the first few hours of the day. There were two valve openings on that day. The valve was opened for the first time around noon at valve opening scale 3 out of 6 and the second time around 3.30pm.

Fig.3 illustrates the flow speed as measured with an electromagnetic current meter (dots) versus the flow speed as measured with a method according to the invention (solid line), both over a time period from 12:00 to 18:00. The vertical axis represents the flow speed in m/s, whereas the horizontal axis represents time. As can be seen in Fig. 3, the two peaks and trends are very well described by the method of the present invention.

Combined sewer overflow

The proposed innovative method has been also applied to the data from a combined sewer overflow structure. The structure is instrumented with a combination of sensors. A capacitive type pressure sensor with an associated temperature sensor is installed into the water column, a water level is measured externally by a radar limnimeter and flow speed in the local cross-section is followed by a radar current meter.

Fig. 4 shows the performance of the method according to the invention when applied to a combined sewer overflow event. The vertical axis represents the flow speed in m/s, whereas the horizontal axis represents time. The flow speed as measured with a radar current meter is represented by dots while the flow speed as measured with a method according to the invention is represented by the solid line, both over the same time period. It can be seen that the flow speed variations are well represented for the entire event. For speed values lower than 0.3 m/s, the radar current meter observations are not valid according to its user manual.

Fig. 5 shows comparison of the flow speed measured by the method of the present invention and a radar current meter for an event encountering for both subcritical, as well as supercritical flow regimes. The vertical axis represents the flow speed in m/s, whereas the horizontal axis represents time. The flow speed as measured with a radar current meter is represented by dots while the flow speed as measured with a method according to the invention is represented by the solid line, both over the same time period. It is demonstrated that the method of the present invention works fine even for high flow speeds (reaching as high as 3.5 m/s) and that can be easily implemented in different and/or variable environments. The invention may also be defined as follows:

A method for determining a flow speed of a liquid in a free-surface flow, the method comprising the steps of:

- providing a pressure sensor and placing it at a depth L in the liquid; providing a liquid-depth probe and arranging it to sense the depth L at which the absolute pressure sensor is placed;

providing a data management system and connecting it and/or putting it in communication with the pressure sensor, and with the liquid-depth probe;

measuring, with the pressure sensor, a flow-speed dependent absolute or relative pressure p_a or p_r at the depth L in said liquid,

measuring, with the liquid-depth probe, the depth L at which the a flow- speed dependent absolute or relative pressure p_a or p_r \s measured, - Calculating, with the data management system, a flow speed U of the liquid as a function of the measured a flow-speed dependent absolute or relative pressure p_a or p_r, and the measured depth L

The data management system calculates the flow speed U of the liquid with the following equation (I):

wherein

U \s the flow speed, preferentially expressed in m/s;

a is a numerical pre-factor (dimensionless);

g is the gravitational acceleration, preferentially expressed in m/s²;

p_a is the measured flow-speed dependent absolute pressure at the depth

L in said liquid, preferentially expressed in Pa;

Po is the air pressure above the liquid, preferentially expressed in Pa; L is the measured depth at which the flow-speed dependent absolute pressure p_a is measured, preferentially expressed in m ;

p is the liquid density of the liquid, expressed preferentially in kg/m³; or with the following equation ( ):

wherein

U \s the flow speed, preferentially expressed in m/s;

a is a numerical pre-factor (dimensionless);

g is the gravitational acceleration, preferentially expressed in m/s²;

ρ,- is the measured flow-speed dependent relative pressure at the depth L in said liquid, preferentially expressed in Pa;

L is the measured depth at which the flow-speed dependent relative pressure ρ,- is measured, preferentially expressed in m;

p is the liquid density of the liquid, expressed preferentially in kg/m³;

Preferably, the method further comprises the steps of providing an air pressure sensor and placing it above the liquid, of measuring an air pressure p₀ above the liquid with said air pressure sensor, and of calculating, with the data management system, a flow speed L/ of the liquid as a function of the measured absolute pressure p, the measured depth L, and the measured air pressure p₀. The data management system calculates the flow speed U with the equation (I) hereinabove, wherein p₀ is the measured air pressure above the liquid, expressed in Pa.

Preferably, the method further comprises the steps of providing a temperature sensor and placing it in the liquid; of measuring, with the temperature sensor (5), a temperature 7^~ of the liquid, and of calculating, with the data management system, a flow speed U of the liquid as a function of the measured flow speed dependent pressure p_a or p_r, the measured depth L, and the measured temperature T. Preferably, the method further comprises the steps of providing an air pressure sensor and placing it above the liquid; of measuring an air pressure p₀ above the liquid with said air pressure sensor; and of calculating, with the data management system, a flow speed L/ of the liquid as a function of the measured flow speed dependent absolute pressure p_a, the measured depth L, and the measured air pressure p₀.

Preferably, the method further comprises the steps of providing a temperature sensor and placing it in the liquid; of providing an air pressure sensor and placing it above the liquid; of measuring, with the temperature sensor (5), a temperature T of the liquid; of measuring an air pressure p₀ above the liquid with said air pressure sensor; and of calculating, with the data management system, a flow speed U of the liquid as a function of the measured flow speed dependent absolute pressure p_a, the measured depth L, the measured air pressure p₀ and the measured temperature T.

Preferably, the method further comprises the step of calculating the numerical pre-factor a. Pre-factor a may be a polynomial function of the temperature of the liquid. Preferentially, the pre-factor a is calculated according to the following equation:

a = 0.0025 T³ - 0.0950 T² + 1.1123 T - 1.9000,

wherein T is the measured temperature of the liquid, expressed in °C: or alternatively, pre-factor a is comprised between 1 .8 and 2.8, and more preferentially re-factor a equals 1 .9.

The present invention has been described in terms of specific embodiments, which are illustrative of the invention and not to be construed as limiting. More generally, it will be appreciated by persons skilled in the art that the present invention is not limited by what has been particularly shown and/or described hereinabove.

Reference numerals in the claims do not limit their protective scope. Use of the verbs "to comprise", "to include", "to be composed of", or any other variant, as well as their respective conjugations, does not exclude the presence of elements other than those stated.

Use of the article "a", "an" or "the" preceding an element does not exclude the presence of a plurality of such elements.

Claims

a) Measuring environmental variables comprising:

- a flow speed dependent absolute pressure p_a at a depth L in said

wherein

U \s the flow speed of the liquid;

o is a numerical pre-factor;

g is the gravitational acceleration;

p is the density of the liquid;

Po is the air pressure above the liquid.

The method according to claim 1 , wherein step a) further comprises measuring an air pressure p₀ above the liquid.

a') Measuring environmental variables comprising:

- a flow speed dependent relative pressure p_r at a depth L in said liquid,

- the depth L at which the relative pressure p_r is measured,

b') calculating the flow speed U of the liquid from the following equation:

wherein

L/ is the flow speed of the liquid;

a is a numerical pre-factor;

g is the gravitational acceleration ;

p is the density of the liquid.

4. The method according to any of claims 1 to 3, wherein the value of the numerical pre-factor a is dependent on a temperature 7^~ of the liquid. 5. The method according to claim 4, wherein the numerical pre-factor a is a polynomial function of the temperature T.

6. The method according to claim 4, wherein the numerical pre-factor cr is calculated according to the following equation :

= 0.0025 T³ - 0.0950 T² + 1.1123 T - 1.9000 wherein 7^" is expressed in °C.

7. The method according to any of claims 4 to 6, wherein step a) further comprises measuring the temperature T of the liquid, preferentially at a location where the flow speed dependent pressure p_a or p_r is measured.

8. The method according to any of the previous claims, wherein the density of the liquid p is calculated according to the following equation :

P =

1 + β(Τ - Τ₀)

wherein,

p(T₀) is a reference density of said liquid at a known temperature T₀, β is the volumetric thermic expansion coefficient of the liquid,

7^~ is the temperature of the liquid, T₀ is the temperature at which the reference density of the liquid is known.

9. The method according to any one of claims 1 to 8, wherein:

- the flow speed dependent pressure p_a or p_r is measured with a pressure sensor (4);

- the depth L is measured with a liquid-depth probe (6);

and wherein step b) is performed with a data management system (8), and wherein the data management system (8) is connected to and in communication with the pressure sensor (4) and with the liquid-depth probe (6).

10. The method according to claim 9 wherein the temperature 7^~ is measured with a temperature sensor (5) and wherein the data management system (8) is connected to and in communication with the temperature sensor (5).

1 1 . The method according to any one of the previous claims, wherein the flow speed U \s larger than 0.2 m/s. 12. The method according to any one of the previous claims, wherein the flow speed U is calculated from a plurality of measurements of the environmental variables during a time-integration period over 0,5 s, preferentially over 1 s, and more preferentially over 5 s. 13. A kit of parts (1 ) for the determination of a flow speed of a liquid (2) in a free-surface flow, comprising:

- a pressure sensor (4) able to measure a flow-speed dependent absolute or relative pressure p_a or p_r at a depth L in the liquid (2),

- a liquid-depth probe (6) able to measure the depth L,

- a software which, when executed, gathers data provided by the pressure sensor (4) and the liquid-depth probe (6), and performs the method according to any one of claims 1 to 12 to calculate the flow speed L/ of the liquid (2) in function of the said data.

14. A kit of parts according to claim 13, the kit further comprising:

- an air pressure sensor (7) able to measure an air pressure pO above the liquid (2),

wherein the software, when executed, furthermore gathers data provided by the air pressure sensor (7), and performs the method according to any one of claims 2 or 4 to 12 to calculate the flow speed U of the liquid (2) in function of said data. 15. A kit of parts according to claim 13 or 14, the kit further comprising:

- a temperature sensor (5) able to measure a temperature T of the liquid (2),

wherein the software, when executed, furthermore gathers data provided by the temperature sensor (5), and performs the method according to any one of claims 7 to 12 to calculate the flow speed U of the liquid (2) in function of said data.

16. An apparatus for the determination of a flow speed of a liquid (2) in a free-surface flow comprising:

- a pressure sensor (4) disposed in the liquid (2) at a depth L, and configured to measure a flow-speed dependent absolute or relative pressure p_a or p_r at the depth L;

- a liquid-depth probe (6) configured to measure the depth L;

- a data management system (8) operatively connected to the pressure sensor (4) and the liquid-depth probe (6); and

- a software which, when executed, gathers data provided by the pressure sensor (4), the liquid-depth probe (6), and performs the method according to any one of claims 1 to 12 to calculate the flow speed U of the liquid (2) in function of the said data.

17. An apparatus according to claim 16, the apparatus further comprising:

- an air pressure sensor (7) configured to measure an air pressure pO above the liquid (2); the data management system (8) being operatively connected to the air pressure sensor (7); and

the software, when executed, furthermore gathers data provided by the air pressure sensor (7), and performs the method according to any one of claims 2 or 4 to 12 to calculate the flow speed U of the liquid (2) in function of said data.

18. An apparatus according to claim 16 or 17, the apparatus further comprising: a temperature sensor (5) configured to measure a temperature T of the liquid (2),

the data management system (8) being operatively connected to the temperature sensor (5); and

the software, when executed, furthermore gathers data provided by the temperature sensor (5), and performs the method according to any one of claims 7 to 12 to calculate the flow speed L/ of the liquid (2) in function of said data.