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TECH NOTE: Solid State Flow Elements (11/96)

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Since the turn of the century, "Head" flow devices have been used extensively in virtually all types of flow metering applications. Head meters include; Orifice, Venturi, Nozzle, and Pitot Tube. As a class, they are the still the most popular. This popularity comes from simplicity of design & operation, good accuracy, and cost effectiveness.

With new metering technologies such as Coriolis, Magnetic, and Vortex, it appeared that these meters were to be relegated to more generic and lower precision services. However, all this is changing with today's "SMART" electronics. Now Head meters, when properly outfitted can offer truly remarkable performance complementing their inherent design features. Basic advantages include; no moving parts, NIST traceable accuracy available, no delicate parts, compact & rugged, and familiar operation.


Head flow elements are characterized by a converging-diverging flow path geometry (excluding Pitot tube), and can be broken into three (3) classes; sub-critical for gases and liquids, critical for gases, and cavitating for liquids. The term "critical" refers to the velocity at the smallest section. For sub-critical devices; per Bernoulli’s Law, flow rate is a function of the square root of the differential pressure developed. Should this velocity reach the speed of sound, the device is then considered to be in critical flow. Once critical (or "sonic") flow is reached, a different flow equation applies. This new equation has flow based on inlet conditions only, and not differential pressure. In fact, flow is generally calculated on a mass basis and is a function of the inlet gas density and individual gas characteristics only. With the speed of sound a natural barrier, critical flow elements now make very attractive calibration devices, as well as mass flow controllers for gases.

A third class is that of the cavitating element (liquids only). Much like the Critical or Sonic gas device, the cavitating Venturi has a natural flow limiting phenomenon. Liquid is accelerated through the device resulting in a lowering of the static pressure at the smallest cross section. If this pressure is sufficiently lowered to or below the liquids' vapor pressure, the liquid changes to the gas phase (boils or cavitates). The resulting dramatic change in volume constricts the flow. Consequently for a given upstream condition, the flow will remain unchanged regardless of downstream pressure during this condition. This then creates an attractive solid state flow limiting or control device.


Instrumentation * Controls * Systems * Design * Fabrication

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Sub-critical flow (gases & liquids):

The basic operational principal for sub-critical (less than sonic velocity) Head meters is based on the Bernoulli energy equation. When fluid (liquid or gas) moves from a larger to a smaller flow area, the velocity (or kinetic energy) increases while the static pressure decreases. The resulting difference in static pressure is then in relation with the flow rate. Pitot Tube meters operate similarly except that the pressure difference is based on the variance in static and impact (total, stagnation) pressures. A basic equation for sub-critical and cavitating flow is;

Q = C (DP / RHO) ^ .5

(1) "C" adjusts for parameters such as area, velocity effects, deviation from ideal, thermal and gas effects, etc.

(2) For cavitating flow, P2 (where DP = P1-P2) is such that the static pressure is equal or less than the liquids' vapor pressure at that temperature.

Before modern electronics, the square root function was awkward to handle. In addition, since flow rate is a function of the square root of DP, the DP range had to be quite large to achieve good flow turndown. Today these parameters can be handled with high precision. With "SMART" DP transmitters, turndowns of greater than 10:1 are achievable. On gases with density changes, mass flow rate turndowns can be dramatic.

Critical or Sonic flow (gases only):

For gases a special flow case is realized when the pressure drop through the device is sufficient to cause the velocity at or near the smallest section to reach the speed of sound. This natural barrier is a function of the gas makeup, and inlet density. A basic equation for critical or sonic flow is;

Qm = A C C* Po / [ (R / M) To ] ^ .5

(1) "C" adjusts for deviation from ideal in both flow and flow area. Typical "C" values are from 0.85 to near 1.00.

(2) C* is generally known as the critical flow function or coefficient. C* is principally a function of the gas' isentropic (K) coefficient and is well known for most industrial gases.

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Note that flow, is calculated without the square root of DP function, and that the flow is in mass units. As above, this equation can be handled with great precision with today's electronics. Coupled with precision instrumentation, an extremely accurate calibration, proving, or control system can be assembled.


Because of the historical user basis, the performance of most solid state elements is well known. Associations such as ASME / ANSI / AGA and others have well documented "C" factors. Consequently for some applications, calibration may not be necessary. In this case, the accuracy of a properly constructed element may be about +/- 2% (or better) of READING (about +/-1% of READING for Sonic Nozzles). Calibration for sub-critical elements can improve uncertainty to as good as 0.25%. For Sonic Nozzles (critical flow), uncertainty can approach 0.1%. Repeatability regardless of calibration level is near perfect, since we are dealing with no moving or delicate parts. By combining these precision devices with quality instrumentation, good to state of the art flow instrumentation systems can be assembled.


Venturis, nozzles, and specialty orifices are now making a real comeback on tough, high precision, and other demanding applications. Their smooth interior makes for a durable device in erosive services. Ultra clean versions are available for the semi-conductor, aerospace, and food industries. Sonic (critical flow) Nozzles can be packaged to create gas calibration, metering, and control systems with unequaled accuracy. When fitted with a simple pressure regulator, a Sonic Nozzle makes a MASS FLOW controller for gases. Cavitating venturis can be used for flow control of liquids. In addition, specialty orifices such as the quadrant edged or conical inlet provide attractive solutions for very low flow and/or viscous services. Many general industrial applications are improved with the use of these solid state devices.


In general the devices include an inlet section, a reduced area, and a recovery section. The inlet and recovery section may or may not be an integral part of the element. Typically, the system piping will be part of these elements. Ports are included to measure pressure and optionally temperature. Straightening vanes may also be included. The inlet section may be oversized such that static pressure / temperature is a good measure of the total (stagnation) values. This "plenum" effect also minimizes swirl, pulsation, and other flow abnormalities.

Venturis and nozzles typically are constructed to ASME / ANSI standards which will include either a conical or circular (in cross section) inlet, and a conical recovery or diffuser section. Orifices are built to similar standards (including AGA) for the thin sharp edged type. Quadrant and conical styles are designed around historical criteria.

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