... immiscible1.1
Liquids are considered “miscible” if they may be mixed in any proportion to each other to form a solution. Immiscible liquids refuse to mix thoroughly, and therefore tend to separate. 
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... vessel1.2
A spring-loaded cable float only works with liquid level measurement, while a retracting float will measure liquids and solids with equal ease. The reason for this limitation is simple: a float that always contacts the material surface is likely to become buried if the material in question is a solid (powder or granules), which must be fed into the vessel from above. 
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... necessary1.3
We may prove this mathematically by algebraic substitution. Given that the total mass ($m$) of any liquid sample is equal to the product of that liquid's mass density and its sample volume ( $m = \rho V$), that volume ($V$) for any vessel of constant cross-sectional area ($A$) is given by the expression $V = Ah$, and that hydrostatic pressure is equal to $P = \rho g h$, we may combine these three equations to arrive at $m = {AP \over g}$. This final equation demonstrates how the total mass of liquid stored in a vessel ($m$) of constant cross-sectional area ($A$) is directly proportional to pressure ($P$), and independent of density ($\rho$). 
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... suppression1.4
Or alternatively, zero depression. 
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... elevation1.5
There is some disagreement among instrumentation professionals as to the definitions of these two terms. According to Béla G. Lipták's Instrument Engineers' Handbook, Process Measurement and Analysis (Fourth Edition, page 67), “suppressed zero range” refers to the transmitter being located below the 0% level (the LRV being a positive pressure value), while “suppression,” “suppressed range,” and “suppressed span” mean exactly the opposite (LRV is a negative value). The Yokogawa Corporation defines “suppression” as a condition where the LRV is a positive pressure (“Autolevel” Application Note), as does the Michael MacBeth in his CANDU Instrumentation & Control course (lesson 1, module 4, page 12), Foxboro's technical notes on bubble tube installations (pages 4 through 7), and Rosemount's product manual for their 1151 Alphaline pressure transmitter (page 3-7). Interestingly, the Rosemount document defines “zero range suppression” as synonymous with “suppression,” which disagrees with Lipták's distinction. My advice: draw a picture if you want the other person to clearly understand what you mean! 
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... vessel1.6
As you are about to see, the calibration of an elevated transmitter depends on us knowing how much hydrostatic pressure (or vacuum, in this case) is generated within the tube connecting the transmitter to the process vessel. If liquid were to ever escape from this tube, the hydrostatic pressure would be unpredictable, and so would be the accuracy of our transmitter as a level-measuring instrument. A remote seal diaphragm guarantees no fill fluid will be lost if and when the process vessel goes empty. 
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... PSI1.7
The sea water's positive pressure at the remote seal diaphragm adds to the negative pressure already generated by the downward length of the capillary tube's fill fluid ($-2.43$ PSI), which explains why the transmitter only “sees” 2.46 PSI of pressure at the 100% full mark. 
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... manner1.8
Sometimes this is done out of habit, other times because instrument technicians do not know the capabilities of new technology. 
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... pressure1.9
This is due to limited transmitter resolution. Imagine an application where the elevation head was 10 PSI (maximum) yet the vapor space pressure was 200 PSI. The majority of each transmitter's working range would be “consumed” measuring gas pressure, with hydrostatic head being a mere 5% of the measurement range. This would make precise measurement of liquid level very difficult, akin to trying to measure the sound intensity of a whisper in a noisy room. 
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... changes1.10
Assuming the liquid level is equal to or greater than $x$. Otherwise, the pressure difference between $P_{bottom}$ and $P_{middle}$ will depend on liquid density and liquid height. However, this condition is easy to check: the level computer simply checks to see if $P_{middle}$ and $P_{top}$ are unequal. If so, then the computer knows the liquid level exceeds $x$ and it is safe to calculate density. If not, and $P_{middle}$ registers the same as $P_{top}$, the computer knows those two transmitters are both registering gas pressure only, and it knows to stop calculating density. 
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... measurement1.11
The details of this math depend entirely on the shape of the tank. For vertical cylinders – the most common shape for vented storage tanks – volume and height are related by the simple formula $V = \pi r^2 h$ where $r$ is the radius of the tank's circular base. Other tank shapes and orientations may require much more sophisticated formulae to calculate stored volume from height. See section [*] beginning on page [*], for more details on this subject. 
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... transmitter1.12
Here I will calculate all hydrostatic pressures in units of inches water column. This is relatively easy because we have been given the specific gravities of each liquid, which make it easy to translate actual liquid column height into column heights of pure water. 
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... pressures1.13
Remember that a differential pressure instrument cannot “tell the difference” between a positive pressure applied to the low side, an equal vacuum applied to the high side, or an equivalent difference of two positive pressures with the low side's pressure exceeding the high side's pressure. Simulating the exact process pressures experienced in the field to a transmitter on a workbench would be exceedingly complicated, so we “cheat” by simplifying the calibration setup and applying the equivalent difference of pressure only to the “low” side. 
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... “lighter1.14
This is not unlike the experience of feeling lighter when you are standing in a pool of water just deep enough to submerge most of your body with your feet touching the bottom. This reduction of apparent weight is due to the buoyant force of the water upward on your body, equal to the weight of water that your body displaces. 
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... drum1.15
So-called for its ability to “knock out” (separate and collect) condensible vapors from the gas stream. This particular photograph was taken at a natural gas compression facility, where it is very important the gas to be compressed is dry (since liquids are essentially incompressible). Sending even relatively small amounts of liquid into a compressor may cause the compressor to catastrophically fail! 
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... twist1.16
To anyone familiar with the front suspension of a 1960's vintage Chevrolet truck, or the suspension of the original Volkswagen “Beetle” car, the concept of a torsion bar should be familiar. These vehicles used straight, spring-steel rods to provide suspension force instead of the more customary coil springs used in modern vehicles. However, even the familiar coil spring is an example of torsional forces at work: a coil spring is nothing more than a torsion bar bent in a coil shape. As a coil spring is stretched or compressed, torsional forces develop along the circumferential length of the spring coil, which is what makes the spring “try” to maintain a fixed height. 
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... transmitter1.17
This illustration is simplified, omitting such details as access holes into the cage, block valves between the cage and process vessel, and any other pipes or instruments attached to the process vessel. Also, the position-sensing mechanism normally located at the far left of the assembly is absent from this drawing. 
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... pressures1.18
My own experience with this trend is within the oil refining industry, where legacy displacer instruments (typically Fisher brand “Level-Trol” units) are being replaced with new guided-wave radar transmitters, both for vapor-liquid and liquid-liquid interface applications. 
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... velocity1.19
The speed of sound through any substance is a function of both the substance's density and its bulk modulus (i.e. the compressibility of a substance). Mathematically, $c = \sqrt{B \over \rho}$ where $c$ is the sonic velocity, $B$ is the bulk modulus, and $\rho$ is the mass density. Water and air provide an excellent illustration of this principle: the speed of sound through water happens to be much faster than the speed of sound through air despite the vastly greater mass density of water, only because of the even greater disparity in bulk modulus between water and air. 
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... transducer1.20
In the industrial instrumentation world, the word “transducer” usually has a very specific meaning: a device used to process or convert standardized instrumentation signals, such as 4-20 mA converted into 3-15 PSI, etc. In the general scientific world, however, the word “transducer” describes any device converting one form of energy into another. It is this latter definition of the word that I am using when I describe an ultrasonic “transducer” – a device used to convert electrical energy into ultrasonic sound waves, and vice-versa. 
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...Radar1.21
“Radar” is an acronym: RAdio Detection And Ranging. First used as a method for detecting enemy ships and aircraft at long distances over the ocean in World War II, this technology is used for detecting the presence, distance, and/or speed of objects in a wide variety of applications. 
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... “cage”1.22
In fact, it is a common retrofit practice to install a guided-wave radar level transmitter in the exact same cage that once housed a displacement-style level transmitter. 
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... light1.23
In actuality, both radio waves and light waves are electromagnetic in nature. The only difference between the two is frequency: while the radio waves used in radar systems are classified as “microwaves” with frequencies in the gigahertz (GHz) region, visible light waves range in the hundred of terahertz (THz)! 
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... here1.24
This formula assumes lossless conditions: that none of the wave's energy is converted to heat while traveling through the dielectric. For many situations, this is true enough to assume. 
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... pressure1.25
Or if the chemical composition of the gas or vapor changes dramatically. 
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... here1.26
The pressure and temperature factors in this formula come from the Ideal Gas Law ($PV = nRT$), manipulating that equation to express molecular gas density in terms of pressure and temperature ( $\rho = {n \over V} = {P \over RT}$). The fraction ${P T_{ref} \over P_{ref} T}$ expresses a ratio of molecular densities: $\rho \over \rho_{ref}$. 
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... permittivity1.27
Dielectric permittivity is one of the factors determining the speed of any electromagnetic wave through a substance, but not the only one. The material's magnetic permeability is another factor, but it is far more common to encounter interfaces of gas-liquid or liquid-liquid where differences in permittivity rather than differences in permeability constitute the major reason for differences in radio wave velocity. 
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... liquid1.28
Rosemount's “Replacing Displacers with Guided Wave Radar” technical note states that the difference in dielectric constant between the upper and lower liquids must be at least 10. 
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... calculations1.29
$R = 0.5285$ for the 1/40 interface; $R = 0.02944$ for the 40/80 interface; and $R = 0.6382$ for the 1/80 interface, all based on the formula $R = {\left({\sqrt{\epsilon_{r}} - 1}\right)^2 \over \left(\sqrt{\epsilon_{r}} + 1 \right)^2}$ using the pair of permittivity values at each interface. 
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... measurement1.30
It should be noted that the dielectric constant of the lowest medium (the liquid in a simple, non-interface, level measurement application) is irrelevant for calibration purposes. All we are concerned with is the propagation time of the signal to and from the level of interest, nothing below it. 
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... unknown1.31
For vented-tank level measurement applications where air is the only substance above the point of interest, the relative permittivity is so close to a value of 1 that there is little need for further consideration on this point. Where the permittivity of fluids becomes a problem for radar is in high-pressure (non-air) gas applications and liquid-liquid interface applications, especially where the upper substance composition is subject to change. 
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... type1.32
Probe mounting style will also influence the lower transition zone, in the case of flexible probes anchored to the bottom of the process vessel. 
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... pulse1.33
An approximate analogy for understanding the nature of this pulse may be performed using a length of rope. Laying a long piece of rope in a straight line on the ground, pick up one end and quickly move it in a tight circle using a “flip” motion of your wrist. You should be able to see the torsional pulse travel down the length of the rope until it either dies out from dissipation or it reaches the rope's end. As with the torsional pulse in a magnetostrictive waveguide, this pulse in the rope is mechanical in nature: a movement of the rod's (rope's) molecules. As a mechanical wave, it may be properly understood as a form of sound. 
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... wave1.34
This “dampener” is the mechanical equivalent of a termination resistor in an electrical transmission line: it makes the traveling wave “think” the waveguide is infinitely long, preventing any reflected pulses. For more information on electrical transmission lines and termination resistors, see section [*] beginning on page [*]. 
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... transmitter1.35
This particular transmitter happens to be one of the “M-Series” models manufactured by MTS. 
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... slower-traveling1.36
One reference gives the speed of sound in a magnetostrictive level instrument as 2850 meters per second. Rounding this up to $3 \times 10^3$ m/s, we find that the speed of sound in the magnetostrictive waveguide is at least five orders of magnitude slower than the speed of light in a vacuum (approximately $3 \times 10^8$ m/s). This relative slowness of wave propagation is a good thing for our purposes here, as it gives more time for the electronic timing circuit to count, yielding a more precise measurement of distance traveled by the wave. This fact grants superior resolution of measurement to magnetostrictive level sensors over radar-based and laser-based level sensors. Open-air ultrasonic level instruments deal with propagation speeds even slower than this (principally because the bulk moduli of gases and vapors is far less than that of a solid metal rod) which at first might seem to give these level sensors the advantage in precision. However, open-air level sensors experience far greater propagation velocity variations caused by changes in pressure and temperature than magnetostrictive sensors. Unlike the speed of sound in gases or liquids, the speed of sound in a solid metal rod is very stable over a large range of process temperatures, and practically constant for a large range of process pressures. Another factor adding to the calibration stability of magnetostrictive instruments is that the composition of the medium never changes. With instruments measuring time-of-flight through process fluids, the chemical composition of those fluids often affects the wave velocity. In a magnetostrictive instrument, the waves are always traveling through the same material – the metal of the waveguide bar – and thus are not subject to variation with process changes. 
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... measurement1.37
Regardless of the vessel's shape or internal structure, the measurement provided by a weight-sensing system is based on the true mass of the stored material. Unlike height-based level measurement technologies (float, ultrasonic, radar, etc.), no characterization will ever be necessary to convert a measurement of height into a measurement of mass. 
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... insufficient1.38
If we happened to know, somehow, that the vessel's weight was in fact equally shared by all supports, it would be sufficient to simply measure stress at one support to infer total vessel weight. In such an installation, assuming three supports, the total vessel weight would be the stress at any one support multiplied by three. 
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... process1.39
The particular “micro-brewery” process shown here is at the Pike's Place Market in downtown Seattle, Washington. Three load cells measure the weight of a hopper filled with ingredients prior to brewing in the “mash tun” vessel. 
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... vessel1.40
One practical solution to this problem is to shut down the source of vibration (e.g. agitator motor, pump, etc.) for a long enough time to take a sample weight measurement, then run the machine again between measurements. So long as intermittent weight measurement is adequate for the needs of the process, the interference of machine vibration may be dealt with in this manner. 
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... electrons1.41
Beta particles are not orbital electrons, but rather than product of elementary particle decay in an atom's nucleus. These electrons are spontaneously generated and subsequently ejected from the nucleus of the atom. 
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... half-life1.42
The half-life of a radioactive substance is the amount of time it takes for one-half of the original quantity to experience radioactive decay. To illustrate, a 10-gram quantity consisting of 100% Cobalt-60 atoms will only contain 5 grams of Cobalt-60 after 5.3 years, and then only 2.5 grams of Cobalt-60 after another 5.3 years (10.6 years from the start), and so on. The actual mass of the sample does not change significantly over this time period because the Cobalt atoms have decayed into atoms of Nickel, which still have the same atomic mass value. However, the intensity of the gamma radiation emitted by the sample decreases over time, proportional to the percentage of Cobalt remaining therein. 
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... energy1.43
So much of the incident power is lost as the radar signal partially reflects off the gas-liquid interface, then the liquid-liquid interface, then again through the gas-liquid interface on its return trip to the instrument that every care must be taken to ensure optimum received signal strength. While twin-lead probes have been applied in liquid-liquid interface measurement service, the coaxial probe design is still the best for maintaining radar signal integrity. 
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