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Flow measurement

Flow measurement is the quantification of bulk fluid movement. It can be measured in a variety of ways.

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Units of measurement

Both gas and liquid flow can be measured in volumetric or mass flow rates (such as litres per second or kg/s). These measurements can be converted between one another if the materials density is known. The density for a liquid is almost independent of the liquids conditions, however this is not the case for a gas, whose density highly depends upon pressure and temperature.

In engineering contexts, the volumetric flow rate is usually given the symbol $Q$ and the mass flow rate the symbol $\dot m$ .

Gas

Due to the nature of an Ideal gas or a Real gas, the volumetric gas flow rate will differ for the same mass flow rate when at differing temperatures and pressures. As such gas volumetric flow rate is sometimes measured in "standard cubic centimeters per minute" (abbreviation sccm). This unit, although not an SI unit is sometimes used due to the additional information attached to the unit symbol, which indicates the temperature and pressure of the gas. Many other similar abbreviations are also in use, for two reasons, firstly mass flow and volumetric flow can be equated at known conditions, and secondly due to the imperial system older units such as standard cubic feet per minute or per second may still be used in some countries. It is often necessary to employ standard gas relationships (such as the ideal gas law) to convert between units of mass flow and volumetric flow.

Liquid

For liquids other units used depend on the application and industry but might include gallons (U.S. liquid or imperial) per minute, liters per second, bushels per minute and, when describing river flows, acre-feet per day.

Mechanical flow meters

There are several types of mechanical flow meter

Piston Meter

Because they are used for domestic water measurement, piston meters, also known as rotary piston or semi-positive displacement meters, are the most common flow measurement devices in the UK and are used for almost all meter sizes up to and including 40 mm (1 1/2"). The piston meter operates on the principle of a piston rotating within a chamber of known volume. For each rotation, an amount of water passes through the piston chamber. Through a gear mechanism and, sometimes, a magnetic drive, a needle dial and odometer type display is advanced.

Woltmann Meter

Woltman meters, commonly referred to as Helix meters are popular at larger sizes. Jet meters (single or Multi-Jet) are increasing in popularity in the UK at larger sizes and are commonplace in the EU.

Venturi Meter

Another method of measurement, known as a venturi meter, is to constrict the flow in some fashion, and measure the differential pressure (using a pressure sensor) that results across the constriction. This method is widely used to measure flow rate in the transmission of gas through pipelines, and has been used since Roman Empire times.

Dall Tube

The Dall tube is a shortened version of a Venturi meter with a lower pressure drop than an orifice plate. Both flow meters the flow rate of Dall tube is determined by measuring the pressure drop caused by restriction in the conduit. The pressure differential is measured using diaphragm pressure transducers with digital read out. Since these meters have significantly lower permanent pressure losses than the orifice meters, the Dall tubes have widely been used for measuring the flow rate of large pipeworks.

Orifice Plate

Another simple method of measurement uses an orifice plate, which is basically a plate with a hole through it. It is placed in the flow and constricts the flow. It uses the same principle as the venturi meter in that the differential pressure relates to the velocity of the fluid flow (Bernoulli's principle).

Pitot tube

A Pitot tube is a pressure measuring instrument used to measure fluid flow velocity by determining the stagnation pressure. Bernoulli's equation is used to calculate the dynamic pressure and thence fluid velocity.

Paddle wheel

The paddle wheel translates the mechanical action of paddles rotating in the liquid flow around an axis into a user-readable rate of flow (gpm, lpm, etc.). The paddle tends to be inserted into the flow.

Pelton wheel

The Pelton wheel turbine (better described as a radial turbine) translates the mechanical action of the Pelton wheel rotating in the liquid flow around an axis into a user-readable rate of flow (gpm, lpm, etc.). The Pelton wheel tends to have all the flow travelling around it with the inlet flow focussed on the blades by a jet. The original Pelton wheels were used for the generation of power and consisted of a radial flow turbine with "reaction cups" which not only move with the force of the water on the face but return the flow in opposite direction using this change of fluid direction to further increase the efficiency of the turbine.

Turbine flow meter

The turbine flowmeter (better described as an axial turbine) translates the mechanical action of the turbine rotating in the liquid flow around an axis into a user-readable rate of flow (gpm, lpm, etc.). The turbine tends to have all the flow travelling around it.

Thermal mass flow meters

Thermal mass flow meters generally use combinations of heated elements and temperature sensors to measure the mass flow of a fluid. The fluid temperature is also measured and compensated for. They provide a direct mass flow readout, and do not need any additional pressure temperature compensation over their specified range. Technological progress allows today to manufacture thermal mass flow meters on a microscopic scale as MEMS sensors.

Thermal mass flow meters are used for compressed air, nitrogen, helium, argon, oxygen, natural gas. In fact, most gases can be measured as long as they are fairly clean and non-corrosive.

For liquids a media isolated principle is state of the art. Heat transfer is measured through the wall of a channel. Because in chemistry and biology more and more systems get miniaturized in Lab-on-a-chip-systems thermal MEMS flow sensors are used to measure flow rates in the range of nano litres or micro litres per minute.

Vortex flowmeters

Another method of flow measurement involves placing a bluff body (called a shedder bar) in the path of the fluid. As the fluid passes this bar, disturbances in the flow called vortices are created. The vortices trail behind the cylinder in two rolls, alternatively from the top or the bottom of the cylinder. This vortex trail is called the Von Kármán vortex street after von Karman's 1912 mathematical description of the phenomenon. The speed at which these vortices are created is proportional to the flow rate of the fluid. Inside the shedder bar is a piezoelectric crystal, which produces a small, but measurable, voltage pulse every time a vortex is created. The frequency of this voltage pulse is also proportional to the fluid flow rate, and is measured by the flowmeter electronics.

With f= SV/L where,

f = the frequency of the vortices
L = the characteristic length of the bluff body
V = the velocity of the flow over the bluff body
S = Strouhal number and is a constant for a given body shape

Electromagnetic, ultrasonic and coriolis flow meters

Modern innovations in the measurement of flow rate incorporate electronic devices that can correct for varying pressure and temperature (i.e. density) conditions, non-linearities, and for the characteristics of the fluid.

Magnetic flow meters

The most common flow meter apart from the mechanical flow meters, is the magnetic flow meter, commonly referred to as a "mag meter" or an "electromag". A magnetic field is applied to the metering tube, which results in a potential difference proportional to the flow velocity perpendicular to the flux lines. The physical principle at work is Faraday's law of electromagnetic induction. The magnetic flow meter requires a conducting fluid, e.g. water, and an electrical insulating pipe surface, e.g. a rubber lined non magnetic steel tube.

Ultrasonic flow meters

Ultrasonic flow meters measure the difference of the transit time of ultrasonic pulses propagating in and against flow direction. This time difference is a measure for the average velocity of the fluid along the path of the ultrasonic beam. By using the absolute transit times both the averaged fluid velocity and the speed of sound can be calculated. Using the two transit times $t u p$ and $t d o w n$ and the distance between receiving and transmitting transducers $L$ and the inclination angle $α$ one can write the equations:

$v = \frac{L}{{2\;\sin \left( \alpha \right)}}\;\frac{{t_{up} - t_{down} }}{{t_{up} \;t_{down} }}$ and $c = \frac{L}{2}\;\frac{{t_{up} + t_{down} }}{{t_{up} \;t_{down} }}$

where $v$ is the average velocity of the fluid along the sound path and $c$ is the speed of sound.

Measurement of the doppler shift resulting in reflecting an ultrasonic beam off the flowing fluid is another recent innovation made possible by electronics. By passing an ultrasonic beam through the tissues, bouncing it off of a reflective plate then reversing the direction of the beam and repeating the measurement the volume of blood flow can be estimated. The speed of transmission is affected by the movement of blood in the vessel and by comparing the time taken to complete the cycle upstream versus downstream the flow of blood through the vessel can be measured. The difference between the two speeds is a measure of true volume flow. A wide-beam sensor can also be used to measure flow independent of the cross-sectional area of the blood vessel.

Coriolis flow meters

Using the Coriolis effect that causes a laterally vibrating tube to distort, a direct measurement of mass flow can be obtained in a coriolis flow meter. Furthermore a direct measure of the density of the fluid is obtained. Coriolis measurement can be very accurate irrespective of the type of gas or liquid that is measured; the same measurement tube can be used for hydrogen gas and peanut butter without recalibration.

Laser doppler flow measurement

Blood flow can be measured through the use of a monochromatic laser diode. The laser probe is inserted into a tissue and turned on, where the light scatters and a small portion is reflected back to the probe. The signal is then processed to calculate flow within the tissues. There are limitations to the use of a laser doppler probe; flow within a tissue is dependent on volume illuminated, which is often assumed rather than measured and varies with the optical properties of the tissue. In addition, variations in the type and placement of the probe within identical tissues and individuals result in variations in reading. The laser doppler has the advantage of sampling a small volume of tissue, allowing for great precision, but does not necessarily represent the flow within an entire organ. The flow meter is more useful for relative rather than absolute measurements.