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





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





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.





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





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.





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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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




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




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




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




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




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




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




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)





Pointer & Dial arrangement – When calibrated

with known inputs, gives an indication of pressure

signal impressed on bourdon tube.





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.





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





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.





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





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



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