Patent Publication Number: US-2021172774-A1

Title: Volumetric flow sensor for tubular conduits and method

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Patent Application No. 62/946,197, filed on Dec. 10, 2019, entitled “VOLUMETRIC FLOW SENSOR FOR TUBULAR ARCHITECTURES,” the disclosure of which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     Technical Field 
     Embodiments of the subject matter disclosed herein generally relate to a volumetric flow sensor and a method for measuring a volumetric flow rate, and more particularly, to a microfluidic channel based sensor for macro-tubular conduits. 
     Discussion of the Background 
     Flow rate measurements in macro-tubes such as pipes are important in determining the performance of various applications for many industries, including agriculture industry, oil and gas, chemicals, water transportations, and desalination. Measuring the flow rates (measured as volume over time) are an essential requirement in product quality control, process analysis, efficient energy management and material utilization such as waste reduction, accounting of yield, and consumption for fluidic industries products. 
     With the growth of fluidic industries, many different types of flow rate sensing techniques have been established for tubular systems. Some of the prominent technologies are pressure-difference based flowmeters, thermal, turbine flowmeter, electromagnetic, vortex, ultrasonic sensors, and the Coriolis flowmeter. However, these types of flow sensors are bulky, rigid, and not compatible with curved tubular architectures. Therefore, the existing sensors significantly disturb the fluid&#39;s velocity inside the pipe, causing permanent and notable pressure drops, except for those non-invasive flowmeters such as the ultrasonic and electromagnetic sensors that are mounted to the outside wall of the pipe. However, magnetism based flowmeters are not suitable for the majority of fluids because of their limitations to electrically conductible fluids only. The ultrasonic flowmeters are large, and it is hard to accurately achieve measurements. The Coriolis flowmeters provide precise measurements, but they are relatively expensive and also generate large pressure drops in the fluid steams in which they are placed. Although several other different types of pipe flowmeters are available on the market, there is still a demand for development and improvement of flow sensors since each type has certain limitations. 
     One of the methods that addresses the above mentioned issues could be the utilization of microsensors placed inside the tubular systems that need to be monitored. Microfluidic flow sensors have been developed in the last decade for measuring the flow rate in small volumes, such as biomedical and analytical chemistry applications ([1], [2]). Some of these micro-flow sensors are based on micro-electromechanical systems (MEMS), optical, thermal, or pressure-based measurement flow sensing technology ([3], [4], [5], [6]). The use of microfabrication sensors provide several advantages such as increasing reliability, performance, functionality, and lowering the cost with decreasing the device dimensions [7]. 
     Therefore, using the advantages of the microfluidic sensors in the tubular systems can overcome the main challenges of the existing flow sensors. However, the existing microfluidic flow sensors still have a complex structure, are fragile and are not very accurate. 
     Thus, there is a need for a new volumetric flow rate sensor (flowmeter) that overcomes the above noted deficiencies of the existing sensors, is inexpensive, accurate, and appropriate for being located in a large or small pipe. 
     BRIEF SUMMARY OF THE INVENTION 
     According to an embodiment, there is a flowmeter for measuring a fluid flow rate in a pipe. The flowmeter includes a base made of a flexible material; a bridge made of a rigid material, wherein the bridge is attached to the base to form a microchannel, and a pressure sensor formed within the base. The microchannel has a height H between 100 and 400 μm. 
     According to another embodiment, there is a flowmeter system for measuring a fluid flow rate in a pipe, and the flowmeter system includes a flowmeter having a base made of a flexible material, a bridge made of a rigid material, wherein the bridge is attached to the base to form a microchannel, and a pressure sensor formed within the base. The flowmeter system also includes a microcontroller configured to receive a pressure reading from the pressure sensor and to estimate the fluid flow rate through a pipe in which the flowmeter is located. 
     According to yet another embodiment, there is a method for measuring a fluid flow rate through a pipe. The method includes attaching a flowmeter to an inside of a pipe, the flowmeter having a base made of a flexible material that directly attaches to the inside of the pipe, a bridge made of a rigid material, wherein the bridge is attached to the base to form a microchannel, and a pressure sensor formed within the base; flowing a fluid through the pipe so that part of the fluid flows through the microchannel; measuring a pressure of the fluid within the microchannel with the pressure sensor; and determining the flow rate of the fluid through the pipe based on the measured pressure within the microchannel. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Fora more complete understanding of the present invention, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a schematic diagram of a flowmeter, which is placed inside of a pipe, for measuring a fluid flow rate through the pipe; 
         FIG. 2  illustrates various elements of the flowmeter; 
         FIG. 3  is a cross-section of a microchannel used by the flowmeter for measuring the flow rate of the fluid; 
         FIG. 4  shows a pressure sensor formed within a base of the flowmeter for measuring a pressure within the microchannel; 
         FIG. 5  shows the placement of the flowmeter within a pipe and the small height of the microchannel relative to the diameter of the pipe; 
         FIG. 6  is a graph showing a flow rate of the fluid through the microchannel versus the flow of the liquid through the pipe, and also showing a relationship between the pressure inside the microchannel versus the fluid flow through the pipe; 
         FIGS. 7A and 7B  illustrate a beginning part of the manufacturing process of the base and pressure sensors of the flowmeter; 
         FIG. 8  illustrates the relationship between the capacitance of the pressure sensor and the measured pressure within the microchannel for the flowmeter; 
         FIGS. 9A to 9C  illustrate a final part of the manufacturing process of the flowmeter in which a bridge is added to the base to form the microchannel; 
         FIG. 10  shows a set up for testing the manufactured flowmeter; 
         FIG. 11  illustrates the relationship between the measured relative capacitance of the flowmeter and the flow rate within the pipe; 
         FIG. 12  illustrates a flowmeter system in which the flowmeter communicates with an external device through a wire that extends through the wall of the pipe in which the flowmeter is located; 
         FIG. 13  illustrates another flowmeter system in which the flowmeter communicates with an external device in a wireless manner through the wall of the pipe in which the flowmeter is located; 
         FIGS. 14A to 14C  illustrate the signal received from various pressure sensors of the flowmeter system, at the external device, using the wireless implementation; and 
         FIG. 15  is a flow chart of a method for measuring a flow rate of a fluid in a pipe with a flowmeter having a microchannel disposed inside the pipe. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The following description of the embodiments refers to the accompanying drawings. The same reference numbers in different drawings identify the same or similar elements. The following detailed description does not limit the invention. Instead, the scope of the invention is defined by the appended claims. The following embodiments are discussed, for simplicity, with regard to a physically flexible liquid flow sensor that is placed inside a tubular pipe and measures a pressure inside the sensor with three pressure sensors. However, the embodiments to be discussed next are not limited to a flexible flow sensor, or to a sensor that is placed inside a tubular pipe, or to a sensor having three pressure sensors, but they may be applied to a rigid sensor and/or to a pipe having any profile, and/or a sensor having more or less pressure sensors. 
     Reference throughout the specification to “one embodiment” or “an embodiment” means that a particular feature, structure or characteristic described in connection with an embodiment is included in at least one embodiment of the subject matter disclosed. Thus, the appearance of the phrases “in one embodiment” or “in an embodiment” in various places throughout the specification is not necessarily referring to the same embodiment. Further, the particular features, structures or characteristics may be combined in any suitable manner in one or more embodiments. 
     According to an embodiment, a flowmeter includes a firm microfluidic channel bridge placed on a physically and mechanically flexible base. This assembly is installed on the inner wall of a tubular system. The flexible platform provides device compatibility with different tubular architectures and curvatures adoptions. The micro-scale fluidic channel overcomes the main disadvantages of the common bulky and rigid flowmeters, which cause flow streams disturbance and significant pressure drops in tube systems. The microchannel flowmeter is based on detecting the dominating dynamic pressure generated by the fluid velocity inside the microchannel as the fluid flow rate through the microchannel is proportional to the flow velocity inside the microchannel. The one or more pressure sensors for the microchannel flowmeter is fabricated inside the base, and they have a sensitivity equal to 10 pf/KPa. The pressure measurement is based on a capacitive pressure sensor because it is compatible with the flexible electronics and it provides low power consumption. 
     More specifically, as shown in  FIG. 1 , a novel liquid volumetric flowmeter (called herein simply flowmeter)  100  is placed inside a pipe  110  having an internal diameter D. The diameter D can be between 1 cm to any larger size. The flowmeter  100  has a base  102  that is placed on the internal surface  110 A of the pipe  110 , a bridge  104  attached to the base  102 , and one or more pressure sensors  106  located in the base  102 . While  FIG. 1  shows the pipe  110  having a circular cross-section, the flowmeter discussed herein is configured to work in a pipe having any cross-section, e.g., rectangular, square, triangular, etc. The base  102  can be made of a flexible material, e.g., polydimethylsiloxane (PDMS), so that the base  102  follows intimately the profile of the internal surface  110 A of the pipe  110 . Other flexible materials may be used as long as they can bend enough to follow the profile of the internal surface of the pipe. However, in another embodiment, the base  102  is made of a rigid material, which does not follow the profile of the internal surface  110 A, in which case a liquid pocket may be formed between the base and the internal surface of the pipe. 
     The flowmeter  100  is shown in  FIG. 2  as extending along a longitudinal axis X 1 , which is parallel to the longitudinal axis X 2  (shown in  FIG. 1  as entering the page) of the pipe  110 . For simplicity, the pipe  110  is omitted in  FIG. 2 . The base  102  is shown in this figure as being flat, and having a footprint larger than the bridge  104 . The bridge  104  is made of a rigid material, for example, poly(methyl-methacrylate) (PMMA), so that an external pressure exerted by the fluid  112 , which flows through the pipe  110 , on the bridge, does not deform the walls of the bridge. This condition is desired because the pressure sensor  106 &#39;s readings should be indicative of only the liquid&#39;s pressure inside the bridge, and not be influenced by the liquid pressure outside the bridge. 
       FIG. 3  shows a cross-sectional view of the base  102  and the bridge  104 . The bridge  104 , when attached to the base  102 , forms an enclosed volume, which defines the microchannel  300 . The bridge  104  has two side walls  104 A and  104 B, and a top wall  104 C. There is no bottom wall for the bridge, and thus the name “bridge.” The two side walls and the top wall define the trench or microchannel  300 . The sizes of the microchannel are the height H, the width W, and the length L. The height H is selected to obtain the microchannel  300 , i.e., a channel for fluid flow which is in the micrometer range. More specifically, the microchannel  300  has a height H between 100 and 400 μm, with a preferred size of substantially 250 μm. The term substantially is defined herein to include any variation of the height within +1-10% of the given value. The width W of the microchannel  300  is selected to be about 3 mm and the length L is selected to be between 3 to 100 mm, with a preferred length of about 60 mm. It is noted that a channel that has the height H larger than 500 μm would likely not work with the concept to be discussed later. A cross-section area A of the microchannel  300  is square in  FIG. 3 , but other shapes may be selected. 
     The bridge  104  is made to be solid and have no openings, except for the input  105 A and the output  105 B. This means that the bridge  104  is attached to the base  102 , for example, with a glue  210 , so that no fluid enters or exists the microchannel  300  except for the input  105 A and the output  105 B. The bridge  104  may be attached to the base  102  by other means, e.g., mechanical means, thermal means, etc. The width W of the bridge is shown in  FIGS. 2 and 3  to be smaller than the width w of the base  102 . In one application, the width W is much smaller than the width w, i.e., it can be a couple of times (2 to 10) smaller. This situation happens when it is desired that the width w of the base  102  is made to be almost the same to the internal circumference of the surface  110 A of the pipe  110 . By making the width w of the base so large, it is possible to further fix the flowmeter to the internal surface of the pipe due to the natural adherence properties of the PDMS material, i.e., without using a glue or a mechanical means. 
     The pressure sensor  106  is shown in  FIG. 4  having a top electrode  402  and a bottom electrode  404  that sandwich a hole  400  formed into the base  102 . The hole  400  may be filled with air or with any other dielectric material. The two electrodes  402  and  404  and the air pocket  400  act as a capacitive pressure sensor, so that when the fluid inside the microchannel  300  has a higher pressure, it squeezes the top plate  402  toward the bottom plate  404 , which results in the dielectric air gap  400  being reduced. This change in the thickness of the dielectric material can be measured with corresponding electronics and associated with the pressure exerted by the liquid on the pressure sensor, as discussed later. More then one pressure sensors may be formed in the base  102  to improve the reading&#39;s accuracy. Note that the pressure sensor  106  has one electrode directly exposed to the fluid flowing through the microchannel  300  and also that electrode is fully formed within the microchannel  300 . 
     The flowmeter illustrated in  FIGS. 1 to 4  does not require an external flow path or tube contractions to prevent fluid flow interruption, pressure drop, and/or energy loss. Instead, the flowmeter uses the volumetric flow rate generated inside the tubular system  110  to drive a small fluidic volume inside the microchannel  300  for volumetric flow rate measurement under the laminar flow condition using the microfabrication advantages. In other words, the flowmeter  100  uses exclusively the microchannel  300  for performing a pressure measurement of only the fluid flowing through the microchannel and from this information, estimates the flow rate of the fluid inside the pipe. 
     As previously discussed, the base of the flowmeter is made as a physically flexible platform to adapt to different pipe diameters and curved architectures. The designed flowmeter&#39;s base, which is made of PDMS, has excellent physical and chemical properties since it is compatible with the microfabrication process, provides high flexibility, thermal stability, and is a low-cost material. The PDMS base contains one or more pressure sensors  106 , which are based on a capacitive mechanism. The capacitive pressure sensor  106  was selected among other pressure sensing technologies because of the high stability and reliability even under mechanical deformations and it can be tailored easily with different sizes for different sensing pressure ranges. Therefore, it can provide good sensitivity of the flow&#39;s pressure for different pipe diameters and bending radii. The PDMS base may patterned to include encapsulated air, which is used as the dielectric material for the pressure sensor, and which is sandwiched between sputtered copper layers on the PDMS base, which act as conductive parallel plates for the capacitive structure. 
     The rigid microchannel bridge  104  was installed on top of the capacitive pressure sensor  106  on the base  102  to form the fluidic microchannel  300  because it is not possible, in large scale cross-section areas, i.e., for pipes, to measure the flow rate directly using the pressure change in the pipe. Because the static pressure generated by the fluid&#39;s weight inside the pipe  110  is much higher than the dynamic pressure generated by the fluid flow, by creating the microchannel  300 , the size of the static pressure term is reduced, to be less than the dynamic pressure term. Note that the static pressure is multiplied by the microchannel height (which is less than 500 μm), and the dynamic pressure is divided over the square of the cross-section area A of the microchannel  300  (the area is very small, which makes the dynamic pressure large). Therefore, the bridge  104  provides a small cross-section area A regardless of the pipe  110 &#39;s dimensions, which makes the dynamic pressure to dominate over the static pressure. For this reason, the microchannel  300  is made of a solid material, e.g., PMMA, to avoid channel deformation under different applied pressures from the surrounding fluidic environment. Also, the PMMA material is compatible with the PDMS base and the microfluidic fabrication processes. 
     The design of the microchannel  300  with micro-sized height H and a rectangular cross-section area offers a negligible flow disturbance in the pipe, compared to the existing technologies that generate large pressure drops and energy losses due to their large size. Another advantage of the microchannel  300  is the formation of a constant cross-section area A regardless of the pipe&#39;s dimensions. This means that no special correction is needed for different pipe diameters. Moreover, the Reynold number is small for the microchannel  300  because it is proportional to its height. Therefore, the microchannel provides a laminar flow irrespective of the flow type in the pipe  110 . The laminar flow simplifies the overall system physics and mathematical equations. 
     The operating principle of the flowmeter  100  is now discussed in more detail. The capacitive pressure sensor  106  inside the microchannel  300  is placed to measure the absolute pressure P total  generated by (1) the fluid&#39;s weight and (2) the fluid flow&#39;s velocity inside the microchannel  300 . The measured pressure using the capacitive pressure sensor  106  corresponds to the total pressure P Total , which is a combination of the static pressure P Static  and the dynamic pressure P Dynamic , as expressed in equation (1). 
         P   Total   =P   Static   +P   Dynamic .  (1)
 
     The dynamic pressure P Dyamic  is proportional to the square of the volumetric flow rate Q of the fluid, as expressed in equation (2), while the static pressure P Static  is proportional to the high of the microchannel  300 . 
     
       
         
           
             
               
                 
                   
                     
                       P 
                       Total 
                     
                     = 
                     
                       
                         ρ 
                          
                         g 
                          
                         H 
                       
                       + 
                       
                         
                           1 
                           2 
                         
                          
                         ρ 
                          
                         
                           
                             Q 
                             2 
                           
                           
                             A 
                             2 
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     where ρ is the liquid density, H is the microchannel  300 &#39;s height, and g is the gravity acceleration. 
     The total pressure is measured using the capacitive pressure sensor  106 , where its capacitance value is proportional to the applied pressure, as shown by equation (3): 
     
       
         
           
             
               
                 
                   
                     C 
                     = 
                     
                       
                         
                           ɛ 
                           0 
                         
                          
                         
                           ɛ 
                           r 
                         
                          
                         
                           A 
                           1 
                         
                       
                       d 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     where d is the thickness of the base  102 , as shown in  FIG. 4 , which also coincides with the thickness of the dielectric pocket of air  400 , ε r  is the dielectric relative permittivity of the material (air in this case), ε 0  is the permittivity of the free space (8.854×1012 F/m), and A 1  is the area of the conductive parallel plates  402 ,  404 , which have the sizes of 3 mm×3 mm in this embodiment. Other sizes and shapes may be used. 
     When the pressure exerted by the fluid  112  inside the microchannel  300  increases, the dielectric layer&#39;s height d decreases, and thus the capacitance C value of the pressure sensor  106  increases. Thus, based on the readings from the capacitor, it is possible to calculate the pressure inside the microchannel  300 . Knowing the exact profile of the microchannel  300  and also the profile and sizes of the pipe  110 , it is then possible to link the pressure readings to the flow rate within the pipe  110 . 
     The simulated capabilities of the flowmeter  100  were studied using a numerical analysis performed with a commercially available tool. The numerical analysis was performed to understand the relationship between the microchannel  300 &#39;s flow rate and the pipe  110 &#39;s flow rate and to ensure fully developed flow conditions inside the microchannel  300 . The simulation replicates the fluid flow dynamics inside a 3-dimensional (3D) pipe that was based on the Navier-Stock equation. The microchannel&#39;s dimensions were set to be 250 μm for the high H, 3 mm for the width W, and 60 mm for the length L. The simulated microchannel was attached to an internal wall  110 A of the tube  110  with a 3.8 cm inner diameter, as illustrated in  FIG. 5 . The flowmeter  100  is placed into the tube  110  so that the microchannel  300  has its longitudinal axis X 1  parallel to the longitudinal axis X 2  of the tube  110 . This arrangement is also used when the actual flowmeter  100  is placed into an actual tube or pipe.  FIG. 5  shows, at scale, the extremely low profile (i.e., height) of the microchannel  300  relative to the pipe  110 . To simplify the calculations, three points were selected inside the inner wall of the microchannel  300 , and the pressure measurements were recorded at each of these three selected points. Thus, in this embodiment, three different pressure sensors were formed in the wall of the base  102 . 
       FIG. 6  shows the results of numerical analysis for the flowmeter  100 . The numerical analysis was used to find the correlation between the tubular flowrate (flow in the pipe  110 ) and the microchannel flowrate (flow in the microchannel  300 ), followed by finding the pressure range at the selected points inside the microchannel  300 . As shown in  FIG. 6 , the flow rate in the microchannel  300  (which is plotted on the Y axis in the graph, on the right hand side) is found to be proportional to the flow rate in the pipe  110  (which is plotted on the X axis in the graph) because the total flow rate is equal to the summation of the flow rates in the individual branches. Also, the results in  FIG. 6  show that the pipe flow rate is proportional to the total pressure (plotted on the Y axis in the graph, on the left hand side) at the selected points since the dynamic pressure varies as a function of the fluid&#39;s velocity or flow rate. As a result, the pipe flow rate is proportional to the microchannel flow rate as well as the dynamic pressure generated on the channel&#39;s walls, which ensures that the pressure readings performed with the pressure sensor  106  inside the microchannels  300  are proportional to the flow rate inside the pipe  110 , which is desired to be measured. In other words, this analysis proves that by measuring the pressure inside the microchannel  300 , it can be determined the pipe flow rate, i.e., the volumetric flow. 
     Based on these observations, the flowmeter  100  has been manufactured as now discussed. In this embodiment, the flowmeter  100  was manufactured with a lithography-free process making it a low cost, simple and affordable device. The flowmeter has two parts, which are the rigid PMMA microchannel bridge  104  and the PDMS mechanically flexible base  102  with a capacitive pressure sensor  106  as discussed above. The physically flexible  102  was fabricated as shown in  FIGS. 7A and 7B  using three PDMS layers  700 ,  702 , and  704 . In one application, each of the PDMS layers  700 ,  702 , and  704  has a 500 μm thickness. Other values may be used for the thickness. Kapton tape may be used as a shadow mask on the first and third layers  700  and  704 . The Kapton tape is placed to cover the entire surface of the layer and then it was patterned using a CO 2  laser to form 3 mm squares, which correspond to squares  710  on the first and third layers in  FIG. 7A . These patterned squares of Kapton tape were peeled off from the surfaces of the two layers to form corresponding active areas for the capacitance pressure sensors  106 . 
     The exposed PDMS surfaces were treated with oxygen plasma to modify the surface from hydrophobic to hydrophilic by increasing the surface roughness to provide better metal adhesion on its surface. Then, these two PDMS layers  700  and  704  were sputtered with 200 nm thickness of copper to form conductive plates  712 ,  714  for the capacitance sensors. Note that the plate  712  is formed on the top square  710  of the PDMS material for the layer  704  while the plate  714  is formed on the bottom square  710  of the PDMS material for the layer  700 , in  FIG. 7A . The Kapton tape was then completely removed from the PDMS layers  700  and  704 , leaving the active areas with a thin coated layer  712  and  714  of copper. 
     The second PDMS layer  702  was patterned all the way through the PDMS layer thickness using the CO 2  laser to form trenches or holes  720 . These trenches are filled by air, which performs as a dielectric material for the capacitance sensors  106 . The three prepared PDMS layers  700 ,  702 , and  704  were arranged in the order shown in  FIG. 7A  and then the layers were assembled and bonded together, as shown in  FIG. 7B , using an oxygen plasma technique by exposing the surfaces to oxygen plasma for 60 seconds followed by bringing the surfaces together. The bonds were enhanced by baking the bonded layers for 60 seconds at 80° C. Copper electrodes  722  and  724  were bonded to the flexible plates  712  and  724 , respectively using a silver paste  726 . After curing the silver paste, the entire assembly was packaged using a PDMS layer  730  to protect it and protect the copper electrodes  712  and  714 , and to fix the positions of the layers  700 ,  702 , and  704  to prevent air leaking. 
     The base  102  having the pressure sensors  106  shown in  FIG. 7B  has been characterized before adding the bridge  104 , as now discussed. Although the capacitance values of the pressure sensors  106  can be correlated directly to the tube  110 &#39;s flowrate, without finding the exact pressure inside the microchannel  300 , as illustrated in  FIG. 6 , finding the pressure of the pressure sensors  106  gives a better understanding of the flowmeter. Also, it allows to compare the results with the numerical analysis, and to validate the operating condition of the capacitive pressure sensor  106  before characterizing the tubular flow rates. For this stage, the capacitive pressure sensors  106  on the flexible PDMS base  102  in  FIG. 7B  were characterized before completing the fabrication process of the flowmeter. The pressure sensors  106  were characterized at different water depths, from 0 to 65 cm with a 5 cm incremental depth step, as shown in  FIG. 8 , on top axis X. The different water depths were projected into different pressure ranges using equations (1) and (2), as illustrated on the bottom axis X. The total pressure is equal to the static pressure (=ρ h g) because the dynamic pressure is equal to zero for this case. For this characterization stage, the values for the three capacitance pressure sensors  106  were recorded at different water depths and then the averaged capacitance readings at each depth were calculated. The pressure sensors were characterized first on a flat surface (see line  800 ) and then on a concave surface position using a 3.8 cm bending diameter (see line  810 ). The corresponding capacitances for various depths or pressures are plotted in the figure on the Y axis. 
     The pressure sensor results for the flexible base  102  show that the capacitance is linearly proportional to the applied pressure and depth, as shown in  FIG. 8 . Both characterization results for different surface conditions, i.e., flat and concave surfaces, displayed almost the same pressure sensitivity that is equal to 10 pf/KPa. The device showed almost identical behavior under flat and concave surface positions. It is expected that the initial capacitance value is slightly higher for the device experiencing the concave position due to the stress generated from the mechanical deformation of the flexible sensory platform. 
     After the pressure sensor characterization, the microchannel bridge  104  was fabricated, as shown in  FIG. 9A . The microchannel bridge  104  was fabricated using a 1 mm thickness PMMA sheet. The sheet was patterned using the CO 2  laser to form a 250 μm trench depth into the rectangular shaped piece of the sheet, the rectangular shaped piece having a 3 mm width and a length of 60 mm, as also shown in  FIG. 9A . Then, the rectangular shaped piece was cut off from the sheet to obtain the bridge  104  with the trench. After that, the microchannel bridge  104  was attached to the prepared, flexible sensory base  102  using the oxygen plasma bonding method, to obtain the microchannel  300 , and essentially the flowmeter  100 , as shown in  FIG. 9B . To ensure a good bonding between the bridge  104  and the base  102 , the flowmeter  100  can be repackaged with a thin PDMS coat  900 . A cross-section of the flowmeter  100  obtained with the method discussed herein is shown in  FIG. 9C . 
     For the next characterization stage, the entire flowmeter  100  was tested as the microchannel  300  was formed by attaching the bridge  104  to the flexible sensory base  102  as previously explained. A laboratory transparent polyvinyl chloride (PVC) pipe system  1000  was built with a 3.8 cm inner diameter D 2  and a 60 cm total system&#39;s length L 2 , as shown in  FIG. 10 . The flowmeter  100  was attached to the inner wall  110 A of the pipe  110 . The volumetric flow sensor  100  was characterized using a pump controller  1010  (Catalyst FH100DX Pump) to generate a precise flow rate. The pump was connected to the pipe system and to a fluid reservoir  1020 . The flowmeter  100  was tested with water  112  at different flow rates, from 0 to 2000 ml/min. Each flow rate was run for 1 minute to stabilize the selected flow rate before collecting data. At each flow rate, the capacitance was recorded from the three pressure sensors  106  using a general-purpose source meter  1030 , for example, a Keithley 2400A-SCS. 
     With this setup, the ΔC/C 0  (called herein the relative change in the capacitance) was calculated for each capacitance, where C and C 0  are the capacitance values with and without an applied pressure. Finally, the three ΔC/C 0  calculated values were averaged for each flow rate. Determining the average for the capacitance reading between the three selected points helps with smoothing the graph and creating a single graph to correlate the recorded capacitance values to the tubular flow rate. 
       FIG. 11  shows the results of the readings from the flowmeter  100  when operating under different flow rate conditions. As the numerical analysis indicated, the readings of the capacitance pressure sensor  106  are proportional to the flow rate Q in the microchannel  300  and the tubular system  110 . The tubular flow rate (plotted on the X axis) is proportional to the microchannel  300 &#39;s flow rate because the flow streams in the tubular system are generating the driving force for the fluids to flow inside the microchannel as it was explained and proven previously in the numerical validation section. Using equations (1) and (2), it is possible to assert that the microchannel  300 &#39;s flow rate and the dynamic pressure change proportionally, which in turn increases the total pressure, whereas the static pressure is constant for a particular fluid and temperature. The results show in  FIG. 11  indicate that the flowmeter is sensitive from 500 ml/min to 2000 ml/min. This can be explained by the fact that at flow rates lower than 500 ml/min, there is a small force that is not likely to drive the fluid  112  inside the microchannel  300 , for the given channel dimensions. In other words, the change in the pressure is lower than the pressure sensitivity range. The almost straight line  1100  shown in  FIG. 11  indicates that by using the pressure sensor  106 , a controller that receives readings from the flowmeter  100 , may be programmed to determine the change in the capacitance of the pressure sensor, and based on the calibrated sensor values, to determine the corresponding flow rate through the pipe  110 . The part  1110  of the curve  1100  does not show a unique mapping between the relative change in the capacitance and the flow rate, which means that this part of the curve cannot be used form measuring the volumetric flow through the pipe. 
     The flowmeter  100  has been shown in the above embodiments as being placed inside the pipe  110  with no wires leaving the sensor. However, for the flowmeter to exchange data with the controller, either a wired communication or a wireless communication needs to be established between the one or more pressure sensors  106  and the controller. Both implementations are possible and both are now discussed with regard to  FIGS. 12 and 13 .  FIG. 12  shows the wired implementation of a flowmeter system  1200  in which one or more wires  1210  extend through the wall  111  of the pipe  110 , from the flowmeter  100  to a connection box  1212 . The connection box  1212  may include electronics for facilitating data exchange between the flowmeter and an external controller  1220 . The figure also illustrates the fluid flow A through the microchannel  300  and the fluid flow B through the pipe  110 . If the connection between the pressure sensor  106  and the controller  1220  (which can include a processor  1222  and a memory  1224 ) is fully wired, then additional wires  1214  electrically connect the connection box  1212  to the controller  1220 . Alternatively, it is possible that the connection box  1212  includes a transmitter or transceiver  1216  that communicates in a wireless manner with a corresponding transceiver  1226 , which is part of the controller  1220 . The two transceivers may use any protocol and any frequency spectrum (FM, Wi-Fi, Bluetooth, etc.) for communication and data exchange. One or more of these devices may also be fitted with an appropriate power source to supply electrical energy to the transceivers. The embodiment illustrated in  FIG. 12  can be implemented in any type of pipe, i.e., even a type made of a material that suppress electromagnetic waves from passing through the wall. 
     However, if the pipe  110  is made of a material that allows electromagnetic waves propagation through its walls, e.g., PVC, than it is possible to have the flowmeter  100  made to include a power source, a microcontroller and a transmitter so that no wires are piercing the wall of the pipe.  FIG. 13  shows the flowmeter system  1200  including the flowmeter  100  having the microcontroller  1220  and a battery  1320  attached to the base  102 . The figure also shows one pressure sensor  106  and one of its terminal  722 . Wires  1330  are visible and they are configured to link the pressure sensor  106  to the microcontroller  1220 . For this embodiment, the flowmeter  100  was integrated with commercially available electronics  1220  to create a standalone functional system installed inside a pipe. In one application, a Bluetooth Low Energy (BLE) enabled Programmable System on Chip (PSoC) from Cypress™ can be used as the controller  1220 . This controller has an internal capacitance to digital convertor (CDC) to connect the three capacitive pressure sensors  106  to the controller without the need for additional Integrated Circuits (ICs), or passive components. The raw CDC values from the pressure sensors  106  can be converted into a capacitance unit using a calibration plot that is obtained prior to deploying the flowmeter. Furthermore, the PSoC has the BLE functionality built-in to enable sending the data wirelessly through the pipe  110 . The flowmeter system  1200 , which includes the flowmeter  100  and the controller  1220 , is powered using a coin cell battery  1320  due to the advantage of the low power consumption of the chip. The battery  1320  can be replaced with an energy generation device that uses the fluid flow to generate energy. The controller was connected to the pressure sensors with the wires  1330  and everything was packaged via a PDMS layer  1340  for insulation. 
     For a plastic pipe with 4 cm in diameter and filled with the fluid  112 , the BLE can easily communicate with a mobile device  1350 , e.g., laptop, tablet, smartphone, etc., up to 10 m in range. A test was performed with the flowmeter  100  being connected to the controller  1220 , and the flowmeter was submerged in water up to 50 cm depths. The data measured by the pressure sensor was sent in real-time from the three sensors to the smartphone  1350 . The curves  1400  to  1420  corresponding to the readings from the three pressure sensors  106  are shown in  FIGS. 14A to 14C , respectively. It is noted that the three curves are similar to each other. It is also noted that only one pressure sensor is needed for measuring the flow rate through the pipe  110 . In this embodiment, three pressure sensors are used to improve the accuracy of the estimated flow rate, and for redundancy. 
     A method for measuring a fluid flow rate through a pipe  110  is now discussed with regard to  FIG. 15 . The method includes a step  1500  of attaching a flowmeter  100  to an inside of the pipe  110 . The flowmeter  100  has a base  102  made of a flexible material that directly attaches to the inside of the pipe  110 , a bridge  104  made of a rigid material, where the bridge  104  is attached to the base  102  to form a microchannel  300 , and a pressure sensor  106  formed within the base  102 . The method further includes a step  1502  of flowing a fluid through the pipe  110  so that part of the fluid flows through the microchannel  300 , a step  1504  of measuring a pressure of the fluid within the microchannel  300  with the pressure sensor  106 , and a step  1506  of determining the flow rate of the fluid through the pipe  110  based on the measured pressure within the microchannel  300 . Some of the steps of the method may be performed within the controller  1220  or in the external device  1350 , or they be distributed in both these elements. 
     The disclosed embodiments provide a flowmeter that is capable of accurately measuring the flow of a liquid through a pipe, by estimating a pressure inside a microchannel formed within the pipe. It should be understood that this description is not intended to limit the invention. On the contrary, the embodiments are intended to cover alternatives, modifications and equivalents, which are included in the spirit and scope of the invention as defined by the appended claims. Further, in the detailed description of the embodiments, numerous specific details are set forth in order to provide a comprehensive understanding of the claimed invention. However, one skilled in the art would understand that various embodiments may be practiced without such specific details. 
     Although the features and elements of the present embodiments are described in the embodiments in particular combinations, each feature or element can be used alone without the other features and elements of the embodiments or in various combinations with or without other features and elements disclosed herein. 
     This written description uses examples of the subject matter disclosed to enable any person skilled in the art to practice the same, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the subject matter is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims. 
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