3.1 introduction

Chapter 3 covers the theoretical and computational details of differential pressure flow. There are two purposes:

Introduce some basic information of fluid flow to industry users, especially differential pressure flow technology

Explain the basic assumptions and methods of Rosemount differential pressure flow product engineering

Be careful

Deep understanding of the chemical and physical characteristics that affect the differential pressure flow is very helpful for technicians to master all aspects of a specific application project, but the installation and daily operation of the differential pressure flow meter do not need to know these. The most important thing is to know that even the simplest applications can be very complex.

Available resources

There are many resources available for engineers to solve complex problems. These include:

Application and sales engineering resources available from designated product suppliers;

Industry training and discussion of experts and peers in user conferences and formal seminars;

The supplier shall provide software toolbox and utility tools to simplify the specified application engineering;

A large number of technical documents and books on this subject.

The following sections describe the differential pressure flow from a practical point of view - the technology used for the recommended application types (gas, liquid, steam), the analysis of available products (transmitters, primary components) from a hardware and software perspective, and the precautions for installation and use.

3.2 physical characteristics and engineering of fluid and flow

The concepts used in the theory and calculation of differential pressure flow mainly come from two aspects of hydrodynamics: fluid kinematics (Research on moving fluid) and hydrodynamics (Research on force effect caused by fluid motion). The basic differential pressure flow equation is based on the conservation of energy and is applicable to almost all types of fluid measurement in industrial or commercial applications.

The advantages of using differential pressure device to measure flow are: simplified sensing system, multiple types of primary elements, ability to verify the measurement results and wide application range of differential pressure flow technology.

By being familiar with the theory and operation of the differential pressure flow measurement device, the challenges in the use of the differential pressure flow meter can be overcome.

3.3 developed flow and undeveloped flow

Flow profile conditions on the measurement plane should be considered when evaluating flowmeter performance and its use in potential applications. If the velocity profile does not change significantly when flowing downstream, the flow is considered to have "developed". In order to obtain the developed flow, it is necessary to have sufficient straight pipe length or install devices upstream to eliminate excessive turbulence or steady flow. Since the flowmeter is mainly tested in the developed flow, if the measuring point occurs in the case of the undeveloped flow, the possible impact on the flowmeter performance must be considered separately.

Undeveloped flow has different effects on different types of flow meters. The type of pipe fittings and valves installed upstream of the measurement location results in additional turbulence in the pipe, resulting in undeveloped flow. Therefore, the manufacturer will usually provide a flow meter installation diagram to achieve the specified performance.

3.4 Reynolds number

Reynolds number is an important dimensionless parameter used in hydrodynamics. It is defined as the ratio of fluid inertia force to viscous force. With the aid of Reynolds number, the fluid flow can be simulated, so that the specific flow characteristics can be converted into general values. In flow metering, the Reynolds number is used to define a common measurement range for all fluid types. This greatly simplifies the evaluation, size selection and use of flow meters.

For flow in the tube, the Reynolds number is equal to:

The flow in the tube is characterized by the Reynolds number range. These ranges or flow states are identified by a large number of conceptual studies conducted by scientists and engineers on the transition of fluid flow in a tube between high and low speeds. This transformation leads to the change of the velocity profile in the tube, which has a great influence on the hydrodynamics and the ability to measure the velocity.

The flow state at very low Reynolds number is called "laminar" flow, or the flow rate at each layer. From the tube wall to the tube axis, the flow rate continues to increase. The velocity profile of laminar flow is parabolic. In this case, fluid viscosity plays an important role in keeping the flow pattern in the stable layer.

With the increase of flow velocity, the laminar state begins to change and the flow changes. The parabola shape of the velocity profile begins to flatten, and the layers decompose into smaller eddies. When the flow velocity is large, the laminar flow zone exists only in the pipe wall and is very thin. The flow through the rest of the tube becomes turbulent. Although the velocity profile is flattened, the velocity at the center is still the highest. Figure 3.4. A shows a profile of two flow types. The relationship between Reynolds number and flow state is as follows:

Re < 2000 = laminar flow

2000 ≤ re ≤ 4000 = transition flow

Re > 4000 = turbulence

The turbulent flow pattern contains most of the velocity range of the fluid used in industrial and commercial pipelines. Unless the viscosity of the fluid is high, it is rarely encountered that the pipe size causes the flow to be laminar. Therefore, the application of differential pressure flowmeter technology is limited to turbulence, that is to say, turbulence can be used in most applications.

Calculation of pipe Reynolds number

The basic Reynolds number equations are described in terms of flow rate, inner diameter, fluid density and viscosity. Since the Reynolds number is dimensionless, the mass, volume / length, and time units must remain constant.

Table 3.4.1: basic units of Reynolds number

Poise is the unit of measurement of dynamic viscosity. Viscosity is usually measured in centipoise (CP) in US units and PAS in SI units. To convert to the above viscosity units,

Although density and viscosity can be found, the flow rate is usually not in the flowmeter specification sheet. However, the expected minimum flow and maximum flow will be given. The Reynolds number can be calculated using the flow rate, not the flow rate.

For units other than base units, conversion factors are required.

Special case: non circular pipe

For non-circular pipes, hydraulic diameter is used instead of pipe diameter. It is defined as the cross-sectional area multiplied by 4 divided by the wetted perimeter