Lec_2_Intro

Instrumentation and Systems

Objectives of todays lecture

Define quantities, units, and standards.

Define Basic units and derived units.

Quantities

A quantity is a quantifiable or assignable property recognized to phenomena, bodies, or substance, examples are speed of a car and mass of an electron.

A physical quantity is a quantity that can be used in the mathematical equations of science and technology.

Units

A unit is a particular physical quantity, defined and adopted by convention, with which other particular quantities of the same kind are compared to express their value.

The value of a physical quantity is the quantitative expression of a particular physical quantity as the product of a number and a unit, the number being its numerical value. Thus, the numerical value of a particular physical quantity depends on the unit in which it is expressed.

Units

For example, the value of the height h of a light pole is h = 16 m. Here h is the physical quantity, its value expressed in the unit "meter," unit symbol m, is 16 m, and its numerical value when expressed in meters is 16.

Standards

In all conversations, the physical quantities are presented with their proper values compared to the standard, the units. The general unit of a physical quantity is defined as its dimension. A unit system can be developed by choosing, for each basic dimension of the system, a specific unit. For example, the internationally established (SI) units are the meter for length, the kilogram for mass, and the second for time, abbreviated as the mks system of units.

All Physical quantities in Physics can be classified into; 1. Base or fundamental quantities 2. Derived quantities.

Base quantities and units

These units were chosen based on the principles that they are easily and accurately reproducible and unchanging with time. The definitions of these base units are given in Appendix A.

Derived quantities and units

These are physical quantities which are derived from the seven base quantities by mathematical operations such as multiplication, division.

Their units are similarly derived as products or quotients of the seven base units.

Unit less or Dimensionless Quantities A unit less or dimensionless quantity is a ratio

of 2 quantities having the same or no units. Common examples include:

1. Relative density of material = density of material / density of water

2. Strain = deformation of material / original length of material

3. refractive index = sin i / sin r

Prefixes of Units

As physical quantities can take a wide range of values, prefixes such as kilo, centi and milli are used together with units to simplify the expressions for both very large and very small quantities.

Prefixes of Units

Measurement

During experiments, an engineer has to make a lot of measurements, collect and analyze data, and make decisions about the validity of his approaches and procedures. He must have a clear idea about the results he is going to obtain. In this respect, he may develop models of his expectations and compare the outcomes from the experiments to those from the model. He uses various measuring instruments whose reliabilities have outmost importance in successes of his decisions.

Define Measurement

Measurement is the process of observing and recording the observations that are collected as part of research effort. (General)

Measurement is the process or result of determining the magnitude of a quantity relative to a unit of measurement. (Technical)

Levels of Measurement

Nominal Measurements: Numerical values just name the attributes uniquely. Ordering is not implied.

Ordinal Measurements: Attributes can be ranked in order; however difference between attributes have no meaning.

Interval Measurements: Distance between attributes have meaning in this case; however, ratio between attributes are meaning less.

Ratio Measurements: A meaningful ratio-comparison can be obtained among these attributes.

Levels of measurement

Basic Steps in Development of Instruments Development of Mathematical Model for

Identification of Parameters to be measured.

Identification of characteristics to be possessed by a general Instruments.

Qualitative and Quantitative models for determination of Instrument design details.

Selection of geometrical and physical parameters.

Characteristics of measurement systems To choose the instrument, most suited to a particular

measurement application, we have to know the system characteristics.

The performance characteristics may be broadly divided into two groups, namely static and dynamic characteristics.

Static characteristics the performance criteria for the measurement of

quantities that remain constant, or vary only quite slowly. Dynamic characteristics the relationship between the system input and output

when the measured quantity (measurand) is varying rapidly

Generalized Instrument System

Characteristics of measuring instruments True value: standard or reference of known

value or a theoretical value. Accuracy: closeness to the true value; closeness

with which an instrument reading approaches the true or accepted value of the variable (quantity) being measured. It is considered to be an indicator of the total error in the measurement without looking into the sources of errors.

Precision: a measure of the reproducibility of the measurements; given a fixed value of a variable, precision is a measure of the degree to which successive measurements differ from one another i.e., a measure of reproducibility or agreement with each other for multiple trials.

Range: Range refers to values of measured to which a measuring system will respond properly. Values outside the range will not produce useful output.

Span: The difference between upper and lower values of range is the span of instrument.

Least Count: Least count is the smallest difference between two indications that can be detected on an instrument scale.

Readability: The closeness with which the scale of instrument may be read is termed as readability.

Resolution: the smallest change in measured value to which the instrument will respond, i.e. the smallest incremental quantity that can be reliably measured.

Sensitivity: the ability of the measuring instrument to respond to change in the measured quantity. It is expressed as the ratio of the change of output signal or response of the instrument to a change of input or measured variable.

Error: deviation from the true value of the measured variable.

Linearity: the percentage of departure from the linear value, i.e., maximum deviation of the output curve from the best-fit straight line during a calibration cycle.

Tolerance: maximum deviation allowed from the

conventional true value. It is not possible to build a perfect system or make an exact measurement. All devices deviate from their ideal (design) characteristics and all measurements include uncertainties (doubts). Hence, all devices include tolerances in their specifications. If the instrument is used for high-precision applications, the design tolerances must be small. However, if a low degree of accuracy is acceptable, it is not economical to use expensive sensors and precise sensing components.

Validity of measurement

For experiment (or process control), it is extremely important for a measuring system to give a valid and reliable output. Due to imperfectness in system these readings are never exact. However, the difference between measured value and actual (true) value of measured should be small enough such that the output can be used for intended purpose.

Reliability refers to how well a measuring system reproduce a certain reading; validity refers to how close is the reading of measuring system to the actual (true) value of measured. In technical terms, reliability is known as precision and validity as accuracy.