ME 464

INSTRUMENTATION

Dr. F. W. Adam
 Course Outline
• Introduction to instrumentation: Instrument types and their
performance characteristics.
• Analyses of systematic and random errors during
measurement processes.
• Signal conditioning and recording.
• Temperature measuring devices: liquid-in-glass
thermometers, thermocouples, varying resistance methods,
thermistors and optical pyrometers.
• Pressure measuring devices: Bourden tubes and
manometers.
• Force and Torque measuring devices: strain gauge methods,
load cells and dynamometers.
• Flow measurements: Bernoulli’s theorem, orifice plate and
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venture tube.
Grading

•Homework & Attendance 10%

•Midsem Exam 20%
•Final Exam 70%
REFERENCE BOOKS
❑ Fundamentals of Industrial Instrumentation
and Process Control, William C. Dunn
❑ Measurement and Instrumentation Principles,
Alan S. Morris
❑ BASIC INSTRUMENTATION MEASURING DEVICES
AND BASIC PID CONTROL, Science and Reactor
Fundamentals
 LECTURE 1
INTRODUTION TO INSTRUMENTATION

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DEFINITION
• Instrumentation is defined as the art and science of measurement
and control.
• An instrument is a device that measures and/or regulates process
variables such as flow, temperature, level, or pressure.
• Instruments include many varied appliances which can be as simple
as valves and transmitters, and as complex as analyzers.

• Instruments often comprise control systems of varied processes

such as refineries, factories, and vehicles.

• The control of processes is one of the main branches of applied

instrumentation.

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 APPLICATION OF MEASUREMENT SYSTEM
• The application of measurement systems can be classified into
three major areas.
• The first of these is their use in regulating trade, applying
instruments that measure physical quantities such as length,
volume and mass in terms of standard units
• The second application area of measuring instruments is in
monitoring functions.
• Use as part of automatic feedback control systems

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 Choosing appropriate measuring instruments
To carry out such an evaluation properly, the instrument engineer must have a
wide knowledge of the range of instruments available for measuring particular
physical quantities, and he/she must also have a deep understanding of how
instrument characteristics are affected by particular measurement situations and
operating conditions. specification of the instrument characteristics required:
• the environmental conditions that the instrument will be subjected to
• The extent to which the measured system will be disturbed
• cost (the initial cost of an instrument often has a low weighting in the evaluation
exercise)
• relative suitability
• Durability
• maintainability
• constancy of performance

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MEASUREMENT SYSTEM

• A measuring system exists to provide information about the

physical value of some variable being measured.

• In simple cases, the system can consist of only a single unit that
gives an output reading or signal according to the magnitude of
the unknown variable applied to it.

• The term measuring instrument is commonly used to describe a

measurement system

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ELEMENTS OF THE MEASURING SYSTEM

• There are three basic elements of a measuring system.

• They are the sensing element, the conversion element,

and the signal processing element.

• Other systems may have in addition to these, the signal

transmission and the signal presentation or recording
unit

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PRIMARY SENSOR

• The first element in any measuring system is the primary sensor:

this gives an output that is a function of the measure and (the
input applied to it).

• For most but not all sensors, this function is at least

approximately linear.

• Some examples of primary sensors are a liquid-in-glass

thermometer, a thermocouple and a strain gauge

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 VARIABLE CONVERSION ELEMENT

• Variable conversion elements are needed where the output variable

of a primary transducer is in an inconvenient form and has to be
converted to a more convenient form.

• For instance, the displacement-measuring strain gauge has an output

in the form of a varying resistance.

• The resistance change cannot be easily measured and so it is

converted to a change in voltage by a bridge circuit, which is a
typical example of a variable conversion element.

• In some cases, the primary sensor and variable conversion element

are combined, and the combination is known as a transducer.
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SIGNAL PROCESSING ELEMENT

• Signal processing elements exist to improve the quality of the

output of a measurement system in some way.

• A very common type of signal processing element is the electronic

amplifier, which amplifies the output of the primary transducer or
variable conversion element, thus improving the sensitivity and
resolution of measurement.

• Other types of signal processing element are those that filter out
induced noise and remove mean levels etc. In some devices, signal
processing is incorporated into a transducer, which is then known
as a transmitter.
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SIGNAL TRANMISSION ELEMENT
• Signal transmission is needed when the observation or application
point of the output of a measurement system is some distance
away from the site of the primary transducer.

• The signal transmission element has traditionally consisted of

single or multi-cored cable, which is often screened to minimize
signal corruption by induced electrical noise.

• However, fibre-optic cables are being used in ever increasing

numbers in modern installations, in part because of their low
transmission loss and imperviousness to the effects of electrical
and magnetic fields.

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SIGNAL RECORDING UNIT

❑ The final optional element in a measurement system is the

point where the measured signal is utilized.

❑ In some cases, this element is omitted altogether because the

measurement is used as part of an automatic control scheme,
and the transmitted signal is fed directly into the control
system.

❑ In other cases, this element in the measurement system takes

the form either of a signal presentation unit or of a signal-
recording unit.

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A DIAGRAM SHOWING ELEMENTS OF A
MEASURING SYSTEM

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 Instrument types and performance characteristics

❑ Active and passive instruments

❑ Null-type and deflective-type instruments

❑ Analogue and digital instruments

❑ Indicating instruments and instruments with a signal output

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Active and Passive Instruments
Instruments are divided into active or passive ones according to
1. whether the instrument output is entirely produced by the
quantity being measured
2. whether the quantity being measured simply modulates the
magnitude of some external power source.

1 Pressure measuring device Petrol-tank level indicator

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 DEFLECTION-TYPE VRS NULL-TYPE INSTRUMENT
DEFLECTION-TYPE

• The pressure gauge just mentioned is a

good example of a deflection type of
instrument,
• The value of the quantity being measured is
displayed in terms of the amount of
movement of a pointer
NULL-TYPE
• Here, weights are put on top of
the piston until the downward
force balances the fluid pressure.
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ANALOGUE INSTRUMENTS VRS DIGITAL INSTRUMENTS
ANALOGUE INSTRUMENTS
• An analogue instrument gives an output that varies
continuously as the quantity being measured changes.
• The output can have an infinite number of values within the
range that the instrument is designed to measure.
• The deflection-type of pressure gauge described earlier is a
good example of an analogue instrument.
DIGITAL INSTRUMENTS
• A digital instrument has an
output that varies in discrete
steps and so can only have a
finite number of values
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 INDICATING INSTRUMENTS.

• The class of indicating instruments normally includes all null-

type instruments and most passive ones.

• Indicators can also be further divided into those that have an

analogue output and those that have a digital display.

• A common analogue indicator is the liquid-in-glass

thermometer.

• Another common indicating device, which exists in both

analogue and digital forms, is the bathroom scale.

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SIGNAL-TYPE OUTPUT INSTRUMENTS

• Instruments that have a signal-type output are commonly used as

part of automatic control systems.

• In other circumstances, they can also be found in measurement

systems where the output measurement signal is recorded in
some way for later use. .

• Usually, the measurement signal involved is an electrical voltage,

but it can take other forms in some systems such as an electrical
current, an optical signal or a pneumatic signal.

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INTELLIGENT INSTRUMENTS
• Intelligent instruments contain extra sensors that measure the
value of environmental inputs and automatically compensate the
value of the output reading

• They have the ability to deal very effectively with systematic errors
in measurement systems, and errors can be attenuated to very low
levels in many cases.

• The processor within an intelligent instrument allows it to apply

pre-programmed signal processing and data manipulation
algorithms to measurements.

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FUNCTIONS OF INTELLIGENT INSTRUMENTS
INCLUDE;
• Correction for the loading effect of measurement on the measured
system
• Signal damping with selectable time constants
• Switchable ranges(using several primary sensors within the
instrument that each measure over a different range)
• Switchable output units(e.g. display in imperial or SI units
• Linearization of the output
• Self –diagnosis of the faults
• Remote adjustment and control of instrument parameters from up
to 1500 meters away via 4-way, 20mA signal lines

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SMART AND NON-SMART INSTRUMENTS

• The advent of the microprocessor has created a new division

in instruments between those that do incorporate a
microprocessor (smart) and those that don’t (non smart)
• A smart sensor is a sensor with local processing power that
enables it to react to local conditions without having to refer
back to a central controller

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FUNCTIONS OF SMART SENSORS VARY,

• Remote calibration capability

• Self-diagnosis of faults

• Automatic calculation of measurement accuracy and compensation

for random errors

• Adjustment for measurement of non-linearities to produce a linear

output

• Compensation for the loading effect of the measuring process on the

measured system
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 PERFORMANCE CHARACTERISTICS
OF INSTRUMENTS AND
MEASUREMENT SYSTEMS

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Static Characteristics of instruments

• In the choice of an instrument for a particular

application, a number of attributes are considered.
• These include accuracy, precision, sensitivity of the
instrument, etc.
• All these attributes are collectively called the static
characteristics of the instrument

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ACCURACY
• The accuracy of an instrument is a measure of how close the
output reading of the instrument is to the correct value.

• In practice, it is more usual to quote the inaccuracy figure rather

than the accuracy figure for an instrument

• Inaccuracy is the extent to which a reading might be wrong, and is

often quoted as a percentage of the full-scale reading of an
instrument.

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PRECISION
• Precision is the term used to
describe an instrument's degree of
freedom from random errors.
• Precision is often, though
incorrectly, confused with accuracy.
• High precision does not imply
anything about measurement
accuracy.
• A high-precision instrument may
have a low accuracy.
• The degree of repeatability or
reproducibility in measurements
from an instrument is an
alternative way of expressing its
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TOLERANCE
• Tolerance is a term that is closely related to accuracy and defines
the maximum error that is to be expected in some value.

• Strictly speaking, tolerance is not a static characteristic of a

measuring instrument but it is made mention because the accuracy
of some instruments is sometimes quoted as a tolerance figure

• For instance, crankshafts are machined with a diameter tolerance

quoted as so many microns (10-6 m), and electric circuit
components such as resistors have tolerances of perhaps 5%.

• One resistor chosen at random from a batch having a nominal value

1000 W and tolerance 5% might have an actual value anywhere
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between 950 W and 1050 W
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 Range or Span
The range or span of an instrument defines the
minimum and maximum values of a quantity
that the instrument is designed to measure.

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Sensitivity of Measurement
• The sensitivity of measurement is a measure of the change in
instrument output that occurs when the quantity being measured
changes by a given amount.
• Thus, sensitivity is the ratio:
Scale of deflection
Value of measure producing deflection

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WORKED EXAMPLE Solution:

The following resistance values of

If these values are plotted on a
a platinum resistance thermometer graph, the straight-line
were measured at a range of relationship between resistance
change and temperature
temperatures. Determine the change is obvious.
measurement sensitivity of the
instrument in ohms/°C. For a change in temperature of
30°C, the change in resistance
Resistance(Ω) Temperature (⁰C) is 7Ω.

307 200 Hence the measurement

sensitivity = 7/30 = 0.233
314 230
Ω/°C.
321 260

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328 290
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 SENSITIVITY OF MEASUREMENT TO
DISTURBANCE.
• All calibrations and specifications of an instrument are only valid
under controlled conditions of temperature, pressure etc.

• These standard ambient conditions are usually defined in the

instrument specification.

• As variations occur in the ambient temperature etc., certain static

instrument characteristics change, and the sensitivity to
disturbance is a measure of the magnitude of this change.
• Zero drift or bias describes the effect where the zero reading of
an instrument is modified by a change in ambient conditions
❑
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Diagrams that show zero drift(a) and sensitivity drift(b)

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A diagram showing both zero drift and sensitivity
drift.

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EXAMPLE
A spring balance is calibrated in an environment at a temperature of
20°C and has the following deflection/load. Determine the zero drift
and sensitivity drift per °C change in ambient temperature
characteristic.
Table 2-1. 1 : Load characteristics at a
temperature of 20° C
Loading(Kg) 0 1 2 3

Deflection(mm) 0 20 40 60

Table 2-1. 2: Load characteristics at a

temperature of 30 °C
Loading(Kg) 0 1 2 3

Deflection(mm) 5 27 49 71

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 SOLUTION

Hint
At 20°C, deflection/load characteristic is a straight line. Sensitivity =
20 mm/kg.

At 30°C, deflection/load characteristic is still a straight line.

Sensitivity = 22 mm/kg.

Bias (zero drift) = 5mm (the no-load deflection)

Sensitivity drift = 2 mm/kg

Zero drift/°C = 5/10 = 0.5 mm/°C

Sensitivity drift/°C =22-20/10= 2/10 = 0.2 (mm per kg)/°C
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THRESHOLD

❑ If the input to an instrument is gradually increased from zero,

the input will have to reach a certain minimum level before the
change in the instrument output reading is of a large enough
magnitude to be detectable.

❑ This minimum level of input is known as the threshold of the

instrument. As an illustration, a car speedometer typically has
a threshold of about 15 km/h.

❑ This means that, if the vehicle starts from rest and accelerates,
no output reading is observed on the speedometer until the
speed reaches 15 km/h.
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RESOLUTION
❑ When an instrument is showing a particular output reading,
there is a lower limit on the magnitude of the change in the
input measured quantity that produces an observable change in
the instrument output.

❑ Like threshold, resolution is sometimes specified as an absolute

value and sometimes as a percentage of full scale deflection.

❑ Using a car speedometer as an example again, this has

subdivisions of typically 20 km/h.

❑ This means that when the needle is between the scale markings,
we cannot estimate speed more accurately than to the nearest 5
km/h.
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 HYSTERESIS If the input measured quantity to the
instrument is steadily increased from a
negative value, the output reading varies
in the manner shown in curve A.

If the input variable is then steadily

decreased, the output varies in the
manner shown in curve B.

The non-coincidence between these

loading and unloading curves is known as
hysteresis.

Two quantities are defined, maximum

input hysteresis and maximum output
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Figure
2 2-1. 4 hysteresis.
DEAD SPACE
❑ Dead space is defined as the range of different input values
over which there is no change in output value.

❑ Any instrument that exhibits hysteresis also displays dead

space.

❑ Some instruments that do not suffer from any significant

hysteresis can still exhibit a dead space in their output
characteristics, however.

❑ Backlash in gears is a typical cause of dead space.

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GRAPH OF AN INSTRUMENT WITH DEAD SPACE

Backlash is commonly
experienced in gear sets
used to convert between
translational and
rotational motion (which
is a common technique
used to measure
translational velocity).
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DYNAMIC CHARACTERISTICS OF AN INSTRUMENT

•Zero Order measurement systems

𝑋𝑜𝑢𝑡 = 𝑘𝑋𝑖𝑛
•First Order measurement systems
𝑑𝑋𝑜𝑢𝑡
𝐴 + 𝐵𝑋𝑜𝑢𝑡 = 𝐶𝑋𝑖𝑛
𝑑𝑡
•Second Order measurement systems
𝑑 2 𝑋𝑜𝑢𝑡 𝑑𝑋𝑜𝑢𝑡
𝐴 2
+ 𝐵 + 𝐶𝑋 𝑜𝑢𝑡 = 𝐷𝑋𝑖𝑛
𝑑𝑡 𝑑𝑡
 DYNAMIC CHARACTERISTICS OF AN INSTRUMENT

• Zero order instrument First order instrument

characteristic characteristic

1
𝐺𝑎𝑖𝑛 = ; 𝑇 𝑖𝑠 𝑡𝑖𝑚𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
1 + 𝑇𝑠
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 DYNAMIC CHARACTERISTICS OF AN INSTRUMENT
Second order instrument

𝜔𝑛 2
𝐺𝑎𝑖𝑛 = 2
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 PERFORMANCE SPECIFICATION OF LINEAR
SYSTEMS IN TIME-DOMAIN
The Figure below illustrates a typical unit-step response of a linear
analog control system. With reference to the unit-step response,
performance criteria commonly used for the characterization of
linear control systems in the time domain are Maximum Percent
Overshoot, Delay Time, Rise Time, Settling Time.
 TRANSIENT RESPONSE SPECIFICATIONS

Peak Time, 𝒕𝒑
It is the time at which the maximum amplitude occurs.
𝑦 𝑡 = 1 − 𝑒 −δ𝜔𝑡 sin(𝜔𝑑 𝑡 + ∅)
𝒅𝒚 𝜋 𝜋
|𝒕=𝒕𝒑 𝐠𝐢𝐯𝐞𝐬 𝒕𝒑 = =
𝒅𝒕 𝜔𝑛 1 − δ2 𝜔𝑑
The peak time corresponds to one-half cycle of the frequency of
damped oscillation.
Rise Time, 𝒕𝒓
Time required for the step response to rise from 10 to 90 percent of its
final value.
Maximum Overshoot, 𝑴𝒑
The maximum overshoot occurs at the peak time
𝑴𝒑 = 𝒚𝒎𝒂𝒙 − 𝒚𝒔𝒔 = 𝒚 𝒕𝒑 − 𝟏
𝜋δ
−
𝑴𝒑 = 𝑒 1−δ2
TRANSIENT RESPONSE OF A PROTOTYPE SECOND-
ORDER SYSTEM

Maximum Percent Overshoot

𝒚𝒎𝒂𝒙 − 𝒚𝒔𝒔
𝒚𝒔𝒔
Delay Time, 𝒕𝒅
Time required for the step response to reach 50 percent of its final value

Settling Time, 𝒕𝒔
Time required for the step response to decrease and stay within a
specified percentage of its final value. A frequently used figure is 5
percent and 2 percent.
Settling Time can be approximated for damping ratios in the range 0 < δ
< 0.7
For 2 percent band

𝟒
𝒕𝒔 =
δ𝜔𝑛
For 5 percent band
𝟑. 𝟏𝟐
𝒕𝒔 =
δ𝜔𝑛
EXAMPLE
A balloon is equipped with temperature and altitude measuring
instruments and has radio equipments that can transmit the output
readings of these instruments back to ground. The balloon is
initially anchored to the ground with the instrument output readings
in steady state. The altitude-measuring instrument is approximately
zero order and the temperature transducer first order with a time
constant of 15 seconds. The temperature on the ground, T0, is 10°C
and the temperature Tx at an altitude of x meters is given by the
relation: Tx = To - 0.01x. If the balloon is released at time zero, and
thereafter rises upwards at a velocity of 5 m/s, draw a table
showing the temperature and altitude measurements reported at
intervals of 10 seconds over the first 50 seconds of travel. Show
also in the table the error in each temperature reading. What
temperature
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does the balloon report at an altitude of 5000 meters?
SOLUTION
Let the temperature reported by the balloon at some general time t
be Tr. Then Tx is related to Tr by the relation:
𝑇𝑥 𝑇0 − 0.01𝑥
𝑇𝑟 = =
1 + 𝛽𝑠 1 + 𝛽𝑠

10 − 0.05𝑡
𝑇𝑟 =
1 + 15𝑠
Velocity=distance/time; distance =x
It is given that x = 5t, and β = 15, thus
Find laplace of both sides of the equation
The transient or complementary function part of the solution (Tx = 0)
is given by: Trcf = Ce - t/15
The particular integral part of the solution is given by:
T5 rpi = 10.75- 0.05t
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 Thus, the whole solute on is given by:
Tr = Trcf + Trpi = Ce-t/15 + 10.75- 0.05t
Applying initial conditions:
At t = 0, Tr = 10, Thus C = -0.75

therefore: Tr = 10.75- 0.05t - 0.75e-t/15

Using the above expression to calculate Tr for various values of t,

the following table can be constructed:

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 Time Altitude x=5t Tx=10−0.05𝑡 TEMPERATURE READING TEMPERATURE ERROR
Tr = 10.75- 0.05t - 0.75e-t/15 (Tr-Tx)

0 0 10 10 0
10 50 9.5 9.86 0.36
20 100 9 9.55 0.55
30 150 8.5 9.15 0.65
40 200 8 8.70 0.70
50 250 7.5 8.22 0.72
(b) At 5000 m, t = 1000 seconds.
Calculating Tr from the above expression:
Tr = 10.75- 0.05(1000) - 0.75e-(1000)/15
The exponential term approximates to zero and so Tr can be written
as: Tr =10 - 0.05(985) = -39.25°C

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This result might have been inferred from the table above where it
can be seen that the error is converging towards a value of 0.75.

For large values of t, the transducer reading lags the true

temperature value by a period of time equal to the time constant of
15 seconds.

In this time, the balloon travels a distance of 75 meters and the

temperature falls by 0.75°.

Thus for large values of t, the output reading is always 0.75° less than
it should be.

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 Assignment I-1

• A load cell is calibrated in an environment at a temperature of

21°C and has the following deflection/load characteristic:
Load(kg) 0 50 100 150 200
Deflection(mm) 0 1 2 3 4
• When used in an environment at 35°C, its characteristic
changes to the following:
Load(kg) 0 50 100 150 200
Deflection(mm) 0.2 1.3 2.4 3.5 4.6
(a) Determine the sensitivity at 21°C and 35°C (b) Calculate the
total zero drift and sensitivity drift at 35°C. (c) Hence determine
the zero drift and sensitivity drift coefficients (in units of µm/°C
and(µm per kg)/(°C)).
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 Assignment I-2
An unmanned submarine is equipped with temperature and depth
measuring instruments and has radio equipment that can transmit
the output readings of these instruments back to the surface. The
submarine is initially floating on the surface of the sea with the
instrument output readings in steady state. The depth measuring
instrument is approximately zero order and the temperature
transducer first order with a time constant of 50 seconds. The
water temperature on the sea surface, To, is 20°C and the
temperature Tx at a depth of x metres is given by the relation: Tx =
To - 0.05x (a) If the submarine starts diving at time zero, and
thereafter goes down at a velocity of 0.5 metres/second, draw a
table showing the temperature and depth measurements reported
at intervals of 100 seconds over the first 500 seconds of travel.
Show also in the table the error in each temperature reading. (b)
What temperature does the submarine report at a depth of 20 km?
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