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7/29/2019 Basics Lec 2
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GIK Institute of Engineering Sciences and Technology.
Basic Instrumentation & Measurements
Readability
Closeness with which scale of instrument may
be read12 inch better readability than 6 inch
Least Count
Smallest difference between two indications that can be
detected on instrument scale
Readability & Least Count both depend on
Scale length
Spacing of graduation
Size of pointer
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GIK Institute of Engineering Sciences and Technology.
Basic Instrumentation & Measurements
For digitally read out instrument readability &
least count have little meaning.
Sensitivity
Ratio of linear movement of pointer on an
analog instrument to the change in the measured
variable causing this motion.
Example: 1mV recorder having 25cm scale
lengthSensitivity = 25cm/1mV
Assumption Measurement is linear
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GIK Institute of Engineering Sciences and Technology.
Basic Instrumentation & Measurements
Hysteresis
When there is difference in readings depending
upon whether value of measured quantity isapproached from above or below.
Causes Mechanical friction, magnetic effects,
Thermal effects, etc.
Accuracy
Deviation of reading from a known input. Generally
expressed as %age of full scale reading
Example 100kPa pressure gage with 1% error means
accurate within ± 1kPa over entire range of gage.
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GIK Institute of Engineering Sciences and Technology.
Basic Instrumentation & Measurements
Precision
Its ability to reproduce a certain reading with a given
accuracy.
Example Known voltage = 100V
Meter reads 104,105,103,105
Meter not dependable for accuracy better than
5%
But precision is ±1 is indicated
Meter can be calibrated up to ±1V
Conclusion accuracy can be improved only up to
precision
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GIK Institute of Engineering Sciences and Technology.
Basic Instrumentation & Measurements
UncertaintyIn many experiments we may not have a
known value with which to compare I
instrument reading yet we may feel fairlyconfident that with in certain ± range our
instrument gives true value. This is called
uncertainty.
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GIK Institute of Engineering Sciences and Technology.
Basic Instrumentation & Measurements
Calibration:
Instrument are checked against a known standard& subsequently reduce error in accuracy.
Procedure:Comparison of instruments with either
1) primary standard
2) Secondary standard with higher accuracy thaninst.
3) know input source
&
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Basic Instrumentation & Measurements
Example:
Flow meter may be calibrated by
1) Comparison with a standard flow-measurement
facility of NIST.
2) Compare it with another flow meter of known
accuracy.
3) Directly calibrate it with a primary measurement
s/a weighing a certain amount of water in a tank & recording time elapsed for this quantity to
flow through water .
B i I t t ti & M t
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Basic Instrumentation & Measurements
Standards:
NIST USA
IBWM France
Fundamental units : length, mass, ….
1m = 39.37 inches1 pound mass (lbm) = 453.59237gms
In 1960
1 standard meter = 1,650,763.73 wavelength of orange-red
light of krypton-86 lap
B i I t t ti & M t
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Basic Instrumentation & Measurements
In 1982
1 standard meter = Distance light travels in1/ 299,794,458 of a second.
1inch = 2.54cm
Time (s)
previous 1/86400 of a mean solar day
In 1967
Duration of 9,192,631,770 periods of radiation
transition hyperfine levels of fundamentalsstate of the atom of cesium-133.
B i I t t ti & M t
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Basic Instrumentation & Measurements
Standard units of electrical quantities are derived
from mech. units of F, m , l & time (do yourself)
0K = 0C+273.15
R = 0F+459.670F = 9/5 0C+32.0
Dimensions & units:
Dimension:
Physical variable used to specify behavior or nature of a particular system.
Example: length of a rod is dimension of rod.
B i I t t ti & M t
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Basic Instrumentation & Measurements
L=length t=time
M=mass T=Temp
F=force
Unit:
When we say a particular rod is five meter long, meter is the unit
F α time rate of change of momentum
F = k d (mv)/ dτ
If m = constt. F = km (dv/ dτ)F = k (ma) = 1/gc (ma)
B i I t t ti & M t
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Basic Instrumentation & Measurements
gc = m/s2 or slug .ft /lbf-s2 or…
Work and energy have same dimensions so same
units
1 Nm = 1 joule (J)
Basic unitsLength = m
Mass = kg
Time = s
Electrical current = A
Temperature = K
Luminous intensity = cd
B i I t t ti & M t
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Basic Instrumentation & Measurements
Supplemental units
• Plane angle = rad
• Solid angle = sr.
Generalized Measurement system
Most measurement system may be divided into
three parts.1 A detector transducer stage:
Detects physical variable & perform mech /electtransformation.
2 Intermediate stage:Modifies direct signal to amplification .
Basic Instr mentation & Meas rements
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Basic Instrumentation & Measurements
3 Final stage:
Acts to indicate or record.
Example:Bourdon tube pressure gauge.
Transducer:
Transforms one physical effect into another.
Bourdon tube – Detector Transducer stage converts pressure signal to mechanical displacement of tube.
Gearing arrangement - Int. stage (amplifies thedisplacement of the end of tube)
Basic Instrumentation & Measurements
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Basic Instrumentation & Measurements
Pointer & Dial arrangement – When calibrated
with known inputs, gives an indication of pressure
signal impressed on bourdon tube.
Basic Instrumentation & Measurements
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Basic Instrumentation & Measurements
Analysis of experimental data
Experiment should always know validity of data
Error will always be there regardless of care
Experimental uncertainty
Possible value the error may have.
Types of errors
Due to gross blunder in apparatus/instruments
construction.
Basic Instrumentation & Measurements
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Basic Instrumentation & Measurements
Systematic/ Bian. Errors
Fixed errors that cause repeated readings to be
in errors by roughly the same amount but for
some unknown reasons (thermometer).
Random errors
Personal or electronic fluctuations in app./instMostly difficult to destinguish between the
systematic and random errors
Basic Instrumentation & Measurements
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Basic Instrumentation & Measurements
Error Analysis Example
P = EIE = 100V±2V I = 10A±.2A
P = 1000W
Worst possibleP = (100±2)(10±.2)
= 1040.4W or = 960.4W
So uncertainty in power = +4.04 or -3.96%If your data is even worse common sense tells
you throwaway.
Basic Instrumentation & Measurements
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Basic Instrumentation & Measurements
Uncertainty Analysis
Degree of accuracy with which data has beentaken
P = 100kPa ± 1kPa
We may add adds to certain experimental data
based on total lab. Experience
Let R = R(x1,x2,x,3,-------,xn)
R= Result deducted from some experiment
Xi= Individual variables
Basic Instrumentation & Measurements
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Basic Instrumentation & Measurements
Let wR
= Uncertainty in R
& w1,w2,w3,----wn = ties in ind. Variables
Then
wR = [(∂R/ ∂x1* w1)2 + (∂R/ ∂x2 * w2)
2 + ---
------+ (∂R/ ∂xn * wn)2]
Try to find uncertainty in
P = EI Example
Basic Instrumentation & Measurements
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Basic Instrumentation & Measurements
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