1. Mechanical Measurements
& Instrumentation
2nd Lecture
Nada Rikabi
nadarikabi@yahoo.com
29 April 2014

2. Today’s Lecture
 Measurement Participants
 Measurement System
 Instruments Reading Quality
 Uncertainty of Measurement
 Basic statistical calculations
22 April 2014 Mechanical Measurement - 3rd year 2

3. Measurement Participants
 Measurement: the quantitative comparison between a
predefined standard and a measurand to produce a
measured result.
 Measurement involves 3 main participants:
(i) the measurand
(ii) the measurement system
(iii) the observer or control unit
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4. Measurement System
 The function of measurement system is to provide
information about the physical value of the
measurand.
 In some cases, the system is made up of only a single
component which gives an output signal according to
the magnitude of the variable applied to it.
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5. Measurement System
 However, in most cases, the measurement system is
made up of several components which can be broadly
summarized as:
i. Transducers
ii. Signal conditioning elements
iii. Signal utilization elements
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6. Measurement System
Transducer
 A transducer is a device which converts a property
difficult to measure into another property more easily
measured.
 The transducer often comes into contact with the
measured and takes a sample of it, which is then
converted into another form of output that is a
function of the initial value of the input.
 It is sometimes referred to as the sensing element.
 An Example of transducer is: Mercury bulb in
mercury-in-glass thermometers.
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7. Measurement System
Signal Conditioning
 Signal Conditioning: This becomes necessary in
order to improve the quality of the signal obtained
from the transducer and present it in a more
convenient form for further processing or
transmission.
 An example include: Capillary tube in mercury-in-
bulb-thermometer
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8. Measurement System
Signal Utilization
 Signal Utilization or Data Presentation
Element : The final element in a measurement
system is utilize either in form of a display,
recorder or control system.
 In more sophisticated( (‫ر‬ ّ‫متطو‬ system; the signal
conditioning block can be subdivided into a
series of blocks, each in its turn modifying the
signal.
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9. Measurement System
Example
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10. Measurement System
Summary
 Detector/Sensor ‫كاشف‬) ): device which detects and
responds to measurand
 Transducer: converts measurand to an analog more easily
measured (force-displacement, resistance-voltage)
 Signal Cond.: amplify, filter, integrate, differentiate,
convert freq. to voltage, etc.
 – Computer: widely used today
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11. Instruments Reading Quality
The following terms are often employed to
describe the quality of an instruments reading.
Range
 The region between the limits within which a
quantity is measured, received or transmitted,
expressed by starting the lower and upper
range values.
 Example: 0 to 150 ° F, 20 to 200 psi.
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12. Instruments Reading Quality
Span
 The algebraic difference between the upper and
lower range values.
 For example:
a) Range 0 to 150 °F , span 150 ° F.
b) Range -20 to 200 ° F, span 220 ° F.
c) Range 20 to 150 psi, span 130 psi.
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13. Instruments Reading Quality
Measured Variable
 A quantity property or condition that is
measured. Sometimes referred to as the
measurand.
 Example: Temperature, Pressure, rate of flow.
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14. Instruments Reading Quality
Accuracy
 The accuracy of an instrument indicates the deviation
of the reading from a known value
 Accuracy is typically expressed as:
1. Percentage of full scale reading (upper range
value). Example: A 100 kpa pressure gage having
an accuracy of ±1% would be accurate of ± 1 kpa
over the entire range of the gage.
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15. Instruments Reading Quality
2. Percentage of span.
Example: A pressure gage has span of 200 kpa,
Accuracy of ±0.5%.
To one reading of 150 kpa is taken, then the true value
of measurement will be between
3. Percentage of the actual reading.
Thus, for a ± 2% of reading voltmeter, we would have
an inaccuracy of ± 0.04 volts for a reading of 2 volts.
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16. Example 1
A temperature transducer has a range of 20 to 250 °C. A
measurement results in a value of 55°C for the
temperature. Compare the errors if the accuracy is:
a) ± 0.5 % FS.
b) ± 0.75 % of span.
c) ± 0.8 % of reading.
What is the possible temperature in each case?
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17. Example 1 - solution
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18. Uncertainty of Measurement
 Uncertainty of measurement is the doubt that
exists about the result of any measurement.
 Uncertainty is important to make good quality
measurements and to understand the results. It
is also important in calibration (must be
reported on the certificate).
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19. Basic statistical calculations
 To increase the amount of information you get
from your measurements take a number of
readings and carry out some basic statistical
calculations.
 The two most important statistical calculations
are to find the average or arithmetic mean, and
the standard deviation for a set of numbers.
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20. Standard Deviation
 The standard deviation of a set of measurements is an
indication of how much the measurements vary from
their average value.
 To get the standard deviation of a set of numbers, we
do the following:
1. square all the deviations from the mean,
2. add them together,
3. divide by the number of measurements, and
4. take the square root.
 The standard deviation is the root mean square of the
deviations.22 April 2014 Mechanical Measurement - 3rd year 20

21. Example 2
Calculate the average (arithmetic mean) and the
standard deviation of the following readings
The readings are: 16, 19, 18, 16, 17, 19, 20, 15,
17 and 13
Answer:
 To find the average, add them together and
divide by the number of values
mean
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17
10
170


n
x
x

22. Example 2
 Standard deviation:
find the difference between each reading and the average;
And square each of them;
Next, find the total and divide by n-1 (n=10 in this case);
 The standard deviation, s, is found by taking the square root of
the total;
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23. Example 3
 Suppose we measure the temperature of a
metal table five times using a thermometer and
get the following results:
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Index
Result
(°C)
Deviation
(°C)
Square of
Deviation
(°C2)
1 28.0 +2 4
2 25.0 -1 1
3 26.0 0 0
4 27.0 +1 1
5 24.0 -2 4
Average 26 0.0 2
The mean square deviation is 2 °C2. The standard deviation is the
root mean square deviation, which is √2 = 1.4 °C.