Handout – Unit Conversions (Dimensional Analysis)
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Calculating Growing Degree Days by Jim Nugent District Horticulturist Michigan State University
Calculating Growing Degree Days By Jim Nugent District Horticulturist Michigan State University Are you calculating degree day accumulations and finding your values don't match the values being reported by MSU or your neighbor's electronic data collection unit? There is a logical reason! Three different methods are used to calculate degree days; i.e., 1) Averaging Method; 2) Baskerville-Emin (BE) Method; and 3) Electronic Real-time Data Collection. All methods attempt to calculate the heat accumulation above a minimum threshold temperature, often referred to the base temperature. Once both the daily maximum and minimum temperatures get above the minimum threshold temperature, (i.e., base temperature of 42degrees, 50degrees or whatever other base temperature of interest) then all methods are fairly comparable. However, differences do occur and these are accentuated in an exceptionally long period of cool spring temperatures, such as we experienced this year. Let me briefly explain: 1. Averaging Method: Easy to calculate Degree Days(DD) = Average daily temp. - Base Temp. = (max. + min.) / 2 - Base temp. If answer is negative, assume 0. Example: Calculate DD Base 50 given 65 degrees max. and 40 degrees min. Avg. = (65 + 40) / 2 = 52.5 degrees DD base 50 = 52.5 - 50 = 2.5 degrees. But look what happens given a maximum of 60 degrees and a minimum of 35 degrees: Avg. = (60 + 35) / 2 = 47.5 DD base 50 = 47.5 - 50 = -2.5 = 0 degrees. The maximum temperature was higher than the base of 50° , but no degree days were accumulated. A grower called about the first of June reporting only about 40% of the DD50 that we have recorded. -
Metric System Units of Length
Math 0300 METRIC SYSTEM UNITS OF LENGTH Þ To convert units of length in the metric system of measurement The basic unit of length in the metric system is the meter. All units of length in the metric system are derived from the meter. The prefix “centi-“means one hundredth. 1 centimeter=1 one-hundredth of a meter kilo- = 1000 1 kilometer (km) = 1000 meters (m) hecto- = 100 1 hectometer (hm) = 100 m deca- = 10 1 decameter (dam) = 10 m 1 meter (m) = 1 m deci- = 0.1 1 decimeter (dm) = 0.1 m centi- = 0.01 1 centimeter (cm) = 0.01 m milli- = 0.001 1 millimeter (mm) = 0.001 m Conversion between units of length in the metric system involves moving the decimal point to the right or to the left. Listing the units in order from largest to smallest will indicate how many places to move the decimal point and in which direction. Example 1: To convert 4200 cm to meters, write the units in order from largest to smallest. km hm dam m dm cm mm Converting cm to m requires moving 4 2 . 0 0 2 positions to the left. Move the decimal point the same number of places and in the same direction (to the left). So 4200 cm = 42.00 m A metric measurement involving two units is customarily written in terms of one unit. Convert the smaller unit to the larger unit and then add. Example 2: To convert 8 km 32 m to kilometers First convert 32 m to kilometers. km hm dam m dm cm mm Converting m to km requires moving 0 . -
Standard Conversion Factors
Standard conversion factors 7 1 tonne of oil equivalent (toe) = 10 kilocalories = 396.83 therms = 41.868 GJ = 11,630 kWh 1 therm = 100,000 British thermal units (Btu) The following prefixes are used for multiples of joules, watts and watt hours: kilo (k) = 1,000 or 103 mega (M) = 1,000,000 or 106 giga (G) = 1,000,000,000 or 109 tera (T) = 1,000,000,000,000 or 1012 peta (P) = 1,000,000,000,000,000 or 1015 WEIGHT 1 kilogramme (kg) = 2.2046 pounds (lb) VOLUME 1 cubic metre (cu m) = 35.31 cu ft 1 pound (lb) = 0.4536 kg 1 cubic foot (cu ft) = 0.02832 cu m 1 tonne (t) = 1,000 kg 1 litre = 0.22 Imperial = 0.9842 long ton gallon (UK gal.) = 1.102 short ton (sh tn) 1 UK gallon = 8 UK pints 1 Statute or long ton = 2,240 lb = 1.201 U.S. gallons (US gal) = 1.016 t = 4.54609 litres = 1.120 sh tn 1 barrel = 159.0 litres = 34.97 UK gal = 42 US gal LENGTH 1 mile = 1.6093 kilometres 1 kilometre (km) = 0.62137 miles TEMPERATURE 1 scale degree Celsius (C) = 1.8 scale degrees Fahrenheit (F) For conversion of temperatures: °C = 5/9 (°F - 32); °F = 9/5 °C + 32 Average conversion factors for petroleum Imperial Litres Imperial Litres gallons per gallons per per tonne tonne per tonne tonne Crude oil: Gas/diesel oil: Indigenous Gas oil 257 1,167 Imported Marine diesel oil 253 1,150 Average of refining throughput Fuel oil: Ethane All grades 222 1,021 Propane Light fuel oil: Butane 1% or less sulphur 1,071 Naphtha (l.d.f.) >1% sulphur 232 1,071 Medium fuel oil: Aviation gasoline 1% or less sulphur 237 1,079 >1% sulphur 1,028 Motor -
American and BRITISH UNITS of Measurement to SI UNITS
AMERICAN AND BRITISH UNITS OF MEASUREMENT TO SI UNITS UNIT & ABBREVIATION SI UNITS CONVERSION* UNIT & ABBREVIATION SI UNITS CONVERSION* UNITS OF LENGTH UNITS OF MASS 1 inch = 40 lines in 2.54 cm 0.393701 1 grain gr 64.7989 mg 0.0154324 1 mil 25.4 µm 0.03937 1 dram dr 1.77185 g 0.564383 1 line 0.635 mm 1.57480 1 ounce = 16 drams oz 28.3495 g 0.0352739 1 foot = 12 in = 3 hands ft 30.48 cm 0.0328084 1 pound = 16 oz lb 0.453592 kg 2.204622 1 yard = 3 feet = 4 spans yd 0.9144 m 1.09361 1 quarter = 28 lb 12.7006 kg 0.078737 1 fathom = 2 yd fath 1.8288 m 0.546807 1 hundredweight = 112 lb cwt 50.8024 kg 0.0196841 1 rod (perch, pole) rd 5.0292 m 0.198839 1 long hundredweight l cwt 50.8024 kg 0.0196841 1 chain = 100 links ch 20.1168 m 0.0497097 1 short hundredweight sh cwt 45.3592 kg 0.0220462 1 furlong = 220 yd fur 0.201168 km 4.97097 1 ton = 1 long ton tn, l tn 1.016047 t 0.984206 1 mile (Land Mile) mi 1.60934 km 0.62137 1 short ton = 2000 lb sh tn 0.907185 t 1.102311 1 nautical mile (intl.) n mi, NM 1.852 km 0.539957 1 knot (Knoten) kn 1.852 km/h 0.539957 UNITS OF FORCE 1 pound-weight lb wt 4.448221 N 0.2248089 UNITS OF AREA 1 pound-force LB, lbf 4.448221 N 0.2248089 1 square inch sq in 6.4516 cm2 0.155000 1 poundal pdl 0.138255 N 7.23301 1 circular inch 5.0671 cm2 0.197352 1 kilogram-force kgf, kgp 9.80665 N 0.1019716 1 square foot = 144 sq in sq ft 929.03 cm2 1.0764 x 10-4 1 short ton-weight sh tn wt 8.896444 kN 0.1124045 1 square yard = 9 sq ft sq yd 0.83613 m2 1.19599 1 long ton-weight l tn wt 9.964015 kN 0.1003611 1 acre = 4 roods 4046.8 -
Units and Conversions
Units and Conversions This unit of the Metrology Fundamentals series was developed by the Mitutoyo Institute of Metrology, the educational department within Mitutoyo America Corporation. The Mitutoyo Institute of Metrology provides educational courses and free on-demand resources across a wide variety of measurement related topics including basic inspection techniques, principles of dimensional metrology, calibration methods, and GD&T. For more information on the educational opportunities available from Mitutoyo America Corporation, visit us at www.mitutoyo.com/education. This technical bulletin addresses an important aspect of the language of measurement – the units used when reporting or discussing measured values. The dimensioning and tolerancing practices used on engineering drawings and related product specifications use either decimal inch (in) or millimeter (mm) units. Dimensional measurements are therefore usually reported in either of these units, but there are a number of variations and conversions that must be understood. Measurement accuracy, equipment specifications, measured deviations, and errors are typically very small numbers, and therefore a more practical spoken language of units has grown out of manufacturing and precision measurement practice. Metric System In the metric system (SI or International System of Units), the fundamental unit of length is the meter (m). Engineering drawings and measurement systems use the millimeter (mm), which is one thousandths of a meter (1 mm = 0.001 m). In general practice, however, the common spoken unit is the “micron”, which is slang for the micrometer (m), one millionth of a meter (1 m = 0.001 mm = 0.000001 m). In more rare cases, the nanometer (nm) is used, which is one billionth of a meter. -
Lesson 1: Length English Vs
Lesson 1: Length English vs. Metric Units Which is longer? A. 1 mile or 1 kilometer B. 1 yard or 1 meter C. 1 inch or 1 centimeter English vs. Metric Units Which is longer? A. 1 mile or 1 kilometer 1 mile B. 1 yard or 1 meter C. 1 inch or 1 centimeter 1.6 kilometers English vs. Metric Units Which is longer? A. 1 mile or 1 kilometer 1 mile B. 1 yard or 1 meter C. 1 inch or 1 centimeter 1.6 kilometers 1 yard = 0.9444 meters English vs. Metric Units Which is longer? A. 1 mile or 1 kilometer 1 mile B. 1 yard or 1 meter C. 1 inch or 1 centimeter 1.6 kilometers 1 inch = 2.54 centimeters 1 yard = 0.9444 meters Metric Units The basic unit of length in the metric system in the meter and is represented by a lowercase m. Standard: The distance traveled by light in absolute vacuum in 1∕299,792,458 of a second. Metric Units 1 Kilometer (km) = 1000 meters 1 Meter = 100 Centimeters (cm) 1 Meter = 1000 Millimeters (mm) Which is larger? A. 1 meter or 105 centimeters C. 12 centimeters or 102 millimeters B. 4 kilometers or 4400 meters D. 1200 millimeters or 1 meter Measuring Length How many millimeters are in 1 centimeter? 1 centimeter = 10 millimeters What is the length of the line in centimeters? _______cm What is the length of the line in millimeters? _______mm What is the length of the line to the nearest centimeter? ________cm HINT: Round to the nearest centimeter – no decimals. -
Toolkit 1: Energy Units and Fundamentals of Quantitative Analysis
Energy & Society Energy Units and Fundamentals Toolkit 1: Energy Units and Fundamentals of Quantitative Analysis 1 Energy & Society Energy Units and Fundamentals Table of Contents 1. Key Concepts: Force, Work, Energy & Power 3 2. Orders of Magnitude & Scientific Notation 6 2.1. Orders of Magnitude 6 2.2. Scientific Notation 7 2.3. Rules for Calculations 7 2.3.1. Multiplication 8 2.3.2. Division 8 2.3.3. Exponentiation 8 2.3.4. Square Root 8 2.3.5. Addition & Subtraction 9 3. Linear versus Exponential Growth 10 3.1. Linear Growth 10 3.2. Exponential Growth 11 4. Uncertainty & Significant Figures 14 4.1. Uncertainty 14 4.2. Significant Figures 15 4.3. Exact Numbers 15 4.4. Identifying Significant Figures 16 4.5. Rules for Calculations 17 4.5.1. Addition & Subtraction 17 4.5.2. Multiplication, Division & Exponentiation 18 5. Unit Analysis 19 5.1. Commonly Used Energy & Non-energy Units 20 5.2. Form & Function 21 6. Sample Problems 22 6.1. Scientific Notation 22 6.2. Linear & Exponential Growth 22 6.3. Significant Figures 23 6.4. Unit Conversions 23 7. Answers to Sample Problems 24 7.1. Scientific Notation 24 7.2. Linear & Exponential Growth 24 7.3. Significant Figures 24 7.4. Unit Conversions 26 8. References 27 2 Energy & Society Energy Units and Fundamentals 1. KEY CONCEPTS: FORCE, WORK, ENERGY & POWER Among the most important fundamentals to be mastered when studying energy pertain to the differences and inter-relationships among four concepts: force, work, energy, and power. Each of these terms has a technical meaning in addition to popular or colloquial meanings. -
Dimensional Analysis and the Theory of Natural Units
LIBRARY TECHNICAL REPORT SECTION SCHOOL NAVAL POSTGRADUATE MONTEREY, CALIFORNIA 93940 NPS-57Gn71101A NAVAL POSTGRADUATE SCHOOL Monterey, California DIMENSIONAL ANALYSIS AND THE THEORY OF NATURAL UNITS "by T. H. Gawain, D.Sc. October 1971 lllp FEDDOCS public This document has been approved for D 208.14/2:NPS-57GN71101A unlimited release and sale; i^ distribution is NAVAL POSTGRADUATE SCHOOL Monterey, California Rear Admiral A. S. Goodfellow, Jr., USN M. U. Clauser Superintendent Provost ABSTRACT: This monograph has been prepared as a text on dimensional analysis for students of Aeronautics at this School. It develops the subject from a viewpoint which is inadequately treated in most standard texts hut which the author's experience has shown to be valuable to students and professionals alike. The analysis treats two types of consistent units, namely, fixed units and natural units. Fixed units include those encountered in the various familiar English and metric systems. Natural units are not fixed in magnitude once and for all but depend on certain physical reference parameters which change with the problem under consideration. Detailed rules are given for the orderly choice of such dimensional reference parameters and for their use in various applications. It is shown that when transformed into natural units, all physical quantities are reduced to dimensionless form. The dimension- less parameters of the well known Pi Theorem are shown to be in this category. An important corollary is proved, namely that any valid physical equation remains valid if all dimensional quantities in the equation be replaced by their dimensionless counterparts in any consistent system of natural units. -
Chapter 5 Dimensional Analysis and Similarity
Chapter 5 Dimensional Analysis and Similarity Motivation. In this chapter we discuss the planning, presentation, and interpretation of experimental data. We shall try to convince you that such data are best presented in dimensionless form. Experiments which might result in tables of output, or even mul- tiple volumes of tables, might be reduced to a single set of curves—or even a single curve—when suitably nondimensionalized. The technique for doing this is dimensional analysis. Chapter 3 presented gross control-volume balances of mass, momentum, and en- ergy which led to estimates of global parameters: mass flow, force, torque, total heat transfer. Chapter 4 presented infinitesimal balances which led to the basic partial dif- ferential equations of fluid flow and some particular solutions. These two chapters cov- ered analytical techniques, which are limited to fairly simple geometries and well- defined boundary conditions. Probably one-third of fluid-flow problems can be attacked in this analytical or theoretical manner. The other two-thirds of all fluid problems are too complex, both geometrically and physically, to be solved analytically. They must be tested by experiment. Their behav- ior is reported as experimental data. Such data are much more useful if they are ex- pressed in compact, economic form. Graphs are especially useful, since tabulated data cannot be absorbed, nor can the trends and rates of change be observed, by most en- gineering eyes. These are the motivations for dimensional analysis. The technique is traditional in fluid mechanics and is useful in all engineering and physical sciences, with notable uses also seen in the biological and social sciences. -
Antarctic Primer
Antarctic Primer By Nigel Sitwell, Tom Ritchie & Gary Miller By Nigel Sitwell, Tom Ritchie & Gary Miller Designed by: Olivia Young, Aurora Expeditions October 2018 Cover image © I.Tortosa Morgan Suite 12, Level 2 35 Buckingham Street Surry Hills, Sydney NSW 2010, Australia To anyone who goes to the Antarctic, there is a tremendous appeal, an unparalleled combination of grandeur, beauty, vastness, loneliness, and malevolence —all of which sound terribly melodramatic — but which truly convey the actual feeling of Antarctica. Where else in the world are all of these descriptions really true? —Captain T.L.M. Sunter, ‘The Antarctic Century Newsletter ANTARCTIC PRIMER 2018 | 3 CONTENTS I. CONSERVING ANTARCTICA Guidance for Visitors to the Antarctic Antarctica’s Historic Heritage South Georgia Biosecurity II. THE PHYSICAL ENVIRONMENT Antarctica The Southern Ocean The Continent Climate Atmospheric Phenomena The Ozone Hole Climate Change Sea Ice The Antarctic Ice Cap Icebergs A Short Glossary of Ice Terms III. THE BIOLOGICAL ENVIRONMENT Life in Antarctica Adapting to the Cold The Kingdom of Krill IV. THE WILDLIFE Antarctic Squids Antarctic Fishes Antarctic Birds Antarctic Seals Antarctic Whales 4 AURORA EXPEDITIONS | Pioneering expedition travel to the heart of nature. CONTENTS V. EXPLORERS AND SCIENTISTS The Exploration of Antarctica The Antarctic Treaty VI. PLACES YOU MAY VISIT South Shetland Islands Antarctic Peninsula Weddell Sea South Orkney Islands South Georgia The Falkland Islands South Sandwich Islands The Historic Ross Sea Sector Commonwealth Bay VII. FURTHER READING VIII. WILDLIFE CHECKLISTS ANTARCTIC PRIMER 2018 | 5 Adélie penguins in the Antarctic Peninsula I. CONSERVING ANTARCTICA Antarctica is the largest wilderness area on earth, a place that must be preserved in its present, virtually pristine state. -
Three-Dimensional Analysis of the Hot-Spot Fuel Temperature in Pebble Bed and Prismatic Modular Reactors
Transactions of the Korean Nuclear Society Spring Meeting Chuncheon, Korea, May 25-26 2006 Three-Dimensional Analysis of the Hot-Spot Fuel Temperature in Pebble Bed and Prismatic Modular Reactors W. K. In,a S. W. Lee,a H. S. Lim,a W. J. Lee a a Korea Atomic Energy Research Institute, P. O. Box 105, Yuseong, Daejeon, Korea, 305-600, [email protected] 1. Introduction thousands of fuel particles. The pebble diameter is 60mm High temperature gas-cooled reactors(HTGR) have with a 5mm unfueled layer. Unstaggered and 2-D been reviewed as potential sources for future energy needs, staggered arrays of 3x3 pebbles as shown in Fig. 1 are particularly for a hydrogen production. Among the simulated to predict the temperature distribution in a hot- HTGRs, the pebble bed reactor(PBR) and a prismatic spot pebble core. Total number of nodes is 1,220,000 and modular reactor(PMR) are considered as the nuclear heat 1,060,000 for the unstaggered and staggered models, source in Korea’s nuclear hydrogen development and respectively. demonstration project. PBR uses coated fuel particles The GT-MHR(PMR) reactor core is loaded with an embedded in spherical graphite fuel pebbles. The fuel annular stack of hexahedral prismatic fuel assemblies, pebbles flow down through the core during an operation. which form 102 columns consisting of 10 fuel blocks PMR uses graphite fuel blocks which contain cylindrical stacked axially in each column. Each fuel block is a fuel compacts consisting of the fuel particles. The fuel triangular array of a fuel compact channel, a coolant blocks also contain coolant passages and locations for channel and a channel for a control rod. -
Distances in the Solar System Are Often Measured in Astronomical Units (AU). One Astronomical Unit Is Defined As the Distance from Earth to the Sun
Distances in the solar system are often measured in astronomical units (AU). One astronomical unit is defined as the distance from Earth to the Sun. 1 AU equals about 150 million km (93 million miles). Table below shows the distance from the Sun to each planet in AU. The table shows how long it takes each planet to spin on its axis. It also shows how long it takes each planet to complete an orbit. Notice how slowly Venus rotates! A day on Venus is actually longer than a year on Venus! Distances to the Planets and Properties of Orbits Relative to Earth's Orbit Average Distance Length of Day (In Earth Length of Year (In Earth Planet from Sun (AU) Days) Years) Mercury 0.39 AU 56.84 days 0.24 years Venus 0.72 243.02 0.62 Earth 1.00 1.00 1.00 Mars 1.52 1.03 1.88 Jupiter 5.20 0.41 11.86 Saturn 9.54 0.43 29.46 Uranus 19.22 0.72 84.01 Neptune 30.06 0.67 164.8 The Role of Gravity Planets are held in their orbits by the force of gravity. What would happen without gravity? Imagine that you are swinging a ball on a string in a circular motion. Now let go of the string. The ball will fly away from you in a straight line. It was the string pulling on the ball that kept the ball moving in a circle. The motion of a planet is very similar to the ball on a strong.