Engineering Measurements Instrument Types And Performance Characteristics Part 1 PDF

Classification of Instruments Types Static Characteristics of Instruments ENGN-3220 Engineering Measurements Instrument Types and Performance Characteristics - Part 01 Fall 2024 ENGN-3220: Engineering M...

Classification of Instruments Types Static Characteristics of Instruments ENGN-3220 Engineering Measurements Instrument Types and Performance Characteristics - Part 01 Fall 2024 ENGN-3220: Engineering Measurements 1/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Classification of Instrument Types Measuring instruments can be classified in many ways: 1 Active & Passive 2 Null-Type & Deflection Type 3 Analog & Digital 4 Indicating instruments & instruments with output signal 5 Smart instruments (which incorporates micro-processors) & non-smart instruments. ENGN-3220: Engineering Measurements 2/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Active & Passive Measuring instruments can be divided into active and passive according to whether they have an energy source contained within them. In passive instruments, there is no energy source contained within the instrument, hence the instrument output is entirely produced by the quantity being measured. Active instruments, on the other hand, has an energy source, hence the quantity being measured simply modulates the magnitude of this energy source. ENGN-3220: Engineering Measurements 3/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Active & Passive For example, in a passive pressure gauge... The pressure of the fluid is translated into a movement of a pointer against a scale. The energy expended in moving the pointer is derived entirely from the change in pressure measured: Passive Pressure Gauge there are no other energy inputs to the system. ENGN-3220: Engineering Measurements 4/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Active & Passive (Active) Fuel Tank Level Indicator ENGN-3220: Engineering Measurements 5/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Active & Passive In the previous figure, we have an active fuel tank level indicator. The change in fuel level moves a potentiometer arm, changing the output signal (which is a proportion of the external voltage source). The energy in the output signal comes from the external power source: the primary transducer float system is merely modulating the value of the voltage from this external power source. ENGN-3220: Engineering Measurements 6/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Active & Passive In active measuring instruments, adjustment of the magnitude of the external energy source allows much greater control over measurement resolution. Therefore, active measuring instruments usually have better measurement resolution compared to passive instruments. But what is the “resolution”? It the ability of the measurement system to detect and indicate small changes in the measured quantity. ENGN-3220: Engineering Measurements 7/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Active & Passive In terms of cost, passive instruments are normally cheaper to manufacture. Therefore, the choice between active and passive instruments for a particular application involves carefully balancing the measurement resolution requirements against cost. ENGN-3220: Engineering Measurements 8/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Null-Type & Deflection-Type Null-type instruments require adjustment until a reference level is reached, the dead-weight pressure gauge shown in the figure below is an example. ENGN-3220: Engineering Measurements 9/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Null-Type & Deflection-Type In the dead-weight pressure gauge, weights are put on top of the piston until the downward force balances the fluid pressure. Weights are added until the piston reaches a reference level, known as the null point. Pressure measurement is made in terms of the value of the weights needed to reach this null position. ENGN-3220: Engineering Measurements 10/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Null-Type & Deflection-Type The deflection-type instruments, on the other hand, give an output measurement in the form of either a deflection of a pointer against a scale or a numerical display, the aforementioned passive pressure gauge is an example. In general, the null-type Passive Pressure Gauge instruments are more accurate than deflection types. ENGN-3220: Engineering Measurements 11/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Null-Type & Deflection-Type The deflection-type instrument is clearly more convenient to use. A deflection-type instrument is therefore the one that would normally be used in the workplace. However, for calibration duties, the null-type instrument is preferable because of its superior accuracy. ENGN-3220: Engineering Measurements 12/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Analog & Digital An analog 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. ENGN-3220: Engineering Measurements 13/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Analog & Digital The deflection-type pressure gauge described earlier is an example of an analog instrument. As the input value changes, the pointer moves with a smooth continuous motion. Keep in mind that the number of different positions that the eye can discriminate between is strictly Passive Pressure Gauge limited. This discrimination depends on how large the scale is and how finely it is divided. ENGN-3220: Engineering Measurements 14/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Analog & Digital A digital instrument has an output that varies in discrete steps and so can have only a finite number of values. The “rev-counter” shown in the next figure is an example of a digital instrument. A cam is attached to the revolving body whose motion is being measured, and on each revolution the cam opens and closes a switch, and the switching operations are counted by an electronic counter. This system can count only whole revolutions and cannot discriminate any motion that is less than a full revolution. ENGN-3220: Engineering Measurements 15/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Analog & Digital Rev-counter ENGN-3220: Engineering Measurements 16/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Analog & Digital Nowadays, digital computing systems are widely used in every aspect of life, including measurements. A digital measuring instrument can be directly interfaced with a digital computer, whereas an analog measuring instrument needs an analog-to-digital converter (ADC) in order to be interfaced with a digital computer. ENGN-3220: Engineering Measurements 17/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Indicating Instruments & Instruments with Output Signal Indicating instruments (indicators) give some visual or audio indication of the magnitude of the measured quantity and are commonly found in laboratories and in industries. On the other hand, instruments with a signal output (whose magnitude is proportional to the measured quantity.) are commonly found as part of automatic control systems. ENGN-3220: Engineering Measurements 18/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Indicating Instruments & Instruments with Output Signal Indicators can have an analog (e.g. liquid-in-glass thermometer) or digital output (e.g. digital bathroom scale). One major drawback with indicating devices is that they are prone to human-error while reading and recording a measurement. ENGN-3220: Engineering Measurements 19/61  Active & Passive Classification of Instruments Types Null-Type & Deflection-Type Static Characteristics of Instruments Analog & Digital Indicating Instruments & Instruments with Output Signal Indicating Instruments & Instruments with Output Signal Instruments that have a signal-type output are commonly used as part of automatic control systems. Instruments with a signal-type output can also be found in measurement systems in which the output measurement signal is automatically 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, or an optical signal. ENGN-3220: Engineering Measurements 20/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Static Characteristics of Instruments The static characteristics of a measuring instrument are essentially their steady-state attributes, i.e. when the output measurement value has settled to a constant reading after any initial varying output. The static characteristics include accuracy, sensitivity, linearity, resistance to errors caused by variations in their operating environment, reaction to ambient temperature changes, etc. ENGN-3220: Engineering Measurements 21/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Static Characteristics of Instruments The static characteristics of instruments are given in the data sheet for a particular instrument. Values quoted for instrument characteristics in a data sheet apply only when the instrument is used under specified standard calibration conditions. ENGN-3220: Engineering Measurements 22/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Accuracy & Inaccuracy 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 or measurement uncertainty value rather than the accuracy value for an instrument. Inaccuracy or measurement uncertainty 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. ENGN-3220: Engineering Measurements 23/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Accuracy & Inaccuracy ENGN-3220: Engineering Measurements 24/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Accuracy & Inaccuracy ENGN-3220: Engineering Measurements 25/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Accuracy & Inaccuracy Since the maximum measurement error in an instrument is usually related to the full-scale reading of the instrument, then measuring quantities that are substantially less than the full-scale reading means that the possible measurement error is amplified. ENGN-3220: Engineering Measurements 26/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Accuracy & Inaccuracy For this reason, it is an important system design rule that instruments are chosen such that their range is appropriate to the spread of values being measured, so that the best possible accuracy is maintained in instrument readings. That is, if we are measuring pressures with expected values between 0 and 1 bar, we would not use an instrument with a measurement range of 0-10 bar. ENGN-3220: Engineering Measurements 27/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space 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. ENGN-3220: Engineering Measurements 28/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Tolerance Tolerance is a term that is sometimes confused with accuracy. Accuracy has to do with measuring a physical quantity. Whereas tolerance describes the maximum deviation of a manufactured component from some specified value (usually referred to as the “nominal value”). For instance, electric circuit components such as resistors have tolerances of perhaps 5% (of a nominal value). ENGN-3220: Engineering Measurements 29/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Tolerance ENGN-3220: Engineering Measurements 30/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Precision Precision is a term that describes how an instrument is affected by random errors. If a large number of readings are taken of the same quantity by a high-precision instrument, the spread of readings will be very small. Precision is often, although incorrectly, confused with accuracy. High precision does not imply anything about measurement accuracy. ENGN-3220: Engineering Measurements 31/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Precision A high-precision instrument may have a low accuracy. Note that: low-accuracy measurements from a high-precision instrument are normally caused by a bias in the measurements, which is removable by re-calibration. ENGN-3220: Engineering Measurements 32/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Precision ENGN-3220: Engineering Measurements 33/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Precision ENGN-3220: Engineering Measurements 34/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Precision ENGN-3220: Engineering Measurements 35/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Precision In this context, let’s try to differentiate between two terms: “repeatability” and “reproducibility”. Repeatability describes the closeness of output readings when the same input is applied repetitively over a short time, with the same measurement conditions, same instrument and observer, same location, and same conditions of use maintained throughout. Reproducibility describes the closeness of output readings for the same input when there are changes in the method of measurement, observer, measuring instrument, location, conditions of use, and time of measurement. ENGN-3220: Engineering Measurements 36/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Precision Both terms thus describe the spread of output readings for the same input. This spread is referred to as repeatability if the measurement conditions are constant and as reproducibility if the measurement conditions vary. The degree of repeatability or reproducibility in measurements from an instrument is an alternative way to express its precision. ENGN-3220: Engineering Measurements 37/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space 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. Some manufacturers quote the threshold in absolute values, whereas others quote threshold as a percentage of full-scale readings. ENGN-3220: Engineering Measurements 38/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Resolution Now, what about “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. Resolution is sometimes specified as an absolute value and sometimes as a percentage of the full-scale deflection. ENGN-3220: Engineering Measurements 39/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Resolution A major factor influencing the resolution of an instrument is how finely its output scale is divided into subdivisions. Example: a car speedometer that has subdivisions of 10 miles/h, this means that when the needle is between the scale markings, we cannot estimate speed more accurately than to the nearest 5 miles/h. This value of 5 miles/h thus represents the resolution of the instrument. ENGN-3220: Engineering Measurements 40/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Linearity It is desirable for the output reading of an instrument to be linearly proportional to the quantity being measured. The figure to the right shows a plot of the typical output readings of an instrument when a sequence of input quantities are applied to it (the X marks). ENGN-3220: Engineering Measurements 41/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Linearity Normal procedure is to draw a good fit straight line through the X’s, as shown in the figure. The nonlinearity is then defined as the maximum deviation of any output reading marked X from this straight line. Nonlinearity is usually expressed as a percentage of full-scale reading. ENGN-3220: Engineering Measurements 42/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Linearity ENGN-3220: Engineering Measurements 43/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Linearity ENGN-3220: Engineering Measurements 44/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space 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: ∆Output ∆Input  ChangeChange in reading in measured quantity Based on this definition, the sensitivity is the slope of the input-output graph of a measuring instrument. ENGN-3220: Engineering Measurements 45/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Sensitivity of Measurement ENGN-3220: Engineering Measurements 46/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Sensitivity of Measurement ENGN-3220: Engineering Measurements 47/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Sensitivity to Disturbance All calibrations and specifications of an instrument are valid only 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 for instance, certain static instrument characteristics change, and the sensitivity to disturbance is a measure of the magnitude of such a change. Such environmental changes affect instruments in two main ways, known as zero drift (a.k.a. the bias) and sensitivity drift. ENGN-3220: Engineering Measurements 48/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Sensitivity to Disturbance ENGN-3220: Engineering Measurements 49/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Sensitivity to Disturbance: Zero drift or bias Zero drift or bias describes the effect in which the zero reading of an instrument is modified by a change in ambient conditions. This causes a constant error that exists over the full range of measurement of the instrument. Example: mechanical bathroom scale... Zero drift is normally removable by calibration. Example: thumb-wheel in the mechanical bathroom scale... A zero-drift coefficient defines how much zero-drift there is for a unit change in each environmental parameter to which the instrument characteristics are sensitive. ENGN-3220: Engineering Measurements 50/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Sensitivity to Disturbance: Zero drift or bias ENGN-3220: Engineering Measurements 51/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Sensitivity to Disturbance: Zero drift or bias ENGN-3220: Engineering Measurements 52/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Sensitivity to Disturbance: Sensitivity Drift Sensitivity drift defines the amount by which an instrument’s sensitivity of measurement varies as ambient conditions change. Sensitivity drift is quantified by sensitivity drift coefficients that define how much drift there is for a unit change in each environmental parameter to which the instrument characteristics are sensitive. ENGN-3220: Engineering Measurements 53/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Sensitivity to Disturbance: Sensitivity Drift ENGN-3220: Engineering Measurements 54/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Sensitivity to Disturbance: Sensitivity Drift ENGN-3220: Engineering Measurements 55/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Hysteresis effects The next figure illustrates the output characteristic of an instrument that exhibits 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). ENGN-3220: Engineering Measurements 56/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Hysteresis effects ENGN-3220: Engineering Measurements 57/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Hysteresis effects The non-coincidence between these loading and unloading curves is known as hysteresis. Two quantities are defined, maximum input hysteresis and maximum output hysteresis, as shown in the previous figure. These are normally expressed as a percentage of the full-scale input or output reading, respectively. Hysteresis is commonly observed in instruments that contain springs, friction in moving parts where the friction forces change with the direction of movement, and also in devices with electrical windings formed round an iron core ENGN-3220: Engineering Measurements 58/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Dead Space Dead space is defined as the range of different input values over which there is no change in output value as could be seen in the next figure. Dead space can also be defined for instruments that exhibit hysteresis as shown in the previous figure. ENGN-3220: Engineering Measurements 59/61  Accuracy & Inaccuracy Precision Classification of Instruments Types Threshold & Resolution Static Characteristics of Instruments Linearity & Sensitivity Hysteresis effects & Dead Space Dead Space ENGN-3220: Engineering Measurements 60/61  Classification of Instruments Types Static Characteristics of Instruments References 1 Morris, Alan S., and Reza Langari. Measurement and instrumentation: theory and application. Academic Press, 2021. 2 Morris, Alan S., “Measurement and Instrumentation Principles”, 3rd Edition, Butterworth-Heinemann, 2001 ENGN-3220: Engineering Measurements 61/61