The document discusses various principles and technologies for level measurement. It describes how differential pressure, bubblers, displacers, floats, RF admittance & capacitance, ultrasonic, radar, and nuclear technologies can be used to measure level. It also provides equations for calculating level using principles like hydrostatic pressure, open-tank head measurements, and electrical capacitance. A table compares different technologies for measuring level in liquids, granular materials, and slurries. In addition, the document outlines other technologies like time domain reflectometry, magnetostrictive, conductance, and float switches.

1. 5
Level Measurement
Principles of Level Measurement & Theory . . . . . . . . . . . . . . . . . . 163
Important Level Measurement Technologies . . . . . . . . . . . . . . . . . 164
• Differential Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
• Bubblers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
• Displacers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
• Floats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
• RF Admittance & Capacitance . . . . . . . . . . . . . . . . . . . . . . . . 165
• Ultrasonic/Sonic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
• Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
• Nuclear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
• Table Comparing Level Measurement Technologies . . . . . 167
• Time Domain Reflectometry (TDR) . . . . . . . . . . . . . . . . . . . . 167
• Magnetostrictive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
• Hydrostatic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
• Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
• Float Switch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Level Measurement Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Dielectric Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Weight of Water versus Temperature . . . . . . . . . . . . . . . . . . . . . . . 177
Sound Absorption Coefficient of a Material . . . . . . . . . . . . . . . . . . 179
Radiation Field Intensity in Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

2. Chapter 5/Level Measurement 163
Principles of Level Measurement
Instrument suppliers offer more than 20 different level measurement
technologies. All work, when properly applied. However, each has its
strengths and its weaknesses, and some are not suitable for certain
applications.
Theory
For a given acceleration of gravity, the liquid head in a tank or vessel
generates a force per unit area or pressure (P) that is directly propor-tional
to the liquid level (L) above the measurement point times the
average density (ρ) of the liquid in the column. Solving for L:
L = P/ρ
While this formula is simple, its usage can be complicated. Virtually all
applications using pressure transmitters for liquid level include one or
more of the following issues:
• Transmitter is not located at the zero level point
• Transmitter is remote from the tank, above or below the
primary pressure connection
• Transmitter is isolated from process fluid with a flange or seal
system
• Tank is closed and, hence, subject to pressure or vacuum above
the liquid
• The fluid above the liquid may be the vapor of the liquid itself or
an outside sourced fluid, such as a nitrogen blanket
• Tank pressure reference connection is filled with a vapor (dry leg)
• Tank pressure reference connection is filled with liquid (wet leg)
• External wet legs can exist on both high and low pressure sides
of the transmitter
• Environmental conditions can be different for each of these
external legs
• Environmental conditions are usually different than tank
conditions, e.g., a wet leg temperature might be very different
from the in-tank temperature
• Plus, changes in liquid and vapor densities.
Reference: Dudley Harelson and Jonathan Rowe, Foxboro Division, Invensys, Multivariable Transmitters:
A New Approach to Liquid Level Measurement. Copyright 2004 by ISA. Presented at ISA 2004.

3. 164 ISA Handbook of Measurement Equations and Tables
Important technologies used in level measurement include:
Differential Pressure
Among the most frequently used devices for measuring level, differen-tial
pressure (d/p) transmitters do not measure level by themselves.
Instead, they measure the head pressure that a diaphragm senses due
to the height of material in a vessel. That pressure measurement is mul-tiplied
by a second variable, the product’s density. That calculation
shows the force being exerted on the diaphragm, which is then trans-lated
into a level measurement. Errors can occur, however, due to den-sity
variations of a liquid, caused by temperature or product changes.
These variations must always be compensated for if accurate measure-ments
are to be made. DPs are primarily used for clean liquids and
should not be used with liquids that solidify as their concentrations
increase, such as paper pulp stock.
Bubblers
This simple level measurement has a dip tube installed with the open end
close to the bottom of the process vessel. A flow of gas (usually air) passes
through the tube. When air bubbles escape from the open end, the
air pressure in the tube corresponds to the hydraulic head of the liquid in
the vessel. The air pressure in the bubble pipe varies proportionally
with the change in head pressure. Calibration is directly affected
by changes in product density, however. Because of this, it becomes a
mass measurement.
Displacers
When a body is immersed in a fluid, it loses weight equal to the liquid
weight displaced (Archimedes Principle). By detecting the apparent
weight of the immersed displacer, a level instrument can be devised. If the
cross sectional area of the displacer and the density of the liquid is con-stant,
then a unit change in level will result in a reproducible unit change
in displacer weight. Displacers also are affected by changes in product
density. They should only be used for relatively non-viscous, clean fluids
and work best for short spans.
Floats
Level measuring devices that use a float resting on the surface of the
measured process fluid are legion. Many commodes use a simple, float-driven,
on/off switch, water-leveling apparatus. As the liquid in a process
rises and falls in its vessel, the float rises and falls as well. Indicators
advise the operator and/or the automation links as to the liquid’s level. The
float may directly and mechanically trip a switch, push a magnet, pull a
lever, or raise a pointer. Floats are made of brass, copper, stainless steel,
and many types of plastics, among other materials.

4. Chapter 5/Level Measurement 165
Float technology advantages include low cost, if remote reading is
required; adaptability to wide variations in fluid densities; the ability to
be used in extreme process conditions; unlimited tank height; and high
accuracy.
Disadvantages can include high maintenance requirements; vulnerability
to particulate or product deposition; moving parts exposed to fluids;
limited pressure rating; and not good for use in agitated vessels and for
granular products.
RF Admittance & Capacitance
For applications permitting contact with what’s being measured, radio fre-quency
(RF) is perhaps the most versatile technology for continuous level
measurement. RF uses a constant voltage applied to a rod or cable (sens-ing
element) in the process. The resulting RF current is monitored to infer
the level of the process material. RF technologies handle a wide range of
process conditions – from cryogenics to 1,000°F and from vacuum to 10,000
psi pressure. It can withstand severe service in harsh corrosive environ-ments.
RF also is the most preferred technology for point level measure-ment,
able to achieve short span measurement accuracies many other
technologies cannot achieve. As an intrusive technology, however, insu-lating
granular measurements require special considerations, such as
the moisture range and location of the sensing element to minimize
errors caused by probe movement.
Ultrasonic/Sonic
Ultrasonic transmitters send a sound wave from a piezoelectric transducer
to the contents of the vessel. The device measures the length of time it
takes for the reflected sound wave to return to the transducer. A success-ful
measurement depends on reflection from the process material in a
straight line back to the transducer. Ultrasonic’s appeal is the transducer
does not come in contact with the process material and does not contain
any moving parts. Ultrasonic technology was the first industrially
accepted non-contact level measurement in the process control market.
Today’s ultrasonic devices typically require no calibration and can provide
high accuracy level measurements in both liquid and solids applications.
However, excessive process temperatures and pressure can be a limiting
factor. And, since ultrasonic technology is based on a traveling sound
pressure wave, a constant velocity via its media (air) is required to assure
a high degree of accuracy. Material such as dust, heavy vapors, surface
turbulence, foam and even ambient noise can affect the returning signal.
Because sound travels at a constant known velocity at a given tempera-ture,
the time between the transmit burst and detection of the return echo

5. 166 ISA Handbook of Measurement Equations and Tables
will be proportional to the distance between the sensor and the reflecting
object. The distance between the two can be calculated from:
Distance = Rate x Time
Radar
Radar technology broadened non-contact level technology options.
Radar’s inherent accuracy with its ability to have a more narrow beam
angle avoided many vessel internal obstructions from reflecting false
level signals. Radar is unaffected by vapors, steams, and many of the
undesired affects of condensation that can affect ultrasonic devices.
Properly applied, radar is completely capable of measuring most liquids
and solids level applications. Frequency modulated continuous wave
(FMCW) is fast enough for tank gauging, but normally too slow to meas-ure
the turbulent surfaces encountered in agitated process applications.
Like ultrasonic, radar does not require calibration.
Nuclear
Nuclear level controls are used for continuous measurements, typically
where most other technologies are unsuccessful. For example, they are
extremely suitable for applications involving high temperatures and pres-sures,
or corrosive materials within the vessel. No tank penetration is
needed. Radiation from the source penetrates through the vessel wall and
process fluid. A detector on the other side of the vessel measures the radi-ation
field strength and infers the level in the vessel. The basic unit of radi-ation
intensity is the curie, defined as that source intensity which under-goes
3.70 x 1010 disintegrations per second. For industrial applications,
radiation field intensity is normally measured in milliroentgens per hour.
Radiation field intensity in air can be calculated from:
D
KM
d
= 1000 c 2
where
D = radiation intensity in milliroentgens per hour (mR/hr)
Mc = source strength in millicuries (MCi)
d = distance to the source in inches
K = source constant (0.6 for cesium 137; 2.0 for cobalt 60)

6. Chapter 5/Level Measurement 167
Technology Liquids Granulars Slurries Interfaces
RF Admittance O.K. Use Caution O.K. O.K.
Ultrasonic O.K. Use Caution O.K. Not Practical
Radar O.K. Use Caution O.K. Not Practical
Differential
O.K. Not Practical Use Caution Use Caution
Pressure
Displacers O.K. Not Practical Use Caution Use Caution
Bubblers O.K. Not Practical Use Caution Not Practical
Nuclear O.K. Use Caution O.K. Use Caution
Courtesy of Ametek Drexelbrook. M. Bahner, A Practical Overview of Level Measurement Technologies. Reprinted
with permission.
Other level measurement technologies include:
Time Domain Reflectometry (TDR)
Another contacting level measurement technology, TDR is also known
by trade names such as “guided wire radar,” “radar on a rope,” “reflex
radar,” etc. TDR is a pulse time of flight measurement much like ultra-sonic
and some radar techniques. Like radar, it transmits an electro-magnetic
pulse that travels at the speed of light to the surface of the
material to be measured. It has a more narrow beam, or pulse width,
than radar since it is completely focused on a flexible wire or rod. The
measurement is determined by the transit time divided in half. TDR also
does not require calibration.
Magnetostrictive
Magnetostrictive technology allows very high-accuracy level measure-ments
of non-viscous liquids at ranges up to 50 feet. The technology is
based on a float with embedded magnets that rides on a tube that con-tains
magnetostrictive wire pulsed with a low voltage, high current elec-tronic
signal. When this signal intersects the magnetic field, generated by
the float, a torsional pulse is reflected back to the electronics. This creates
a time of flight measurement. Magnetostrictive devices require no calibra-tion
and no maintenance when properly applied.
Hydrostatic Pressure
A well-established level measurement method, hydrostatic pressure
technology’s basic principle is measuring total head pressure above a
pressure-sensing diaphragm. Measuring water in below-ground wells
is a major application.

7. 168 ISA Handbook of Measurement Equations and Tables
Conductance
Conductivity devices are primarily used for point level measurement.
Materials being measured using conductivity switches must be conduc-tive.
Typically, conductivity switches are used to measure high and/or
low level in liquids such as water, acids, conductive chemicals, etc. The
conductivity electrodes are connected to a relay to provide control and
require little or no calibration.
Float Switch
One of the oldest methods of level measurement, float devices continue
to be used because they are simple to apply and cost effective on
appropriate applications. Because floats are a mechanical level switch,
it is important to use them in applications where coating build up will
not occur. Clean, noncoating liquids are typically good applications for
float measurement.
Variable Displacement Measuring Devices
V
π 2
4
= L
where
V = volume of the displacer
D = diameter of the displacer
L = length of displacer
D
( )
To Determine the Weight of the Displacer
Ww
= (G )
where
Ww = weight of displacer
V = volume of displacer
Gv = volume of a gallon, H2O
Gw = weight of a gallon, H2O
V
G
v
w
References:
1. Ametek Drexelbrook brochure: Level Measurement Solutions …For Every Application.
2. Gillum, Donald R., Industrial Pressure, Level and Density Measurement , ISA—The Instrumentation,
Systems, and Automation Society, 1995.

8. Hydrostatic Head Level
Measurement
p
F
A
=
where
p = pressure on supporting sur-face
F = weight, H2O
A = area of supporting surface
Open-Tank Head-Type Level
Measurement
where
p = pressure corrected for
atmosphere pressure
G = specific gravity
h = vertical height of a column
F = weight, H2O
A = area of supporting surface
Electrical Level Measurement,
Total System Capacitance
CE = C1 +C2 +C3
where
C
. ( − )
log
0 614 1
=
. ( )()
log
K p
l
D
d
3
0 614
=
10
C
K L
D
d
a
2
10
p
F
A
=
P = pGh
Chapter 5/Level Measurement 169
Principles of Level Measuring Devices

9. 170 ISA Handbook of Measurement Equations and Tables
C1 = gland capacitance
C2 = vapor phase capacitance
C3 = liquid phase capacitance
Ka = dielectric constant, vapor phase
Kp = dielectric constant, liquid phase
L = vessel height
l = level height
D = diameter of vessel
d = probe diameter
Hydrostatic Level Measurement in an Open Tank

10. Electrical Level Measurement
C
KA
D
=
where
C = capacitance in microfarads
K = the dielectric constant
A = the area of the plates
D = the distance between plates
Chapter 5/Level Measurement 171
Capacitor Probe in a Tank Probe
in Nonconductive Fluid
Equivalent Capacitance

11. 172 ISA Handbook of Measurement Equations and Tables
Dielectric Constants of Solids
Acetic Acid (36°F) 4.1
Aluminum Phosphate 6.1
Asbestos 4.8
Asphalt 2.7
Bakelite 5.0
Barium Sulfate (60°F) 11.4
Calcium Carbonate 9.1
Cellulose 3.9
Cereals 3-5.0
Ferrous Oxide (60°F) 14.2
Glass 3.7
Lead Oxide 25.9
Lead Sulfate 14.3
Magnesium Oxide 9.7
Mica 7.0
Napthalene 2.5
Nylon 45.0
Paper 45.0
Phenol (50°F) 2.0
Polyethylene 4-5.0
Polypropylene 1.5
Porcelain 5-7.0
Potassium Carbonate (60°F) 5.6
Quartz 4.3
Rice 3.5
Rubber (hard) 3.0
Sand (Silicon Dioxide) 3-5.0
Sulphur 3.4
Sugar 3.0
Urea 3.5
Zinc Sulfide 8.3

12. Chapter 5/Level Measurement 173
Dielectric Constants of Granular and Powdery Materials
Material Loose Packed
Fly Ash 1.7 2.0
Coke 65.3 70.0
Oatmeal 1.47
Molecular 5A, Sieve Dry 1.8
Polyethylene 2.2
Polyethylene, Powder 1.25
Reclaimed Foundry Sand 4.8 4.8
Laundry Detergent 1.3 to 1.7 1.3 to 1.25

13. 174 ISA Handbook of Measurement Equations and Tables
Dielectric Constants of Liquids
Material Temp. °F Constant
Acetone 71 21.4
Ammonia -30 22.0
Ammonia 68 15.5
Aniline 32 7.8
Aniline 68 7.3
Benzene 68 2.3
Bromine 68 3.1
Butane 30 1.4
Carbon Dioxide 32 1.6
Carbon Tetrachloride 68 2.2
Castor Oil 60 4.7
Chlorine 32 2.0
Chlorocyclohexane 76 7.6
Chloroform 32 5.5
Cumene 68 2.4
Cyclohexane 68 2.0
Dibromobenzene 68 8.8
Dibromohexane 76 5.0
Dowtherm 70 3.36
Ethanol 77 24.3

14. Chapter 5/Level Measurement 175
Dielectric Constants of Liquids (cont.)
Material Temp. °F Constant
Ethyl Acetate 68 6.4
Ethylene Chloride 68 10.5
Ethyl Ether -40 5.7
Ethyl Ether 68 4.3
Formic Acid 60 58.5
Freon-12 70 2.4
Glycerine 68 47.0
Glycol 68 41.2
Heptane 68 1.9
Hexane 68 1.9
Hydrogen Chloride 82 4.6
Hydrogen Sulfide 48 5.8
Isobutyl Alcohol 68 18.7
Kerosine 70 1.8
Methyl Alcohol 32 37.5
Methyl Alcohol 68 33.1
Methyl Ether 78 5.0
Naphthalene 68 2.5
Octane 68 1.96
Oil, Transformer 68 2.2

15. 176 ISA Handbook of Measurement Equations and Tables
Dielectric Constants of Liquids (cont.)
Material Temp. °F Constant
Pentane 68 1.8
Phenol 118 9.9
Phenol 104 15.0
Phosphorus 93 4.1
Propane 32 1.6
Styrene (Phenylethene) 77 2.4
Sulphur 752 3.4
Sulphuric Acid 68 84.0
Tetrachloroethylene 70 2.5
Toluene 68 2.4
Trichloroethylene 61 3.4
Urea 71 3.5
Vinyl Ether 68 3.9
Water 32 88.0
Water 68 80.0
Water 212 48.0
Xylene 68 2.4

16. Chapter 5/Level Measurement 177
Weight of One Gallon (U.S.) of Water at Various Temperatures
Temp.
Wt. in Vacuum
Wt. in Vacuum
Wt. in Air
°C
Grams
Pounds
Grams
Wt. in Air
Pounds
0 3784.856 8.34417 3780.543 8.33467
1 3785.078 8.34466 3780.781 8.33518
2 3785.233 8.34500 3780.953 8.33556
3 3785.326 8.34520 3781.060 8.33580
4 3785.355 8.34527 3781.105 8.33590
5 3785.325 8.34520 3781.090 8.33587
6 3785.235 8.34500 3781.015 8.33570
7 3785.089 8.34468 3780.884 8.33541
8 3784.887 8.34424 3780.698 8.33500
9 3784.633 8.34368 3780.358 8.33447
10 3784.326 8.34300 3780.167 8.33383
11 3783.966 8.34221 3779.821 8.33307
12 3783.557 8.34130 3779.426 8.33220
13 3783.099 8.34030 3778.983 8.33122
14 3782.597 8.33919 3778.495 8.33014
15 3782.049 8.33798 3777.962 8.32897
16 3781.458 8.33668 3777.415 8.32770
17 3780.824 8.33528 3776.764 8.32633
18 3780.148 8.33379 3776.103 8.32487
19 3779.430 8.33221 3775.398 8.32332
20 3778.672 8.33054 3774.653 8.32167
21 3777.873 8.32877 3773.868 8.31994
22 3777.035 8.32693 3773.044 8.31813
23 3776.158 8.32499 3772.180 8.31622
24 3775.243 8.32298 3771.279 8.31424

17. 178 ISA Handbook of Measurement Equations and Tables
Weight of One Gallon (U.S.) of Water at
Various Temperatures (cont.)
Temp.
°C
Wt. in Vacuum
Grams
Wt. in Vacuum
Pounds
Wt. in Air
Grams
Wt. in Air
Pounds
25 3774.291 8.32088 3770.340 8.31217
26 3773.320 8.31870 3769.364 8.31001
27 3772.277 8.31644 3768.352 8.30778
28 3771.218 8.31410 3767.306 8.30548
29 3770.123 8.31169 3766.224 8.30309
30 3768.995 8.30920 3765.109 8.30063
31 3768.995 8.30664 3763.961 8.29810
32 3766.641 8.30401 3762.780 8.29550
33 3765.416 8.30131 3761.568 8.29283
34 3764.160 8.29854 3760.324 8.29008
35 3762.874 8.29571 3759.050 8.28728
40 3756.018 8.28059 3752.255 8.27230
45 3748.41 8.2638 3744.42 8.2550
50 3740.19 8.2457 3736.22 8.2369
55 3731.34 8.2261 3727.37 8.2174
60 3721.91 8.2054 3717.95 8.1966
65 3711.88 8.1832 3707.93 8.1745
70 3701.35 8.1600 3697.42 8.1514
75 3690.30 8.1357 3686.38 8.1270
80 3678.72 8.1101 3674.81 8.1015
85 3666.68 8.0836 3662.78 8.0750
90 3654.15 8.0560 3650.27 8.0474
95 3641.21 8.0274 3637.34 8.0189
100 3627.81 7.9979 3623.95 7.9894

18. Sonic and Ultrasonic Level Measurement
Sound Absorption Coefficient of a Material
d
S
S
a
s
=
where
d = sound absorption coefficient
Sa = sound energy absorbed
Ss = sound energy incident upon the surface
Radiation Used in Level Measurement
Radiation Field Intensity in Air
D
where
D = radiation intensity in mR/hr
Mc = source strength in millicurie
d = distance to the source, inches
K = the source constant
1.3 for radium 226
0.6 for cesium 137
2.0 for cobalt 60
KM
d
= 1000 c 2
Chapter 5/Level Measurement 179