According to Bernoulli equation and energy balance (continuous equation), this is a basic flow equation adopting the above physical properties of fluid. D2 and E are geometric terms determined from the geometry of the primary element. CD and Y1 are empirical terms calculated by test derived equation, which are used for fixed parameter set of flow equation, or calculated continuously when using microprocessor flow computer. The differential pressure and ρ change with the change of process conditions such as flow, temperature and pressure.

Differences between empirical and geometric terms

As mentioned above, D2 and E are geometric terms that depend on primary component geometry changes. Orifice, venturi and nozzle are considered as variable section primary element or throat flowmeter. The averaging pitot tube uses the flow rate calculated from the stagnation pressure measurement (see section 3.8 for details)

Each flowmeter has different degree of energy loss, so the flow coefficient value is different. Figure 3.6. B shows the CD values of the three primary throttling elements plotted against the pipe Reynolds number. The calibration coefficient diagram of the main flowmeter in the working range is also called the "characteristic curve" of the flowmeter. Note that the venturi shown is close to the flow line path. Therefore, the energy loss is small and the flow coefficient is close to 1.00. The streamline of the flow measuring nozzle is separated from the pipe wall, so the energy loss is large, but the energy loss of the orifice plate is the largest, because the sudden change of the area leads to more turbulence.

There are two main design drivers for differential pressure flow meters:

The geometry of the flowmeter - including the tube, the position and size of the opening to read the differential pressure signal (also known as the "pressure tap") and the status of the components that make up the flowmeter.

The flow coefficient corresponding to the flowmeter geometry.

More than 100 years ago, the orifice plate or venturi as shown in Fig. 3.6. A was tested. At present, there are many standards that can be used to determine the flow coefficient value and the manufacturing and installation design requirements of various types of flow meters. Through these works, equations are established from a series of calibrations of a large number of pipe sizes and beta values, so as to calculate the flow coefficient. The prediction equations of different types of CD are established and the success is achieved in different degrees. Because the orifice plate is the simplest, the lowest cost and the easiest to improve and maintain, the orifice plate is the most widely used of the four types of primary components. The flow coefficient of each primary element is slightly different, but the equation used to calculate the flow is the same.

3.7 type of cross section flowmeter

There are many design changes in the above four types of primary components. These changes allow differential pressure flow devices to be used in a variety of fluid conditions that may not meet the standard design. In each case, the standard design will be modified in the same basic form of Bernoulli equation, but the flow system and expansion coefficient have been modified. These types of primary elements include Rosemount adjustable orifice, standard orifice, venturi and nozzle.

As discussed in the first chapter, orifice plate industry is the most commonly used type of flowmeter. The orifice diameter or throat diameter is smaller than the pipe diameter, so differential pressure will be formed when throttling. Like all differential pressure flow meters, the basic theory of orifice flowmeter is Bernoulli equation, and the calculation of actual flow depends on CD and Y1.

Note that all of the discussion in the next section applies to concentric orifice plates with right angle edges.

ISO, ASME and AGA standards provide basis for calculation of flow coefficient

At present, three main standards have been formulated, which specify the CD and Y1 coefficients as well as specific structure, installation requirements and uncertainties. ISO 5167 Part 1-4 of international standards organization; ASME mfc-3m of American Society of mechanical engineers; and AGA Report No. 3 of natural gas and hydrocarbon gas of American Natural Gas Association.

Many independent public and private testing laboratories provide a lot of test data, which helps to establish the relationship among Reynolds number, flow coefficient and gas expansion coefficient.

After obtaining more data or completing the latest analysis of the original data, the standard organizations usually constantly check the equation structure adopted by their standards. For example, the ASME mfc-3m Committee updated an equation structure almost identical to ISO 5167 in 2004.

Rosemount adjustable orifice

Rosemount adjustable orifice is designed as one plate with four holes. The main purpose of this kind of orifice is to adjust the flow measured in the area. This self-regulation no longer requires the installation of a separate flow regulator or, in some cases, a straight pipe with a diameter of 40 + after the flow disturbance position.

Rosemount adjusted orifice (COP) technology uses the same Bernoulli equation as standard orifice. Therefore, the relationship between the general flow coefficient and the Reynolds number of the adjustable orifice is the same as that of the standard orifice, but there is a small numerical change, which depends on the specific pressure.

Rosemount adjustable orifice plate shows that four holes are arranged in an orthogonal way around the center.

The four holes on the orifice are equally spaced around the center of the orifice. When the kinetic energy balance of the adjustable orifice is maintained and the continuous equation is used, the result requires that the energy conservation or the flow through the four holes must be the same. In this model, the flow through the hole is forced to be distributed, and even if the velocity distribution of the upstream fluid is extremely asymmetric or circulation is generated, a stable downstream dynamic force can be formed. Because most of the orifice differential pressure signals are formed in the downstream, when the installation position is very close to the typical pipe components or installed in the long straight pipe, the adjusted orifice cop can provide equivalent results. This eliminates the need for flow regulators in the short straight section and provides excellent performance