Could someone with experience give some guidance on the working principle of mass flow meters and vortex flow meters?

A mass flow meter (hereinafter referred to as CMF) is a device that directly measures mass flow, based on the principle that when a fluid moves in a straight line within a rotating frame, a Coriolis force is generated that is proportional to the mass flow rate. Vortex flow meter: Under specific flow conditions, a portion of the fluid’s kinetic energy is converted into fluid vibration, and the frequency of this vibration has a definite proportional relationship with the flow velocity (flow rate)

When a nonlinear, symmetric cylinder is inserted into a pipe, and the flow velocity of the fluid reaches a certain level, a series of vortices are generated at the rear of the cylinder. The frequency f of these vortices is related to the flow velocity v and the width d of the cylinder by the formula f = St × v/d. By using appropriate methods to determine the number of vortices and calculate their frequency, it is possible to determine the flow velocity of the fluid, and thus calculate the flow rate.

Introduction to Mass Flow Meters 1. Indirect Mass Flow Meters 1) Pressure and Temperature Compensated Differential Pressure Flow Meters Example 1: Orifice Plate – Differential Pressure Transmitter When a throttling element with a diameter smaller than that of the pipe is installed in the pipeline, as the fluid flows through it, the sudden reduction in the flow cross-section causes the flow stream to contract locally, resulting in an increase in flow velocity. According to the law of conservation of energy, dynamic pressure energy and static pressure energy can be converted into one another under certain conditions. An increase in flow velocity inevitably leads to a decrease in static pressure energy, thereby creating a static pressure difference between the upstream and downstream sides of the throttling element. The magnitude of this static pressure difference is related to the flow rate of the fluid passing through it. The relationship between differential pressure and flow rate is given by the equation: qm = 0.01252. Here, qm represents the mass flow rate in kg/h; α is the flow coefficient; ε is the expansion coefficient of the flow stream; d is the diameter of the orifice under operating conditions in mm; ΔP represents the differential pressure in kg/f; and ρ is the density of the fluid being measured under operating conditions in kg/m3. The orifice plate functions as a device for generating static pressure differences. The differential pressure transmitter detects these pressure differences and converts them into a standard 4–20 mA signal for transmission. ⑴Smart differential pressure transmitter: An integrated unit that performs measurement and calculation of differential pressure, pressure, and temperature, enabling the transmission and display of mass flow rate signals. (Such as Rosemount – Model 3095FT) ⑵ Intelligent differential pressure transducer: It performs δP detection, square root calculation, and volume flow rate calculation, and displays the results. Standard signal long-distance transmission.  Additionally, pressure and temperature measurement points are added on-site, along with standard signal remote transmission; these values are processed in the DCS system to display the mass flow rate. Or it can be calculated in the flow accumulator, and the mass flow rate is displayed.  ⑶ Ordinary differential type: δP detection was performed (without taking the square root).  In addition, pressure and temperature measurement points were added on-site; standard signals were transmitted remotely, processed in the DCS system, and the mass flow rate was displayed. Or it can be calculated in the flow accumulator, and the mass flow rate is displayed. Example 2: Elbow-type differential pressure transmitter (which may also be derived from Bernoulli’s equation). V – average flow velocity of the fluid; α – overall flow coefficient, which is related to factors such as the structural design of the elbow sensor, the Reynolds number of the fluid, its dynamic viscosity, compressibility coefficient, and pipe roughness. R – Curvature radius at the center of the elbow sensor (mm); △p – Pressure difference between the inner and outer sides of the elbow sensor; D – Average inner diameter of the elbow sensor (mm); ρ – Density of the medium being measured (kg/m3). Requirements: ① The elbow sensor should be a 90º elbow. ②Pressure tapping points are provided with pressure guide holes of 4–13 mm in diameter, drilled at 45º on both the inside and outside sides of the sensor. ③The measurement accuracy can reach 1%. It can be used to measure fluid media such as steam, gases, and liquids; it is capable of withstanding high temperatures, high pressures, and corrosion. It can still function properly even when there are small amounts of particles and flocs present in the fluid.  Example 3: Pitot tube (Anubaa tube) – differential pressure transmitter. Figure 3-1 shows a schematic of flow measurement using a pitot tube.  P0 – total pressure (pressure at the center of the pipe end).  P – static pressure (the pressure of the undisturbed fluid at the same depth).  g – acceleration due to gravity.  γ – specific weight (gf/cm3)