A Flow Measurement Orientation
  The Flow Pioneers
  Flow Sensor Selection
  Accuracy vs. Repeatability

Differential Pressure Flowmeters
  Primary Element Options
  Pitot Tubes
  Variable Area Flowmeters

Mechanical Flowmeters
  Positive Displacement   Flowmeters
  Turbine Flowmeters
  Other Rotary Flowmeters

Electronic Flowmeters
  Magnetic Flowmeters
  Vortex Flowmeters
  Ultrasonic Flowmeters

Mass Flowmeters
  Coriolis Mass Flowmeters
  Thermal Mass Flowmeters
  Hot-Wire Anemometers

A Level Measurement Orientation
  Level Sensor Selection
  Boiling & Cryogenic Fluids
  Sludge, Foam, & Molten   Metals

Pressure/Density Level Instrumentation
  Dry & Wet Leg Designs
  Bubbler Tubes
  Floats & Displacers

RF/Capacitance Level Instrumentation
  Theory of Operation
  Probe Designs
  Installation Considerations

Radiation-Based Level Instrumentation
  Radar & Microwave
  Ultrasonic Level Gages
  Nuclear Level Gages

Specialty Level Switches
  Thermal Switches
  Vibrating Switches
  Optical Switches

  About OMEGA
  Information Resources

  Pressure/Density Level Instrumentation

One of the primary principles underlying industrial level measurement is that different materials and different phases of the same material have different densities. This basic law of nature can be utilized to measure level via differential pressure (that at the bottom of the tank relative to that in the vapor space or to atmospheric pressure) or via a float or displacer that depends on the density differences between phases.

Level measurement based on pressure measurement is also referred to as hydrostatic tank gaging (HTG). It works on the principle that the difference between the two pressures (d/p)

Figure 7-1: Click on figure to enlarge.

is equal to the height of the liquid (h, in inches) multiplied by the specific gravity (SG) of the fluid (see Figure 7-1):

By definition, specific gravity is the liquid's density divided by the density of pure water at 68° F at atmospheric pressure. A pressure gage or d/p cell can provide an indication of level (accurate to better than 1%) over wide ranges, as long as the density of the liquid is constant. When a d/p cell is used, it will cancel out the effects of barometric pressure variations because both the liquid in the tank and the low pressure side of the d/p cell are exposed to the pressure of the atmosphere (Figure 7-1B). Therefore, the d/p cell reading will represent the tank level.

Dry & Wet Leg Designs

When measuring the level in pressurized tanks, the same d/p cell designs (motion balance, force balance, or electronic) are used as on open tanks. It is assumed that the weight of the vapor column above the liquid is negligible. On the other hand, the pressure in the vapor space cannot be neglected, but must be relayed to the low pressure side of the d/p cell. Such a connection to the vapor space is called a dry leg, used when process vapors are non-corrosive, non-plugging, and when their condensation rates, at normal operating temperatures, are very low (Figure 7-1C). A dry leg enables the d/p cell to compensate for the pressure pushing down on the liquid's surface, in the same way as the effect of barometric pressure is canceled out in open tanks.

It is important to keep this reference leg dry because accumulation of condensate or other liquids would cause error in the level measurement. When the process vapors condense at normal ambient temperatures or are corrosive, this reference leg can be filled to form a wet leg. If the process condensate is corrosive, unstable, or undesirable to use to fill the wet leg, this reference leg can be filled with an inert liquid.

In this case, two factors must be considered. First, the specific gravity of the inert fluid (SGwl) and the height (hwl) of the reference column must be accurately determined, and the d/p cell must be depressed by the equivalent of the hydrostatic head of that column [(SGwl)(hwl)]. Second, it is desirable to provide a sight flow indicator at the top of the wet leg so that the height of that reference leg can be visually checked.

Figure 7-2: Click on figure to enlarge.

Any changes in leg fill level (due to leakage or vaporization) introduce error into the level measurement. If the specific gravity of the filling fluid for the wet leg is greater than that of the process fluid, the high pressure side should be connected to the reference leg and the low to the tank.

If the condensate can be used to fill the reference leg, a condensate pot can be mounted and piped both to the high level connection of the tank and to the top of the vapor space. The condensate pot must be mounted slightly higher than the high level connection (tap) so that it will maintain a constant condensate level. Excess liquid will drain back into the tank. It is also desirable either to install a level gage on the condensate pot or to use a sight flow indicator in place of the pot, so that the level in the pot can conveniently be inspected.

Either method (wet or dry) assures a constant reference leg for the d/p cell, guaranteeing that the only variable will be the level in the tank. The required piping and valving must always be provided on both the tank and the reference leg side of the d/p cell, so that draining and flushing operations can easily be performed. When a wet reference leg is used, a low thermal expansion filling fluid should be selected. Otherwise, the designer must correct for the density variations in the reference leg caused by ambient temperature variations.

If smart transmitters are used and if the filling fluid data is known, wet-leg temperature compensation can be provided locally. Alternatively, the host or supervisory control system can perform the compensation calculations.

If it is desired to keep the process vapors in the tank, a pressure repeater can be used. These devices repeat the vapor pressure (or vacuum) and send out an air signal identical to that of the vapor space. The measurement side of the repeater is connected to the vapor space and its output signal to the low pressure side of the d/p cell. If the tank connection is subject to material build-up or plugging, extended diaphragm Type 1:1 repeaters can be considered for the service (Figure 7-2).

While repeaters eliminate the errors caused by wet legs, they do introduce their own errors as a function of the pressure repeated. For example, at 40 psig, repeater error is about 2 in. At 400 psig, it is 20 in. In many applications, the former is acceptable but the latter is not.

d/p Cells

Because the designs of the various d/p cells are discussed in detail in another issue of Transactions, only a brief overview is provided here.

The motion balance cell is well suited for remote locations where instrument air or electric power are not available. If a bellows is used as the sensing element in a motion balance d/p cell, an increase in the pressure on either side causes the corresponding bellows to contract (Figure 7-3A). The bellows is connected to a linkage assembly that converts the linear motion of the bellows into a rotary indicator motion, which can be

Figure 7-3: Click on figure to enlarge.

calibrated to indicate the tank level.

In a force-balance type of d/p cell, the sensing element (often a diaphragm) does not move. A force bar is provided to maintain the forces acting on the diaphragm in equilibrium (Figure 7-3B). In pneumatic d/p cells, this is often achieved by the use of a nozzle and flapper arrangement that guarantees that the pneumatic output signal will always be proportional to the differential pressure across the cell. The output of pneumatic d/p cells is linear and is usually ranged from 3 to 15 psig. The levels represented by such transmitted signals (pneumatic, electronic, fiberoptic or digital) can be displayed on local indicators or remote instruments. Pneumatic transmitters require a compressed air (or nitrogen) supply.

Electronic d/p cells provide ±0.5% of span or better precision typically conveyed via a 4-20 mA signal. The range of these simple and robust cells can be as narrow as a draft range of 0- 1/2 inH2O or as wide as 0-1,000 psid. Some electronic d/p cells can operate at line pressures up to 4,500 psig at 250°F. The drift and inaccuracy of some of these units have been tested for periods of up to 30 months, and the errors did not exceed the ±0.5% of span limit.

Difficult Process Fluids

When the process fluid is a sludge, a viscous polymer or is otherwise hard to handle, the goal is to isolate the dirty process from the d/p cell. A flat diaphragm can be bolted to a block valve on the tank nozzle so that the d/p cell can be removed for cleaning or replacement without taking the tank out of service. If it is acceptable to take the tank out of service when d/p cell removal is needed, an extended diaphragm design can be considered. In this case, the diaphragm extension fills the tank nozzle so that the diaphragm is flush with the inside surface of the tank. This eliminates dead ends or pockets where solids can accumulate and affect the performance of the cell. Flat and extended diaphragm-type d/p cells, pressure repeaters, and chemical seals are available to protect d/p cells under these conditions.

Chemical seals, or diaphragm pressure seals, are available with fill liquids such as water, glycol, alcohol, and various oils. These seals are used when plugging or corrosion can occur on both sides of the cell. A broad range of corrosion-resistant diaphragm and lining materials is available. PFA lining is often used to minimize material build-up and coating. Level measurement accuracy does suffer when these seals are used. Capillary tube lengths should be as short as possible and the tubes should be shielded from the sun. In addition, either low thermal expansion filling fluids should be used or ambient temperature compensation should be provided, as discussed in connection with wet legs. If the seals leak, maintenance of these systems is usually done at the supplier's factory due to the complex evacuation and backfilling procedures involved.

Bubbler Tubes

Bubbler tubes provide a simple and inexpensive but less accurate (±1-2%) level measurement system for corrosive or slurry-type applications. Bubblers use compressed air or an inert gas (usually nitrogen) introduced through a dip pipe (Figure 7-4A). Gas flow is regulated at a constant rate (usually at about 500 cc/min). A differential pressure regulator across a rotameter maintains constant flow, while the tank level determines the back-pressure. As the level drops, the

Figure 7-4: Click on figure to enlarge.

back-pressure is proportionally reduced and is read on a pressure gage calibrated in percent level or on a manometer or transmitter. The dip pipe should have a relatively large diameter (about 2 in.) so that the pressure drop is negligible. The bottom end of the dip pipe should be located far enough above the tank bottom so that sediment or sludge will not plug it. Also, its tip should be notched with a slot or "V" to ensure the formation of a uniform and continuous flow of small bubbles. An alternative to locating the dip pipe in the tank is to place it in an external chamber connected to the tank.

In pressurized tanks, two sets of dip pipes are needed to measure the level (Figure 7-4B). The two back-pressures on the two dip pipes can be connected to the two sides of a u-tube manometer, a differential pressure gage or a d/p cell/transmitter. The pneumatic piping or tubing in a bubbler system should be sloped toward the tank so that condensed process vapors will drain back into the tank if purge pressure is lost. The purge gas supply should be clean, dry, and available at a pressure at least 10 psi greater than the expected maximum total pressure required (when the tank is full and the vapor pressure is at its maximum). An alternative to a continuous bubbler is to use a hand pump (similar to a bicycle tire pump) providing purge air only when the level is being read.

Bubblers do consume inert gases, which can later accumulate and blanket processing equipment. They also require maintenance to ensure that the purge supply is always available and that the system is properly adjusted and calibrated. When all factors are considered, d/p cells typically are preferred to bubblers in the majority of applications.

Elevation & Suppression

If the d/p cell is not located at an elevation that corresponds to 0% level in the tank, it must be calibrated to account for the difference in elevation. This calibration adjustment is called zero elevation when the cell is located above the lower tap, and is called zero suppression or zero

Figure 7-5: Click on figure to enlarge.

depression when the cell is located below the lower tap. Most d/p cells are available with elevation and suppression ranges of 600% and 500% of calibrated span, respectively, as long as the calibrated span does not exceed 100% of the upper range limit of the cell.

For example, assume that an electronic d/p cell can be calibrated for spans between 0-10 psid (which is its lower range limit, LRL) and 0-100 psid (which is its upper range limit, URL). The cell is to be used on a 45-ft tall closed water tank, which requires a hydrostatic range of 0-20 psid. The cell is located about 11 feet (5 psid) above the lower tap of the tank; therefore, a zero elevation of 5 psid is needed. The d/p cell can handle this application, because the calibrated span is 20% of the URL and the elevation is 25% of the calibrated span.

On interface level measurement applications with a wet leg reference, the high pressure side of the d/p cell should be connected to the tank if the specific gravity of the wet leg filling fluid is close to that of the light layer. It should be connected to the reference leg if the wet-leg fluid's SG is closer to that of the heavy layer.

Special Applications

When the process fluid is boiling, such as in a steam drum, a wet reference leg is maintained by a condensate pot, which drains back into the steam drum so that the level of the wet leg is kept constant. Changes in ambient temperature (or sun exposure) will change the water density in the reference leg and, therefore, temperature compensation (manual or automatic) is needed.

Figure 7-5 describes a typical power plant steam drum level application. The differential pressure detected by the level d/p cell is:

Note that the SG of the saturated steam layer (0.03) and that of the saturated liquid layer (0.76) vary not only with drum pressure but also with steaming rate. This causes the swelling of bubbles when the steaming rate rises (and SG2 drops), as well as their collapse when the steaming rate drops (and SG2 rises). Therefore, to make an accurate determination of both the level and the mass of the water in the steam drum, the calculation must consider not only the d/p cell output, but also the drum pressure and the prevailing steaming rate.

Tank Farms

Computerized tank farm systems usually accept level signals from several tanks through field networks. These systems perform the level monitoring tasks using a variety of compensation and conversion algorithms. The algorithms provide density corrections, volumetric or mass conversions, and corrections to consider the shapes of horizontal, vertical or spherical tanks. These systems can perform safety functions, such as shutting off feed pumps to prevent overfilling.

Floats & Displacers

It was more than 2,200 years ago that Archimedes first discovered that the apparent weight of a floating object is reduced by the weight of the liquid displaced. Some 2,000 years later, in the late 1700s, the first industrial application of the level float appeared, when James Brindley and Sutton Thomas Wood in England and I. I. Polzunov in Russia introduced the first float-type level regulators in boilers.

Floats are motion balance devices that move up and down with liquid level. Displacers are force balance devices (restrained floats), whose apparent weight varies in accordance with Archimedes' principle: the buoyant force acting on an object equals the weight of the fluid displaced. As the level changes around

Figure 7-6: Click on figure to enlarge.

the stationary (and constant diameter) displacer float, the buoyant force varies in proportion and can be detected as an indication of level. Regular and displacer floats are available as both continuous level transmitters and point-sensing level switches.

In industrial applications, displacer floats are often favored because they do not require motion. Furthermore, force can often be detected more

Figure 7-7: Click on figure to enlarge.

accurately than position. However, regular floats are also used, mostly for utilities and in other secondary applications.

Float Level Switches

The buoyant force available to operate a float level switch (that is, its net buoyancy) is the difference between the weight of the displaced fluid (gross buoyancy) and the weight of the float. Floats are available in spherical (Figure 7-6A), cylindrical (Figure 7-6B), and a variety of other shapes (Figure 7-6C). They can be made out of stainless steel, PFA, Hastelloy, Monel, and various plastic materials. Typical temperature and pressure ratings are -40 to 80°C (-40 to 180° F) and up to 150 psig for rubber or plastic floats, and -40 to 260°C (-40 to 500°F) and up to 750 psig for stainless steel floats. Standard float sizes are available from 1 to 5 inches in diameter. Custom float sizes, shapes, and materials can be ordered from most manufacturers. The float of a side-mounted switch is horizontal; a permanent magnet actuates the reed switch in it (Figure 7-6B).

Floats should always be lighter than the minimum expected specific gravity (SG) of the process fluid. For clean liquids a 0.1 SG difference might suffice, while for viscous or dirty applications, a difference of at least 0.3 SG is recommended. This provides additional force to overcome the resistance due to friction and material build-up. In dirty applications, floats should also be accessible for cleaning.

Floats can be attached to mechanical arms or levers and can actuate electrical, pneumatic, or mechanical mechanisms. The switch itself can be mercury (Figures 7-6A and 7-6C), dry contact (snap-action or reed type, shown in Figure 7-6B), hermetically sealed, or pneumatic. The switch can

Figure 7-8: Click on figure to enlarge.

be used to actuate a visual display, annunciator, pump, or valve. The electric contacts can be rated light-duty (10-100 volt amps, VA) or heavy-duty (up to 15 A @ 120 Vac). If the switch is to operate a circuit with a greater load than the rating of the switch contacts, an interposing relay needs to be inserted. If the switch is to be inserted in a 4-20 mA dc circuit, gold-plated dry contacts should be specified to ensure the required very low contact resistance.

Applications & Installations

In the tilt switch (Figure 7-6C), a mercury element or relay is mounted inside a plastic float; the float's electrical cable is strapped to a pipe inside the tank or sump. As the level rises and falls, the float tilts up and down, thus opening and closing its electric contact. The free length of the cable determines the actuation level. One, two, or three switches can be used to operate simplex and duplex sump-pump stations. A simplex (one pump) system will use a single switch wired in series with the motor leads so that the switch directly starts and stops the pump motor (Figure 7-7).

A duplex (two pump) application might use three switches: one at the tank bottom (LO) to stop both pumps, another in the middle (HI) to start one pump, and the last at the top (HI-HI) to actuate the second pump, as well as perhaps an audible

Figure 7-9: Click on figure to enlarge.

and/or visual alarm.

Figure 7-8A illustrates how a side-mounted float switch might actuate an adjacent, sealed reed switch. The main advantage of this design is that the lever extension tends to amplify the buoyant force generated by the float. Therefore the float itself can be rather small. The main disadvantage is that the tank must be opened in order to perform maintenance on the switch. If the buoyant force of the float is used mechanically to actuate a snap-action switch, a force of only one ounce is needed.

In top (or bottom) mounted magnetic float switches (Figure 7-8B), the magnet is in the cylindrical float that travels up or down on a short vertical guide tube containing a reed switch. The float's motion is restrained by clips and can be only 1/2 in or less. These float and guide tubes are available with multiple floats that can detect several levels. The switch assembly itself can be either inserted directly into the tank or side-mounted in a separate chamber.

A magnetic piston operated switch also can be mounted in an external chamber (Figure 7-8C). As the magnet slides up and down inside a non-magnetic tube, it operates the mercury switch outside the tube. These switches are completely sealed and well suited for heavy duty industrial applications up to 900 psig and 400°C (750°F), meeting ASME code requirements. These

Figure 7-10: Click on figure to enlarge.

switches can be side, top, or cage mounted (Figure 7-9) and can serve both alarm and control functions on steam drums, feedwater heaters, condensate pots, gas/oil separators, receivers, and accumulators. Light-duty caged float switches are also available for service ratings up to 250 psig at 200°C (400°F) and 400 psig at 40°C (100°F)--suitable for many boilers, condensate receivers, flash tanks, day tanks, holding tanks, and dump valve controls. The cages can be provided with level gages. Multiple switches are available for multiple-switching applications such as boiler level alarms and controls.

Displacer Switches

Whereas a float usually follows the liquid level, a displacer remains partially or completely submerged. As shown in Figure 7-10A, the apparent weight of the displacer is reduced as it becomes covered by more liquid. When the weight drops below the spring tension, the switch is actuated. Displacer switches are more reliable than regular floats on turbulent, surging, frothy, or foamy applications. Changing their settings is easy because displacers can be moved anywhere along the suspension cable (up to 50 ft). These switches are interchangeable between tanks because differences in process density can be accommodated by changing the tension of the support spring.

Testing the proper functioning of a regular float switch may require filling the tank to the actuation level, while a displacer switch can be tested simply by lifting a suspension (Figure 7-10A). Displacer switches are available with heavy-duty cages and flanges for applications up to 5000 psig at 150°C (300°F), suitable for use on hydraulic accumulators, natural gas receivers, high pressure scrubbers, and hydrocarbon flash tanks.

Continuous Level Displacers

Displacers are popular as level transmitters and as local level controllers, particularly in the oil and petrochemical industries. However, they are not suited for slurry or sludge service because coating of the displacer changes its volume and therefore its buoyant force. They are most accurate and reliable for services involving clean liquids of constant density. They should be temperature-compensated, particularly if variations in process temperature cause significant changes in the density of the process fluid.

When used as a level transmitter, the displacer, which is always heavier than the process fluid, is suspended from the torque arm. Its apparent

Figure 7-11: Click on figure to enlarge.

weight causes an angular displacement of the torque tube (a torsion spring, a frictionless pressure seal). This angular displacement is linearly proportional to the displacer's weight (Figure 7-10B).

Standard displacer volume is 100 cubic inches and the most commonly used lengths are 14, 32, 48, and 60 in. (Lengths up to 60 ft are available in special designs.) In addition to torque tubes, the buoyant force can also be detected by other force sensors, including springs and force-balance instruments. When the buoyant force is balanced by a spring, there is some movement, while with a force-balance detector, the displacer stays in one position and only the level over the displacer varies.

Displacer units are available with both pneumatic and electronic outputs and can also be configured as local, self-contained controllers. When used in water service, a 100 cubic inch displacer will generate a buoyant force of 3.6 pounds. Therefore, standard torque tubes are calibrated for a force range of 0-3.6 lbf and thin-walled torque tubes for a 0-1.8 lbf range.

For oil refineries and other processes that are operated continuously, the American Petroleum Institute recommends (in API RP 550) that displacers be installed in external standpipes with level gages and isolating valves (Figure 7-11). This way it is possible to recalibrate or maintain the displacer without interrupting the process.

Interface Applications

When measuring the interface between a heavy liquid and a light liquid (such as oil on water), the top connection of the displacer is placed into the light and the bottom connection into the heavy liquid layer. If the output of such a transmitter is set to zero when the chamber is full of the light liquid, and to 100% when it is full with the heavy phase, the output will correspond to the interface level. Naturally, when interface is being measured, it is essential that the two connections of the displacer chamber be located in the two different liquid layers and that the chamber always be flooded. Displacer diameter can be changed to match the difference in liquid densities, and displacer length can be set to match the vertical range of the level interface variation.

Regular floats can also be used for interface detection if the difference in SG between the two process liquids is more than 0.05. In such applications, a float density is needed that is greater than the lighter liquid and less than the heavier liquid. When so selected, the float will follow the interface level and, in clean services, provide acceptable performance.

Continuous Level Floats

Of the various float sensor designs used for continuous level measurement, the oldest and arguably most accurate is the tape level gage (Figure 7-12A). In this design, a tape or cable connects the float inside the tank to a gage board or an indicating take-up reel mounted on the outside of the tank. The float is guided up and down the tank by guide wires or travels inside a stilling well. These level indicators are used in remote, unattended, stand-alone applications, or they can be provided with data transmission electronics for integration into plant-wide control systems.

To install the tape gage, an opening is needed at the top of the tank and an anchor is required at its bottom. When properly maintained, tape gages are accurate to ± 1/4 in. It is important to maintain the guide wires under tension, clean and free of corrosion, and to make sure that the tape never touches the protective piping in which it travels. If this is not done, the float can get stuck on the guide wires or the tape can get stuck to the pipe. (This can happen if the level does not change for long periods or if the tank farm is

Figure 7-12: Click on figure to enlarge.

located in a humid region.)

Another continuous level indicator is the magnetic level gage, consisting of a magnetic float that travels up and down on the inside of a long, non-magnetic (usually stainless steel) pipe. The pipe is connected to flanged nozzles on the side of the tank. The pipe column is provided with a visual indicator, consisting of -in triangular wafer elements. These elements flip over (from green to red, or any other color) when the magnet in the float reaches their level (Figure 7-12B). Alarm switches and transmitter options are available with similar magnetic coupling schemes (Figure 7-12C). In a similar design, a series of reed switches is located inside a stand-pipe. The change in output voltage as the individual reed switches are closed by the rising magnet is measured, giving an indication of level.

The operation of magnetostrictive sensors is based on the Villari effect. In the magnetic waveguide-type continuous level detector, the float (or floats, when detecting interface) travels concentrically up and down outside a vertical pipe. Inside the pipe is a concentric waveguide made of a magnetostrictive material. A low current interrogation pulse is sent down the waveguide, creating an electromagnetic field along the length of the waveguide. When this field interacts with the permanent magnet inside the float, a torsional strain pulse (or waveguide twist) is created and detected as a return pulse. The difference in the interrogation time and the return pulse time is proportional to the liquid level in the tank.

This tank level sensing method is highly accurate, to ±0.02 in, and therefore is ideal for precision inventory management operations. The sensor is available in lengths of 2-25 ft and can be inserted into the tank from the top of the vessel through flanged, screwed, or welded connections. For the simultaneous measurement of both interface and total level, a two-float system is available (Figure 7-12D). A resistance temperature detector (RTD) is also available for temperature compensation. Like all other float level instruments, this design too is for clean liquids. Rating is up to 150°C (300° F) and 300 psig. The transmitter output can be 4-20 mA dc analog or fieldbus-compatible digital.

Float Control Valves

Float-operated control valves combine level measurement and level control functions into a single level regulator. While simple and inexpensive, they are limited to applications involving small flows and small pressure drops across the valve. This is because the force available to throttle the valve is limited to that provided by the buoyant force acting on the float, multiplied by the lever action of the float arm. This does not suffice to close large valves against high pressure differentials.

Yet, for simple and unattended applications (like controlling the make-up water supply into a cooling tower basin or draining condensate from a trap), they are acceptable. It is important to understand that float regulators are simple proportional controllers: they are incapable of holding level at a single setpoint. What they can do is open or close a valve as the float travels through its control range. Therefore, instead of a setpoint, regulators have a throttling range. If the range is narrow (floats usually fully stroke their valve over a few inches of float travel), it gives the impression of a constant level.

In fact, level will vary over the throttling range because the only way for the regulator to increase the feed flow (say into a cooling tower basin) is to first let the level drop so that the sinking of the float will further open the valve. The relationship between the maximum flow through a linear valve (Qmax) and the range in liquid level (h) is called the proportional sensitivity of the regulator (Kc = Qmax/h), expressed in units of GPM/inch. The offset of a float regulator is the distance (in inches) between the center of the float range and the amount of elevation of the float required to deliver the flowrate demanded by the process.

References & Further Reading
OMEGA Complete Flow and Level Measurement Handbook and Encyclopedia®, OMEGA Press, 1995.
OMEGA Volume 29 Handbook & Encyclopedia, Purchasing Agents Edition, OMEGA Press, 1995.
Instrument Engineer's Handbook, Bela G. Liptak, editor, CRC Press, 1995.
Instrumentation for Process Measurement and Control, Third Edition, N. A. Anderson, Chilton, 1980.
Measurement and Control of Liquid Level, C. H. Cho, Instrument Society of America, 1982.
Principles of Industrial Measurement for Control Applications, E. Smith, Instrument Society of America, 1984.