Abstract : This paper proposes a differential pressure flow measurement system scheme, focusing on the various components of the differential pressure flow measurement system, and provides a detailed formula derivation for converting the flow rate Q into a linearly related digital output. This system has a simple structure and features convenient, high reliability, and accurate measurement of fluid flow rate, making it widely applicable to flow measurement in various fields. Keywords : Throttling flow meter; Capacitive differential pressure sensor; Transformer bridge; AD736; Square root extractor; MC14433; LED CLC Number: TE151 Document Code: B Article Number: 1004-9134(2005)02—0053-03 0 Introduction Flow measurement has important applications in environmental engineering, transportation, biotechnology, scientific research experiments, marine meteorology, and rivers and lakes. Because flow rate is a dynamic quantity, its measurement is difficult, especially under harsh on-site working conditions, which not only affects its reliability but also makes it difficult to guarantee accuracy. Based on these factors, this paper proposes a differential pressure flow measurement system scheme. Differential pressure flow measurement systems, by converting flow rate into pressure difference, significantly reduce the impact of the aforementioned adverse conditions…1. Furthermore, various types of flow meters have been used to measure the flow rates of liquids, steam, and gases, with differential pressure flow meters using throttling mechanisms being the most widely applied [sup][2.3][/sup]. This is because of their simple structure and abundant data and practical experience. Therefore, throttling devices, as process monitoring instruments, are valued for their reliability more than any other instrument. 1 System Composition and Workflow A simplified block diagram of the differential pressure flow measurement system's composition and workflow is shown in Figure 1. The measured object is the fluid flow rate p. The flow rate generates a static pressure difference through the throttling flow meter, the magnitude of which is related to the fluid flow rate. This difference is then converted into a voltage output by a capacitive differential pressure sensor and a transformer bridge. An RMS AC/DC converter and a squarer condition the signal, and finally, an A/D converter converts the analog signal into a digital signal, which is then displayed via an LED. [b]2 Throttling Flow Meter 2.1 Basic Principle of Throttling Flow Meter[/b] The working principle of a throttling flow meter is shown in Figure 2. When fluid passes through a throttling element installed in a pipe, the flow stream contracts locally, its velocity increases, and its pressure decreases, generating a pressure difference before and after the throttling element. This pressure difference is proportional to the square of the flow rate. Among differential pressure flow meters, the standard orifice plate throttling device is the most widely used due to its simple structure, low manufacturing cost, extensive research, and standardization. As shown in Figure 2, the orifice plate installed in the pipe is a thin plate with a circular hole. The center of the hole is located on the center line of the pipe. Assuming the fluid is incompressible, its viscosity is negligible, and it is steady-flowing, then the fluid passing through sections 1 and 2 can be represented by Bernoulli's equation and the continuity equation: In equations (1) and (2), υ1 and υ2 are the average flow velocities at sections 1 and 2, respectively; P1 and P2 are the pressures at sections 1 and 2, respectively; A1 and A2 are the cross-sectional areas of sections 1 and 2, respectively; and ρ is the fluid density. ρ1 and ρ2 are generally called static pressure and dynamic pressure, respectively. The fluid volumetric flow rate Q can be calculated from equations (1) and (2): Equation (3) is derived under ideal conditions and various corrections must be added in practical applications. As can be seen from Figure 2, the cross-section of the fluid is reduced after passing through the throttling mechanism. Due to the inertia of the fluid, the minimum cross-section A2 of the reduced flow stream should be located slightly further down from the throttling mechanism, that is, A2 should be smaller than the opening area A0 of the throttling mechanism. This phenomenon is called flow contraction. Furthermore, due to the viscosity of the fluid, a correction coefficient 口 must be added to the practical throttling mechanism during actual measurement. Simultaneously, considering the compressibility of the fluid, equation (3) must also be corrected for compressibility. Therefore, equation (3) can be expressed as: From equation (5), it can be seen that the pressure difference is proportional to the square of the flow rate. 2.2 Selection of Throttling Device Orifice plates are generally used to measure clean liquids, gases, and low-speed steam. For high-speed (30 m/s) steam flow measurement, nozzles are often selected, while for dirty flow measurement, venturi tubes can be used. 3. Capacitive Differential Pressure Sensor A commonly used capacitive differential pressure sensor is shown in Figure 3. When the measured differential pressure acts on the two isolation diaphragms, the differential pressure is transmitted to the fixed plate through the silicone oil, causing it to flex and deform, resulting in a differential change in capacitance. According to the derivation, the relationship between the two differential capacitors C1 and C2 of the capacitive differential pressure sensor and the differential pressure (p1, p2) is: In equation (6), 口 is the working radius of the moving plate; T is the initial tension of the moving plate; d0 is the initial distance between the fixed and moving plates. 4. Transformer Bridge The transformer bridge is shown in Figure 4, which is a constant current source. COM is the analog ground. From equations (5) and (6), the AC output voltage of the transformer bridge can be obtained as: 5 RMS AC/DC Converter The system selects the RMS AC/DC converter AD736[sup][6][/sup]. Its main features are: high accuracy, good sensitivity, and fast measurement speed. AD736 adopts a dual in-line package with 8 pins. Its pin arrangement and the high impedance application circuit of AD736 in dual power supply are shown in Figure 5. Pin 2 U[sub]IN[/sub] is the AC input, and pin 6 U[sub]o[/sub] is the DC output. It is the key peripheral component of AD736, used to perform the average value calculation. Its size will directly affect the measurement accuracy of the RMS value, especially at low frequencies. In most cases, +33μF can be selected. 6 Square Root The square root is implemented through a positive square root operation circuit, which is shown in Figure 6. From Figure 7, we can obtain: (K, is the proportional coefficient of the analog multiplier) (12) If the integrated four-quadrant analog multiplier MC1495 is selected, the proportional coefficient K is usually taken as 0,1, so that we can obtain from equation (12): 7 AID Converter and LED Display The 2-digit digital voltmeter is constructed using the 2-digit dual-slope A/D converter MC14433 as shown in Figure 7. The MC14433 converts the input analog quantity into BCD code with Q3-Q0 output. The CD451I translates the BCD code into the input signal Ya-Yg of the seven-digit tube, which is used as the character code of the display. The character code is output from DS4-DS1 and sent to the cathode of the tube via MC1413 to determine which digit of the tube lights up. The polarity sign is also output from Q2. When Q2 is 0, the polarity is negative. When the OR output is low, it indicates that the input is overloaded and the display is off. MC1403 provides the standard voltage of 2V required for the standard reference power supply. Counting results: 3 Conclusion Through the above-mentioned throttling flow meter, capacitive differential pressure sensor, transformer bridge and effective value conversion, square root, A/D conversion, the final count result is the flow rate of the fluid, which shows the flow data very intuitively. References [1] Sun Chuanyou, Sun Xiaobin. Fundamentals of Sensing Technology [M]. Beijing: Electronic Industry Press, 2001 [2] Liu Xinrong. Flow Meter [M]. Beijing: Water Resources and Electric Power Press, 1990 [3] Sun Chuanyou, Sun Xiaobin. Measurement and Control Circuits and Devices [IS]. Beijing University of Aeronautics and Astronautics Press, 2002 [4] Zhang Yulong, et al. Sensor Circuit Design Manual [IS]. Beijing: China Metrology Press, 1989 [5] Sha Zhanyou. Newly Compiled Practical Digital Measurement Technology [M]. Beijing: National Defense Industry Press, 1998 [6] Gao Guangtian. ADI Product Technical Guide [M]. Beijing: Science Publishing House, 1997