Dimensions, Units, and Error CHAPTER 8 Dimensions, Units, and Error

Objectives Sections 8.1 Introduction 8.2 Dimensions and Units Understand the difference between a unit and dimensions Convert quantities between the different systems of measurement Understand the types of error in a measurement Express large numbers in scientific notation Sections 8.1 Introduction 8.2 Dimensions and Units 8.3 Conversion between Different Units 8.4 Errors and Accuracy 8.5 Significant Digits 8.6 Summary

Basic Units and Dimensions Unit is the basic quantity in a given system of measurement yard, meter, inch Some units can be a combination of different basic units Example: Unit of force depends on the choice of the units of mass and acceleration Dimension describes the quantity in terms of Mass, Length, Time and Temperature without specifying any unit. Example:

Basic Units and Dimensions…2 One of the fundamental tenet for any physically valid equation is that dimensions on either side of the equation should be identical. Now F=ma=kx. Now to get the units of stiffness k, In fact dimensional analysis is used to check any proposed equation is valid or not. Groups of quantities can be combined in a manner that the group becomes dimensionless and they oftentimes represent very important fundamental quantities.

8.2 Systems and Measurement There are three major systems of measurement They are BGS (British Gravitational System) EES (English Engineering System) SI System (The current worldwide standard) BGS Here force (not mass), feet (for length) and second (time) are the fundamental units. Since, ,mass is derived unit.

Systems of Measurement…2 The unit of mass is a slug Since weight is a force acting on mass of 1 slug A body with a mass of 1 slug has a weight of 32.174 lb.

Systems and Measurement…3 EES Here the unit of mass is defined such that weight is 1 lbf Mass is 1 lbm For this system use SI SI is the metric system. Fundamental units are grams (weight), cm ( length), and seconds (time).

Conversion between Units We are faced with converting a quantity from one system to another. Use the logic that units should cancel on both sides Example: Conversion of FPS SI Force 1 lb = 4.4482 N Mass 1 slug = 14.5938 kg Length 1 ft = 0.3048 m

Comparison of Units in BGS, EES, and SI Quantity BGS EE SI Mass Slug lbm kilogram Length ft meter (m) Time sec (s) Area Velocity Ft/s M/s Aceleration Density Force Lbf Newton(N) Pressure Pascal (Pa) Energy Ft x Lbf Joule Volume Power Ft x Lbf/s Watt (W)

Order of 10 in metric system Mult. Factor Prefix SI Symbol tera T giga G mega M kilo k hecto h deka da deci d centi c milli m micro nano n pico p femto f atto a

Errors and Accuracy Every quantity is measure in some form or another Accuracy is defined as the difference between true value and measured value All measurements contain error Error has two parts Bias error-inherent in the measurement systems. E.g. graduation in a tape Precision error- Error that arises due to lack of repeatability. Arises due to operator or environmental conditions

Dimensions, Units, and Error CHAPTER 8..concludes Dimensions, Units, and Error