# Application of Archimedes Principle 5 Instrumentation for

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```							5. Instrumentation for level measurements

An accurate level measurement is crucial for the evaluation of the quantity of materials, phase
boundaries, etc. in storage and processing vessels (tanks, wells, reservoirs, columns, etc.). This
apparatus may operate under high pressure, under vacuum or at atmospheric pressure at various
temperatures. Substances may be as follows: liquids, vapours, gases, solids and their combination.
These substances may be corrosive and aggressive. All the above mentioned creates difficulties
for level measurement in industrial environment. We'll consider several widely used instruments.

5.1. Float actuated devices

Float actuated devices measure liquid level using a float, which lies on the surface of the liquid
and changes its position as the liquid level varies. Fig. 5.1 presents a schematic view of a float-
actuated device.

4
Fa
3

5
Fw, c, fr
8

2
hmin
1

hmax
Ffl

hmin
X
hmax       7    6

Figure 5.1. Schematic diagram of a float-and-cable actuated device.

The level of the liquid 1 in the tank 2 is under measurement. A sensitive element 3 (a float of a
cylindrical shape) is placed on the surface of this liquid. This sensor is connected through a cable
4 and two rotating wheels 5 with a balancing weight 6. A position of the balancing weight and a

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pointer 7, attached to it, in respect to a scale 8 determines the level of the liquid in the tank.
Density of the float should be less that that of the liquid. Usually, plastic materials are used for
manufacturing of floats.
Application of these devices assumes that the float is immersed in the liquid by the middle of its
height. Therefore, when density of the liquid changes an error introduces into results of level
measurement. Let’s calculate this error. The condition of balance for the float may be written in
the form:

F fl   Fw,c, fr  FA  0 ,                                   (5.1)
where,

F fl  m fl * g loc                    - gravitational force acted on the float, N ;

 Fw,c, fr                             - resultant force from the balancing weight, cable and friction
in the wheels, N ;
FA                             liq
liq * g loc * S fl * h fl    
- Archimedes’ force acted on the float, N ;
  gas * g loc * S fl * h gas
fl
m fl                                   - mass of the float, kg ;
m
g loc                                  - local gravitational acceleration,      ;
s2
 liq ,  gas                          - density of the liquid under the float and gas (or vapour) above it,
kg
respectively,        ;
m3
2
S fl                                   - horizontal cross-section area of the float, m ;
h liq , h gas
fl      fl                           - heights of the float parts in the liquid and in the gas (or vapour)
above it, respectively,    m.
Equation (5.1) can be re-written as follows:

F fl  Fw,c, fr  (  liq g loc S fl h liq   gas g loc S fl h gas )  0
fl                       fl                 (5.2)

Let for the unchanged level the density of the liquid has increased by the value of  liq . Then,
the depth of immersion of the float into the liquid and gas (or vapour) will change by the value of
 h liq , where the sign “+” stands for the immersion of the float into the gas (or vapour) and the
fl

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sign “-“ stands for the immersion of the float into the liquid. Taking into account that

( F fl  Fw,c, fr ) does not change considerably.

hliq  const ;                         gas  const ;                                       liq   liq ;

hliq  hliq ;
fl      fl                           h gas  h gas .
fl       fl

We can re-write equation (5.2) as follows:

                                                                                          
F fl  Fw,c, fr  (  liq   liq ) g loc S fl (h liq  h liq )   gas g loc S fl (h gas  h gas )  0 ,(5.3)
fl       fl                          fl       fl

Let Ffl  Fw, c, fr  const . Then:

 liq g loc S fl h liq   gas g loc S fl h gas  (  liq   liq ) g loc S fl (h liq  h liq ) 
fl                       fl                                     fl       fl
(5.4)
  gas g loc S fl (h gas  h gas )  0
fl       fl

Neglect the variation of the Archimedes’ force acting from gas on the float, or

 gas g loc S fl h gas   gas g loc S fl (h gas  h gas ) .
fl                        fl       fl                               (5.5)

Now we get:

 liq g loc S fl h liq  (  liq   liq ) g loc S fl (h liq  h liq ) ,
fl                                     fl       fl                  (5.6)
or
liq hliq  ( liq  liq )(hliq  hliq ) .
fl                      fl      fl                                     (5.7)

Finally, we get an error due to change in liquid density:

 liq
h liq  h liq *                    .                                        (5.8)
fl      fl
 liq   liq

These devices have a simple design, high accuracy, wide range of measuring levels and the
possibility of level measurement for aggressive and viscous liquids. However, they are not able to
measure levels in tanks under pressure.

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5.2. Displacer (buoyancy) devices

This method is based on the application of the Archimedes' principle: every body immersed in the
liquid or gas is exposed to the action of a buoyant force (sometimes called as the Archimedes'
force), which acts upwards. This force is equal to the weight of the liquid, gas or vapour
displaced by this body. The immersed body is called a buoy, thus giving the name to the method
of measurement. Fig. 5.2 presents a schematic of this type of device.

4
20-100kPa

4-20mA dc
Fa
3
5
2

hbg
1

hmax
hbl

Fb
hmin
X

Figure 5.2. Buoyancy-type level transmitter.

To measure the level of liquid 1 in a tank 2 a buoy 3 is partly immersed in the liquid. When the
level varies so does the resultant force acting on the buoy as follows:
Fres  Fb  FA                                  (5.9)
where,
Fb  mb g loc                  - gravitational force acted on the buoy, N ;
FA   liq g loc S b hb
liq

- the Archimedes’ force acted on the buoy, N ;
                  gas
gas g loc S b hb

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mb                             - mass of the buoy, kg ;
m
g loc                          - local gravitational acceleration,       ;
s2
 liq ,  gas                  - density of the liquid and the gas (or vapour) above it, respectively,
kg
;
m3
2
Sb                             - a horizontal cross-section area of the buoy, m ;
hb , hbgas
liq
- parts of buoy length in the liquid and in the gas above it,
respectively, m .

Fres  mb g loc  (  liq g loc S b hb   gas g loc S b hbgas ) .
liq
(5.10)

Since the Archimedes’ force acting from the gas on the buoy is negligible comparing with that
from the liquid, and the gravitational force is constant, then the resultant force is proportional to
liq
hb , and, hence, to the level of the liquid.

The displacer element, buoy, is a cylinder of a constant cross-section area, and its density is
greater than that of the liquid. The buoy moves up or down, depending on the level variation. The
resultant force through a lever 4 is converted by a force-balance or electronic transmitter 5 to a
proportional pneumatic (20-100 kPa) or electrical (4-20 mA dc) signal, which is transmitted by
the distance. It means that for each value of the level in the tank will correspond the certain value
of an output signal. The length, diameter, material of the buoy and transmission ratio can be
changed to suit various spans and various liquids. These instruments are used for measurements
of liquid level and interface providing the level to vary within the length of the buoy, and for
density measurements providing the buoy is fully immersed in liquid in the entire range of
measured densities.

It is appropriate now to consider an operational principle of a pneumatic transmitter, which is
used for converting level variations into the standard pneumatic signal. To be more precise, these
transmitters can be used to convert a mechanical motion (which may be caused by the variation of
any process variable) into the standard pneumatic signal. Fig. 5.3 shows a schematic view of the
pneumatic transmitter.

When level of the liquid goes up, the Archimedes’ force moves the buoy 1 in the same direction.
A membrane 2 separates the measuring part of the pneumatic transmitter from the part with a
high process pressure in the tank where the level is to be measured. The motion of the buoy
through levers 3 (rotates clockwise) and 4 (rotates clockwise) transmits to the force bar 5 (rotates

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clockwise). The force bar is connected with the flapper 6, which approaches to the nozzle 7. The
pressure supplied to a pneumatic amplifier 8 is equal to 140 kPa. The pressure from this amplifier
is fed to the nozzle, and then to atmosphere. When the flapper approaches to the nozzle, the
pressure in the nozzle increases. This pressure enters the pneumatic relay in the pneumatic
amplifier, where it is amplified, and so the value of the output pressure increases. The output
pressure is transmitted to a measuring or controlling instrument, and is applied to the feedback
bellows 9, thus increasing the counterclockwise moment of force acting from the lever 10 (rotates
clockwise) on the force bar 5. This moment of force is sufficient to restore the force bar to the
balance. When the balance has reached the output pressure is linearly related to the value of the
measured liquid level. A gain adjustment holder 11 is used for the variation of the measuring
range. An additional weight 12 is used for damping the vibration of levers. Zero adjustment can
be achieved by the spring 13.

5.2.1. Flapper-nozzle system

Fig. 5.3 shows a flapper-nozzle system and Fig. 5.4 shows a relationship between the output
pneumatic signal and the distance between the flapper and the nozzle.

The diameter of the supply restriction 1 is 0.2-0.3 mm, whereas that of the nozzle 2 is 0.8 mm.
The distance between the flapper 3 and the nozzle determines the output pressure in the chamber
between them. This pressure is measured by the pressure gauge 4. Small nozzle diameters
increase gain, but also increase the danger of clogging. Large nozzle diameters increase the air
consumption. The variation of the nozzle clearance by 0.04 mm gives the change in the output
pressure from 20 to 100 kPa. Formulars below are taken from(from Bentley J. P. Principles of
Measurement Systems, Longman, 1995, p. 315):

Fout  For  Fn                                           (5.11)

Pout V  nRT
abs
(5.12)

n  (mass _ in _ g / molecular _ weight ) 
 (mass _ in _ kg *103 / molecular _ weight )                     (5.13)
1000m

w
wV
mout               abs
* Pout                                    (5.14)
1000RT

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12

14

10

4       9              6
5
3

11
7
2

Pout=20-100 kPa

1                          13       8
Psup=140 kPa

Figure 5.3. A pneumatic transmitter.

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Output                                               Nozzle
gage
pressure, P            ;                 x           clearance
out
Volume, V
Patm

Fout
Dor
Dn
gage                                           For             Fn
Ps                       = 140 kPa

1                                          2    3

Figure 5.4. A flapper-nozzle system.
1 - restriction, Dor = 0.2 mm;                  2 - nozzle, Dn = 0.8 mm;                       3 - flapper.

140

120                                                                                 Series1
Output pressure, kPa

100

80

60

40

20

0
0.00            0.02          0.04                 0.06               0.08               0.10
Displacement, mm

Figure 5.5. Nozzle air pressure vas distance between the flapper and the nozzle.

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wV    dP abs
Fout           * out                                     (5.15)
1000RT   dt


For  C d       D or 2  air ( Psabs  Pout )
2                      abs
(5.16)
4

Fn  Cd Dn x 2  air ( Pout  Patm )
abs
(5.17)

abs
dPout
For the steady state condition:                    0 and Fout  0 (from Bentley J. P. Principles of
dt
Measurement Systems, Longman, 1995, p. 316):.

So,        For  Fn ,   and

2
Dor
( Psgage  Pout )  Dn x Pout
gage          gage
(5.18)
4
Finally,
Psgage
Pout 
gage
(5.19)
2
Dn x 2
1  16 4
Dor

C d  0 .6                    - discharge coefficient;
2
Dn                            - diameter of the nozzle, m ;
2
Dor                           - diameter of the orifice (restriction), m ;
kg
Fn                            - mass flowrate of air through the nozzle,       ;
s
kg
For                           - mass flowrate of air through the orifice,      ;
s
kg
Fout                          - mass flowrate of air in transmission line,       ;
s
m                             - mass of air, kg ;
n                             - number of moles of air in volume V ;

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V  3.2 *10 3 , m3             - volume of air;
gage
Patm , Pout , Psgage            - atmospheric pressure, output and supply air pressure (age), Pa ;
abs
Pout , Psabs                    - absolute output and supply air pressure (gauge), Pa ;
J
R  8.314,                      - ideal gas constant;
K * mol
T                               - absolute ambient temperature, K ;
kg
w  29,                         - molecular weight of air;
kmol
x                               - displacement of flapper,     m;
kg
 air  1.0,                    - density of air.
m3

5.2.2. Pneumatic relay amplifier

gage
(5.20)

and                                      Frest  ky                                         (5.21)

So,                                      y             gage
Pout                                  (5.22)
k
where,

2
Adiaf                    - the area of the diaphragm, m ;
Fdefl                    - resultant deflecting force on the diaphragm, N ;
Frest                    - spring restoring force, N ;
N
k                        - effective stiffness of the diaphragm,      ;
m
y                        - deflection of the diaphragm,   m.

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Pline
gage
K relay               from _ 1 _ to _ 20                       (5.23)
Pout
gage

Psgage = 140 kPa                                    Fs

F s,amp
3
6

gage
P       line

5
F line

F vent
y                                                         Fn
gage
4                                 P         out   F out
x

2        1

Figure 5.6. Pneumatic relay amplifier (from Bentley J. P. Principles of Measurement Systems,
Longman, 1995, p. 317):.

1       - flapper;
2       - nozzle;
3       - orifice;
4       - diaphragm;

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5          - double vent;
6          - transmission line.

5.2.3. Simplified model of pneumatic torque-balance transmitter
(from Bentley J. P. Principles of Measurement Systems, Longman, 1995, p. 319-320):

gage
Ps        = 140 kPa

7

gage
P      line

gage
Vent                      P   out

gage
F                                     P       line

4

b                      a
x

F0
1       2                     3                                    6          5

Figure 5.7. Pneumatic torque-balance transmitter.

1       – beam;
2       - pivot;

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3      - negative feedback bellows;
4      - nozzle;
5      - flapper;
7      - pneumatic relay amplifier.
Anticlockwise moments:              TACM  Fb  F0 a .                                (5.24)

Clockwise moment:                      TCM  P gage Abel a .
line                                    (5.25)

a). Condition of a perfect torque balance:

Pline Abel a  Fb  F0a .
gage
(5.26)

A simple model for a torque-balance transmitter:

b       F
Pline 
gage
F 0 .                                 (5.27)
aAbel   Abel

The sensitivity of the transmitter

b
Ktr          .                                        (5.28)
aAbel

Example:

b
If,        1;          Abel  5 *104 , m2 ;         F0  10 , N , then
a

For     F  from _ 0 _ to _ 40, N                    Pline  from _ 20 _ to _ 100, kPa.
gage

b). Condition of imperfect torque balance:

Anticlockwise moments:                 TACM  Fb  F0 a .                             (5.29)

Clockwise moment:                      TCM  P gage Abel a .
line                                    (5.30)

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T  TACM  TCM  Fb  F0a  P gage Abel a .
line                                   (5.31)

Pline  Kbel KKrel T .
gage
(5.32)

An accurate model for torque-balance transmitter is as follows:

* Fb  F0 a  .
Kbeam KKrel
Pline 
gage
(5.33)
1  Kbeam KKrel * aAbel 
where,

Abel  5 *104 , m2          - effective area of bellows;
F                            - input force, i.e. resultant force from buoy, for example, N ;
F0  10 , N                  - zero spring force;
Pa
K  5 *10 9 ,                - sensitivity of flapper-nozzle;
m
m
Kbeam  6 *105 ,            - stiffness of beam/spring arrangement, i.e. the change in
N *m
flapper/nozzle separation ‘x’ for unit change in torque;
K rel  20                   - pneumatic relay sensitivity;
a  b  5 *102 , m         - lever arms length;
K beam KK rel * aAbel  150 - this value is large compared with 1, so the effect of supply
pressure variations is small: for example, an increase in supply
pressure of 104 Pa causes increase in output pressure of only 0.2%.

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F0

a

gage
+         T ACM                   T                         P        out
gage

+                                x                              P      line

Kbeam        K                   Krel

+                     T CM   -

a            Abel

b                F

Figure 5.8. Block-diagram for a pneumatic torque-balance transmitter.

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5.2.4. Simplified model of pneumatic differential pressure transmitter
(from Bentley J. P. Principles of Measurement Systems, Longman, 1995, p. 321-322):

According to Fig. 5.9 the resultant force on the diaphragm is as follows:

F1  AD * ( P  P2 ) .
1                                              (5.34)

Clockwise moment on the force beam due to the action of F1 :

M 1  F1 * c  AD * ( P  P2 ) * c .
1                                    (5.35)

Anticlockwise moment on the force beam due to the action of the span nut:

M 5  F5 * d .                                       (5.36)

For the condition of balance:

M1  M 5 ,            (5.37)           or      AD * ( P1  P2 ) * c  F5 * d ,              (5.38)

Anticlockwise moment produced by the span nut on the feedback beam:

M 2  F2 * e .                                       (5.39)

Anticlockwise moment produced by the zero spring force on the feedback beam:

M 4  F0 * g .                                       (5.40)

gage
Clockwise moment on the feedback beam produced by Pline           acting on the feedback bellows:

M 3  F3 * f  Pline * Abel * f .
gage
(5.41)

For the condition of balance:

M2  M4  M3 ,                                       (5.42)
or
F2 * e  F0 * g  Pline * Abel * f .
gage
(5.43)

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3
g
gage
P       out
4
F0
e
5
To pneumatic
7                                     f
amplifier
8
F2

F5

P2        P1                                              gage
d                                        F3                         P       line

-                  +
6
2

c

F1

1

Figure 5.9. Simplified model of pneumatic differential pressure transmitter

1 - diaphragm capsule;        2 - force beam;       3 - flapper;             4 - nozzle;
5 - span nut;          6 -feedback bellows; 7 - feedback beam;

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Since,                   F2  F5  F           (5.44),           then we can get a simplified model
for the differential pressure transmitter.

Pline 
gage
* * * ( P  P2 )  * 0 .
1                                           (5.45)
Abel f d              f Abel

gage
Pline    A    c e
sensitivity               D * * ,                                (5.46)
( P  P2 ) Abel f d
1
and
g F0
zero _ pressure          *     .                          (5.47)
f Abel

e
Adjusting the position of the span nut alters the ratio     , and the sensitivity.
d

Adjusting the zero spring force F0 gives a zero pressure (when P  P2 ) of 20 kPa.
1

Abel                    - the effective area of the feedback bellows, m2;
AD                      - effective area of the diaphragm, m2.

The principle of this method is based on the measurement a hydrostatic pressure, caused by a
liquid head, proportional to the level of liquid. There are several modifications of this method
which are utilised in the following measuring systems:

 hydrostatic differential-pressure meters;
 the air-bubble tube or purging system;
 the diaphragm-box system, etc.

Among them the hydrostatic differential-pressure method is the most popular for level
measurements in open (at atmospheric pressure) or in closed (under gauge or vacuumetric
pressures) tanks. Figures 5.10 and 5.11 give us examples of these two cases. A tank 1 at
atmospheric or gauge (or vacuumetric) pressure is filled with liquid 2 which level is to be
measured. A ‘positive’ chamber of the differential pressure transmitter 3 is connected to the tank
1 by tubing, whereas its ‘negative’ chamber is connected to a surge tank 4 which internal

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diameter is greater than that of tubing. Terms ‘positive’ and ‘negative’ indicate that pressure in
the second chamber is lower compared with that in the first one. This doesn’t mean that the
pressure is negative. A valve 5 is used to equate pressures in these two chambers of the
differential pressure gauge, in order to check its zero point. This valve must be closed during
level measurements. The liquid, which fills the surge tank, should be the same as that under
measurement. Left and right tubes should be close to each other, because variations of an ambient
temperature will cause the same changes in liquid density in both tubes. Since the diameter of the
surge tank is greater than the diameter of tubing, therefore, the liquid displaced by the membrane
in the differential pressure transmitter into the surge tank will not change the level in it. To
eliminate the influence of variations of process pressure P in the big tank on the results of level
measurement, the upper part of the big tank is connected with the upper part of the surge tank by
tubing.

1                                                  1
P

2                                                  2
4                                                   4
H                                                   H
5                                                  P

0                                               0   0                                               0

h1
h1                                     h2                                                  h2
+       -                           5              +       -

3                                                   3
4-20mA                                              4-20mA
P1           P2                                    P1           P2

Figure 5.10. Level measurement in an                     Figure 5.11. Level measurement in a
open tank.                                               closed tank.

The differential pressure measured by the differential pressure transmitter is equal to:

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for an open tank:

P  P  P2  liq gloc ( H  h1 )  liq gloc h2 ,
1                                                                (5.48)

for a closed tank:

1                                     
P  P  P2  P  liq gloc ( H  h1 )  P  liq gloc h2 ,                   (5.49)

where,           liq   - density of the liquid in the tank under measurement, kg/m3;
g loc   - local gravitational acceleration, m/s2.

Since h1  h2 , then            P  liq gloc H .                                             (5.50)

Therefore, the output signal of the differential pressure transmitter is proportional to the P ,
and, finally, to the liquid level H in the tank. In modern instrumentation surged tanks usually are
not used. Instead, a counter-pressure P  liq gloc h1 is created in the ‘negative’ chamber in the
2
case of a pneumatic differential pressure transmitter, or a counter electrical signal corresponded to
the value of P2   liq g loc h1 is generated in an electrical circuit of an electronic differential
pressure transmitter.

Let we use an electronic differential pressure transmitter in Figures 5.10 and 5.11. It is, therefore,
appropriate to describe an operational principle of the electronic force-balance transmitter. In
our case it converts the differential pressure into the standard electrical signal (4-20 mA dc) and
transmits this signal by distance. This type of transmitter with some modifications in its design
may be used for the conversion of any process variable into the standard electrical signal. Fig.
5.12 shows an operational principle of the electronic force-balance transmitter.

When the difference of pressures P  P  P2 increases, then a membrane with a disc in its
1
centre 1 will move to the left, and through a bar 2 the force developed on this membrane will be
transferred to a force bar 4. The force bar rotates clockwise around a cobalt-nickel alloy seal 3. As
the result of these movements a bar 5 moves clockwise, and a ferrite disc 6 moves towards a
differential transformer 7. The output signal (an electromotive force) of this differential
transformer increases and is fed into an amplifier 8, which is powered by a power supply 9. This
signal is amplified and rectified to a direct current, and results the standard electrical output signal
of 4-20 mA dc. This rectified signal (greater than the signal corresponded to the previous

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5

14                          6

7                                           12            8

4
9

P2       P1
3
-                 +
4-20 mA dc

11         10
13

2                 1

Figure 5.12. Schematic of an electronic force balance transmitter.

balanced position of the lever system) enters a winding 10 which is placed between poles of a
permanent magnet 11 and connected with a bar 12. As the result of the interaction of magnetic
fields from the winding and the magnet, the former moves to the left under the force proportional
to the signal from the differential transformer 7, and hence proportional to the measured

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differential pressure P  P  P2 . Thus, the lever system of the transmitter is rebalanced in a
1
new position. The output signal of the transmitter is directly proportional to the P .

Moving a mechanism 14 up and down can perform an adjustment of the span of the transmitter.
Zero adjustment of the transmitter (for the case when P  0 , then output current should be
equal to I = 4 mA dc) can be done by a mechanism 13.

5.4. Capacitance devices

Due to the difference in the dielectric constants of air and liquids, it is possible to measure level
of liquids in tanks by measuring the change in the capacitance (measured between two coaxial
cylinders partly immersed into the liquid) with liquid level. These devices can be used for level
measurement of liquids at pressures up to 6 MPa. If liquid is conductive (specific resistance 105-
106 Ohm*m), then cylinders (electrodes) are covered by an electrical insulation.
Fig. 5.13 shows a schematic view of a capacitance device for level measurements of liquids.

6

5
ha

4

3
hl

2

1

Figure 5.13. Capacitance device for level measurement.

A tank 1 is filled with a liquid 2, which level is to be measured. Two electrodes (coaxial
cylinders) 3 and 4 are immersed in this liquid. The value of capacitance for this device is

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determined by the two capacitances: that of the capacitor formed by the liquid and the electrodes,
and the capacitor formed by air 5 and the electrodes. A measuring device 6 then measures the
variation in the capacitance. In this system, the increase in the total capacitance is directly
proportional to the increase of the level. This technique is best applied to nonconductive liquids,
since it is necessary to avoid the problems generated by conducting materials like acids.

The following formular is taken from Bentley J. P. Principles of Measurement Systems,
Longman, 1995, p. 145):

20 liq hliq       20 air hair
C  Cliq  Cair                                             
R                   R2 
ln  2 
R               ln  
R 
 1                  1
(5.51)
20 liq hliq       20 ( H  hliq )           20

R 

R 

 R2 

 H  ( liq  1)hliq   
ln  2 
R                 ln  2 
R                ln  
R 
 1                    1                   1

where,

C air                      - capacitance of the part of the capacitor filled with air, F;
Cliq                       - capacitance of the part of the capacitor filled with liquid, F;
C                          - total capacitance of the capacitor, F;
hair                       - the height of the capacitor with air, m;
hliq                       - the height of liquid in the capacitor, m;
R1 , R2                    - radii of electrodes, m;
 air                      - dielectric permittivity of air, this value for dry air is assumed equal
to unity, F/m;
 liq                      - dielectric permittivity of liquid, F/m;

 0  8.85415 *1012 - dielectric permittivity for vacuum, F/m.

However, for precise measurements we need to take into account that  air is a function of
pressure, temperature and humidity:

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0.01T     RH * Ps  135   
 air  1          20  P  T  0.0039  ,                        (5.52)
P                      
and
T  273.15
log Ps  7.45 *               2.78 ,                                (5.53)
T  38.3
where,

P                        - air pressure, Pa;
T                        - absolute temperature of air, K;
Ps                       - saturated vapour pressure for a given temperature, Pa;
RH                       - relative humidity of air, %.

For polar dielectrics:                      high dielectric permittivity,   12, F / m ;
 water, acetone, ethyl, methyl alcohol, etc.

For non-polar dielectrics:                  dielectric permittivity,   3, F / m ;
 for condensed gases such as H2, O2 and N2
1.25    1.5, F / m .

For weak-polar dielectrics:                 dielectric permittivity 3    6, F / m .

For precision measurements an additional capacitance element is submerged in liquid to
compensate for changes in the liquid characteristics.
Disadvantages of these devices are listed below:
 these devices are not able to measure level of liquids, which have tendency to crystallise,
and of very viscous liquids;
 they are very sensitive to the variations of dielectric properties of liquids with process
conditions and the variations of capacitances of connecting cables.

The range of level measurements varies from 1 to 20 m. The accuracy is equal to 2.5%.

5.5. Conductance devices

These instruments are used when there is a necessity of liquid control at one specific point or
between maximum and minimum values. Their principle is based on the measurements of
electrolytic conductivity of liquids. Two electrodes 1 and 2 are immersed in liquid 3, which fills a
vessel 4 in Fig. 5.14. These electrodes through electric cables 5 are connected with an electric or
electronic relay 6. Electrodes should be insulated from the vessel. Each of the electrodes forms an

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electrical circuit with the vessel through liquid. Therefore, the material of the vessel should be
conductive. When liquid forms the circuit with the electrode 1, the electric relay starts to operate,
and a signal is sent to a secondary device which detects that the lower limit of the level equal to
hmin has been reached. When liquid is in contact with the electrode 2, this indicates that the upper
limit of the level hmax has been reached.

5                                                         6

2

4

hmax
3

hmin                                                1

Figure 5.14. Conductance-type level system.

These devices may be used for an interface-level control, where one liquid is conductive, whereas
the second liquid is dielectric. The advantage of conductive-type level meters is that they can be
used in vessels under atmospheric or manometric (or vacuumetric) pressures. When employing
electric relays, the best results may be achieved for the most of aqueous solutions of electrolytes
with electrolytic resistivities lower that 20000 Ohm*cm. If one deals with liquids with low
electrolytic conductivity (water, alcohol), the sensitivity of an electric circuit becomes lower, so
electronically operated relays are used to increase the sensitivity of the device.

5.6. Ultrasonic devices

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The operational principle of these devices is based on the phenomenon of reflection of ultrasound
waves from the phase boundary separating liquid and gas. In different media the speed of sound is
different. Therefore, these devices may be used for interface level measurements, and in the case
when the more traditional methods do not work well or do not work at all.

There are two modifications of ultrasound level measuring devices. In the first case ultrasound
passes through gaseous phase; in the second case it passes through the liquid. Figure 5.15 shows
a continuous ultrasound level-measuring device.

7
1
5

2
4                                 4-20 mA dc

6

8
H
3

h

Figure 5.15. Ultrasound level measuring device.

An electrical generator 1 generates electrical signals with a certain frequency. An acoustical
transmitter 2 periodically sends ultrasound signals to the surface of the liquid 3. These ultrasound
waves enter an acoustical receiver 4 after reflection from the surface of the liquid. After receiver
the converted electrical signal is amplified in an amplifier 5 and enters a time interval counter 6
that measures the time between the transmission of a pulse and receipt of the corresponding pulse
echo. Then a converter 7 converts thus measured time into a standard electrical signal 4-20 mA
dc. Since an ultrasound permittivity depends on the properties of a gas, then a thermal

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compensation unit 8 is used to reduce the influence of temperature variation on the results of
measurement. In real industrial environment pressure and chemical composition are additional
factors which affect the velocity of acoustic propagation. These changes can severely affect the
calibration of ultrasound devices. Therefore, additional electronic means are incorporated in these
instruments to correct such changes.

5.7. Nucleonic devices

The phenomenon of reducing the intensity of gamma radiation when passing through liquids or
solids is used in nucleonic devices for measurement of level of liquids and solids. Fig. 5.16

4

1
hmax

2
hmin

3

Figure 5.16. Nucleonic level system.

A small quantity of radioactive substance (Cobalt 60, Radium 226, etc.) is placed in a source unit
1. This unit is attached to the wall of a tank 2 filled with a substance 3 which level is to be
measured. A radiation detector 4, usually Geiger-Mueller tubes, is fixed to the wall of the tank on
the opposite side of the tank. The intensity of gamma-radiation detected by the detector decreases
with the increase of the level of a substance. The absorption of gamma-radiation by the wall of
the tank is constant, whereas that of the gas space above the substance is negligible. A gamma-
detector converts the gamma-radiation into the output signal (a series of small current pulses).

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This signal then is converted into a standard electrical signal, which can be measured by a
secondary device or fed into a controller.

An accuracy of these devices can achieve 1% of the span. The advantage of nucleonic level
devices is that nothing comes in contact with the substance under measurement. Among
disadvantages we can note the high cost and the difficulties with handling of radioactive
materials.

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