A differential pressure flow measurement system consists of a differential pressure primary flow element and a differential pressure flow transmitter.

When the flow of a fluid in a pipe passes a restriction in the piping system, the pressure in the piping system is reduced. Most differential pressure primary flow elements are designed, constructed and operated in a manner such that the flow rate is proportional to the square root of the pressure drop across the restriction. These differential pressure primary flow elements include orifice plates, Venturi tubes, elbows, flow nozzles, low loss flow tubes, single-port and multiple-port Pitot tubes, segmental wedge and V-Cone flowmeters.

Some differential pressure primary flow elements, such as critical flow elements and laminar flow elements, do not follow this (squared) relationship. Therefore, some sections of this article do not apply to these technologies.

### Flow Rates

As mentioned above, the flow rate through a differential pressure primary flow element is proportional to the square root of the pressure drop across the restriction. Table 1 illustrates this relationship.

Flow Rate (in flow units) |
Pressure Drop (in differential pressure units) |

100 | 100 |

50 | 25 |

31.6 | 10 |

25 | 6.25 |

10 | 10 |

This relationship can limit the ability of differential pressure flowmeter technology to measure large flow ranges. In the table, a “reasonable” flow measurement range of 10-100 flow units (10:1 flow turndown) would require a differential pressure flow transmitter range of 1-100 differential pressure units (100:1 differential pressure turndown). Therefore, the “reasonable” 10:1 flow turndown requires a 100:1 differential pressure flow transmitter turndown.

Because many differential pressure flow transmitters measured accurately with an approximate 10:1 differential pressure turndown, differential pressure flowmeter technology was often considered accurate from approximately 30-100 flow units. Improved performance of differential pressure flow transmitters has increased the differential pressure turndown, so somewhat larger flow turndowns may be possible.

The upstream and downstream pressures associated with a differential pressure primary flow element are available at the taps of the element. Both of these taps are piped to ports on the differential pressure flow transmitter that measures the pressure drop. The differential pressure flow transmitter is a device that converts the differential pressure across its ports into an analog signal. When the differential pressure flow transmitter has an integral square root function, its output signal can be linear with flow rate.

Some (multivariable) differential pressure flow transmitters can make multiple measurements, such as differential pressure, pressure and/or temperature, from which the flow rate can be calculated. These transmitters are outside the scope of this article.

Designs

In general, wetted parts (such as diaphragms) that are in contact with the fluid provide movement or force that is related to the differential pressure across the transmitter pressure ports. Differential pressure flow transmitters have been designed using many technologies including, capacitance, differential transformer, force balance, piezoelectric, potentiometer, strain gage and vibrating wire.

The quality of the differential pressure flow transmitter signal can be described by its performance specifications. Therefore, given performance specifications, the (internal) sensing technology and details of (internal) operation are not overly important considerations when considering the purchase of differential pressure flow transmitters (although some sensing technologies may have superior reputations).

Due to the nature of the nonlinear relationship between flow and differential pressure, relatively small differential pressure changes can result in relatively large flow changes at low flow rates. To reduce the noise associated with the flow signal at these flows, some differential pressure transmitters force their output signal to zero flow when the signal falls below a certain (preset) differential pressure. Some transmitters with integral square root extraction use a linear relationship between flow and differential pressure below a certain (preset) flow rate. Other algorithms may be available to stabilize the output signal at low flow rates.

Construction

The construction of differential pressure flow transmitters is such that its wetted parts can be made from materials that can withstand corrosion. In typical installations, impulse tubes are installed such that no flow occurs at the transmitter, so abrasion and wear are usually not important concerns. However, abrasion and wear can affect the performance of a differential pressure primary flow element by affecting its geometry. Differential pressure flow transmitters can measure the flow of many corrosive liquids, gases, and vapors. Differential pressure primary flow elements with appropriate geometries and materials of construction can withstand abrasive fluids.

Differential pressure flow transmitters can be constructed of materials that do not contaminate the fluid. However, they are not generally applied to sanitary service because of limitations on the ability to clean them.

Most differential pressure primary flow elements have straight run requirements, so they are usually not applied where limited straight run is available. In addition, differential pressure primary flow element technology has Reynolds number constraints, so it may find limited application in low flow applications, and where the liquid exhibits high or varying viscosity.

Differential pressure flowmeters measure velocity head, from which the fluid velocity is inferred, after which the volumetric flow rate is inferred. The differential pressure produced is a function of the square of the velocity, so this technology exhibits a relatively small flow turndown as compared with other flowmeter technologies. However, within Reynolds number constraints, the range of accurate flow measurement is relatively easy to change after installation.

Fluid Density

Differential pressure flowmeter measurements are inherently affected by fluid density. Density changes in liquid applications are usually small because of their non-compressible nature and because (in many applications) process temperature has a relatively small affect on density. In gas and vapor applications, both temperature and pressure can affect density and significantly degrade the quality of the flow measurement. Notwithstanding the above, note that changes in fluid composition can affect the density of the fluid.

Flow computers can be used to compensate for density and other operating parameters in applications where degradation of the flow measurement produces unacceptable flow measurement performance. A flow computer can be implemented as a separate hardware device that calculates the compensated flow measurement from field devices, such as differential pressure, pressure and/or temperature instruments. These calculations can also be performed in the process control system. In addition to measuring flow, temperature and pressure, some multivariable differential pressure flow transmitters can perform these calculations internally.

Multivariable flowmeters, such as multivariable differential pressure flow transmitters and other multivariable flowmeter technologies, are outside the scope of this article because even though there is some overlap with information contained here, additional parameters are used to evaluate the relative performance of the different technologies.

Differential pressure flow transmitters generate an electrical signal that represents the differential pressure at its ports. Of importance is how well the differential pressure flow transmitter performs this function. Because performance is the prime concern in many applications, the technology used to effect the measurement is typically a secondary or tertiary matter. VM

*David W. Spitzer, PE, is principal of Spitzer Boyes, LLC, and has more than 30 years experience in instrumentation, process control, electrical and utility engineering. He is the author of several textbooks used in the industry and has taught numerous training seminars. Reach him at www.spitzerandboyes.com. This article was excerpted from “The Consumer Guide to Differential Pressure Flow Transmitters.” *

## Differential Pressure Flow Transmitter Designs

The following principles are used in the design of differential pressure flow transmitters:

**Capacitance**. The differential pressure at the ports causes the wetted diaphragm to move an internal diaphragm located between two fixed plates. The movement of the internal diaphragm causes a capacitance change that can be converted into a signal that is proportional to the applied differential pressure.

**Differential Transformer**. The differential pressure at the ports causes the wetted diaphragm (or bellows) to move the magnetic core in a transformer. The movement of the core causes an electrical imbalance that can be converted into a signal that is proportional to the applied differential pressure.

**Force Balance**. The differential pressure at the ports causes the wetted bellows to create a force that is counteracted by a force generated by an electromagnet (or perhaps a servomotor). A measurement of the generated counteractive force can be converted into a signal that is proportional to the applied differential pressure.

**Piezoelectric**. The differential pressure at the ports causes the wetted diaphragm to apply force on a crystal. This force causes an electric signal to be generated that can be converted into a signal that is proportional to the applied differential pressure.

**Potentiometer**. The differential pressure at the ports causes the wetted diaphragm (or bellows) to move the wiper of a variable resistor (potentiometer). The movement of the wiper causes a resistance change that can be converted into a signal that is proportional to the applied differential pressure.

**Silicon Resonance**. A silicon resonance sensor is a micro-machined semi-conductor structure fabricated on a silicon crystal. The structure is shaped so it can oscillate and resonate at high frequencies. When a differential pressure is applied, part of the structure is under compression while another part of the structure is in tension. The compression and tension forces change the resonant frequency of the structure in a manner proportional to the applied differential pressure.

**Strain Gage**. The differential pressure at the ports causes the wetted diaphragm to apply a force on a strain gage. This force stretches the strain gage and causes the resistance of the strain gage to change. The resistance change causes an electric signal to be generated that can be converted into a signal that is proportional to the applied differential pressure.