Domain 1 - Math and Science PDF

Domain: 1 Advanced Science and Math Conversions: 1 m = 100 cm 1 m = 1000 mm Length 1 m = 1,000,000 microns 1 km = 1000 m 1 mile = 5280 feet 1 mile =1609 meter 1 mile/hour = 1.47 ft/second 1 inch =2...

Domain: 1 Advanced Science and Math Conversions: 1 m = 100 cm 1 m = 1000 mm Length 1 m = 1,000,000 microns 1 km = 1000 m 1 mile = 5280 feet 1 mile =1609 meter 1 mile/hour = 1.47 ft/second 1 inch =2.54 cm 1foot = 30.48 cm 1meter= 3.2 foot 1foot = 12 inch Length Energy 2.54 cm = 1 inch 1 cal = 0.003968 Btu 25.4 mm = 1 inch 1 cal = 4.187 J 12 inches = 1 foot 1 Btu = 252 cal 3 feet = 1 yard 5280 feet = 1 mile Velocity 1760 yards = 1 mile 1 ft/s = 0.3048 m/s 1.6 Km = 1 mile 1 ft/s = 0.8618 mi/h 0.868 nautical miles = 1 US mile 1 ft/s = 0.5921 knots Area 1 m/s = 3.281 ft/s 1 sq. in. = 6.452 sq. cm 1 m/s = 2.237 mi/h 1 sq. in. = 6452 sq. mm 1 mi/h = 0.4470 m/s 1 sq. ft = 144 sq. in. 1 mi/h = 1.467 ft/s 1 sq. ft = 0.09290 sq. m 1 knot = 0.5148 m/s 1 sq. yd. = 9 sq. ft 1 knot = 1.151 mi/h Volume 1 knot = 1.689 ft/s 1 cm3 = 1 mL Density 1 in3 = 16.39 cm3 1 lb/cu. ft = 0.01602 cu. cm 1 ft3 = 1728 in3 1 g/cu. cm = 62.42 lb/cu. ft 1 cu. ft = 0.02832 cu. m 1 g/cu. cm = 1000 kg/cu. m 1 L = 1.057 quarts (US) 1 kg/cu. m = 0.001 g/cu. cm 0.9463 L = 1 quart Pressure 7.4 US gallon = 1 ft3 1 psia = 6.895 kN/m2 1 US gallon = 0.8327 Imperial 1 psia = 0.0680 atm gallons 1 psia = 27.67 in. H2O 1 bar = 14.5 PSI= 0.98 atm=760 mm Hg= 105 N/m2 1 psia = 51.72 mm Hg 1 psig = ADD 14.7 psia 1 mm Hg (Torr) = 0.01934 psia Mass and Weight 16 ounces(oz) = 1 lb 1 g = 1000 mg 2.205 lb = 1kg 1 ton (US) = 2000 lb 1 tonne (Metric ton) = 1000 kg 1 dram = 1771.85 mg 1 bar = 100 kN/m2 1 cal/g/°C = 1 Btu/lb/°F  1 kN/m2 = 0.1450 psia Concentration 1 bar = 0.9869 atm 1 ppm = 1 mg/L 1 kN/m2 = 0.009869 atm 1 bar = 1.020 kg/cm2 1 mg/m3 = 1 × 10−9 g/cm3 Heat Capacity 1 g/cm3 = 1 × 109 mg/m3 1 Btu/lb/°F = 1 cal/g/°C 1 g/m3 = 62.42 lb/ft3 1 Btu/lb/°F = 4187 J/kg·K 1 lb/ft3 = 0.01602 g/cm3 Force, Pressure, or Stress Pound-force 4.45 Newtons Pound-force/square 6.89 Kilopascals inch Illumination Foot-candle 10.76 Lux Foot-lambert 3.426 Candela/square meter Length Inches 25.4 Millimeters Feet 0.305 Meters Yards 0.914 Meters Miles 1.61 Kilometers Area Square inches 645.2 Square millimeters Square feet 0.093 Square meters Square yards 0.836 Square meters Acres 0.405 Hectares Square miles 2.59 Square kilometers Volume Fluid ounce 29.57 Milliliters Gallons 3.785 Liters Cubic feet 0.028 Cubic meters Cubic yards 0.765 Cubic meters Mass Ounce 28.35 Grams Pounds 0.454 Kilograms Temperature Fahrenheit 5(°F − 32)/9 Celsius Celsius 9(°C + 32)/5 Fahrenheit Celsius °C + 273 Kelvin Fahrenheit °F + 460 Rankine Energy 1 British Thermal Unit (Btu) = 1055 J 1 faraday = 9.65 × 104 coulombs 1 g-cal = 4.19 J 1 g-mol at 0°C and 1 atm = 22.4 L  1 g-mol at 25°C and 1 atm = 24.45 L 1 ampere-hour = 3600 coulombs 1 W = 1 J/s = 1 A × 1 V 1 kwh = 3.6 × 106 J Standards STP (physical science) = 0°C and 1 atm STP (ventilation) = 70°F and 1 atm Air density = 0.075 lb/ft3 at 70°F and 1 atm STP (industrial hygiene) = 25°C and 1 atm Density of Water 1 g/cm3 = 1.94 slugs/ft3 weight density = 62.4 lb/ft3 1 US gallon of H2O = 8.345 lb Angles 1 radian = 180°/π Light 1 candela = 1 lumen/steradian 1 foot-candle = 10.76 candela/m2 = 10.76 lux Magnetic Fields 1 tesla = 10,000 gauss Physical Constants Acceleration of gravity = 32.2 ft/s2 = 9.8 m/s2 Velocity of light = 3.0 × 108 m/s Planck’s constant = 6.626 × 10−34 J·s Avogadro’s number = 6.024 × 1023/g-mol Radiation 1 rad = 10−2 gray 1 rem = 10−2 sievert 1 curie = 3.7 × 1010 becquerel 1 becquerel = 1 disintegration/s Volume 1 liter = 1000 cm3 1 liter = 1000 ml 1 m3 = 1000 liter 1 liter = 1.06 qt = 61.02 in3 = 0.03531 ft3 1 ml = 1 cm3 1% by volume = 10,000 part per million (ppm) 1,000,000/100=10,000 1 ft3 = 7.5 gallons 1 gallon of water = 8.34 lb 1 gallon = 3.78 liters 1 liter = 61.02 cu in  1 hour = 3600 seconds Mass 1 kg = 2.2 lb 1 lb = 454 gram 1 ton (US) =2000 lb Pressure 1 atm = 14.7 psi = 760 mm Hg = 33.90 ft. H20 = 760 torr = 101.3 kPa Temperature Tc=Tf-32/1.8 , Tk=Tc+273 , F=460 + R To convert to absolute temperature scales use: oR = oF + 460 oK = oC + 273 Force 1 kilogram- = 9.80665 newton [N] Energy Unit 1 calorie = 4.186 Joule Conversion 1 BTU (British thermal unit) = 1055 Joule 1 foot-pound=1.356 Joule 1 joule = 1 kg · m/s2. Radiation 1 rad = 10‐2 gray , 1 rem = 10‐2 sievert , 1 curie = 3.7x1010 becquerel , 1 becquerel = 1 disintegration/sec Density of Water 1 gm/cm3 = 1.94 slugs/ft3 (weight density = 62.4 lb/ft3) Light 1 candela = 1 lumen/steradian 1 footcandle = 10.76 candela/m2 = 10.76 lux PHYSICAL acceleration of gravity = 32.2 ft/sec2 = 9.8 m/sec2 CONSTANTS velocity of light = 3.0 x 108 m/sec Planck’s constant = 6.626 x 10‐34 J‐sec Avogadro’s number = 6.024 x 1023/ gram‐mole BOOLEAN POSTULATES Area To find the area of a rectangle, you use this formula: Area = length * width The area of a square is found with this formula: Area = s2, where s = side The formula for the area of a triangle is: Area = (1/2) b * h, where b = base and h = height To find the area of a circle, use this formula:  Area = π * r2, where r = radius Volume Shapes Volume Formula Variables l = Length Rectangular V=l×w×h Solid or Cuboid w = Width h = Height Cube V=a 3 a = Length of edge or side r = Radius of the circular base Cylinder V = πr2h h = Height B = Area of base, (B = side2 or length.breadth) Prism V=B×h h = Height Sphere V = (4⁄3)πr3 r = Radius of the sphere B = Area of the base, Pyramid V = (1⁄3) × B × h h = Height of the pyramid TRIGONOMETRIC FUNCTIONS C2= a2 + b2 – 2ab cos 0C A/SinA=b/Sinb=c/Sinc Kinetic Energy K.E.= ½ mv2 K.E. = kinetic energy (N) , m = mass of the object v = speed of the object (velocity) Potential Energy P.E. = mgh, m = mass of the object (kg) g = gravitational acceleration of the earth (9.8 m/s2) , h = height above earth’s surface (m) Elastic Potential energy stored in elastic materials as the result of their stretching or compressing Energy Hooke’s law, states that if a spring is not stretched or compressed, then there is no elastic potential energy stored in it, The spring is said to be at its equilibrium position. P.E. elastic = ½ kx2, k = spring constant (N/m2) x = amount of compression (distance in m) Force A newton N: is the amount of force required to give a 1-kg mass an acceleration of 1 m/s2.  Tension forces are required to pull an object (opposite of compression). Spring force exerted by a compressed or stretched spring Frictional Force F = μN, μ = coefficient of friction N = force acting on the surface in a direction that is normal (perpendicular) to the surface (N) A 40-kg block of wood is sitting on a cement floor with a coefficient of friction of 0.6. Calculate the frictional force that must be overcome to move the block of wood. 1 Newton (N) = 1 Kg*m/s2. 1 kg = 2.2 lb F= 40 * 9.8 = 392 N F = μN = 0.6 x 392 = 235.2 N If there angle = Nsin angle + μ *N cos angle) Force and Distance F1D1 = F2D2, Momentum ρ = mv , ρ = momentum ,m = mass (kg), v = velocity (m/s) Velocity v = v0 + at , v = final velocity, meters per second, m/s vo = original velocity at the start of the acceleration, m/s , a = acceleration m/s2 , t = time, seconds, S = 𝐯𝟎𝐭 + ½ 𝐚𝐭𝟐, 𝐯𝟐 =𝐯𝟎𝟐 + 𝟐𝐚𝐬 s = distance from its original position, m vo = initial velocity before the start of the acceleration, m/s a = acceleration m/s2 , t = time, seconds, s Work done W = FS , W = work done, J, F = force, Newton, N S = distance from its original position in m Newton second Law F = ma/g , m is the mass , a : acceleration, g = 9.8 or 32.2(us) A force is acting at 30° with the horizontal on an object that is displaced 3 m along the horizontal direction. The normal force on the surface is 400 N and the coefficient of friction is 0.35. Calculate the work done by the force. Ffric = 400 N(0.35) Wmodified = (140 N)(3 m)(cos 30°) , Wmodified = 363.7 N. Statistics Definition histogram is a graph used to distribute frequency of the data (incident) mean is the same as the average value of a data set and is found using a calculation ΣXn/n Median is the central number of a data set.( If there are 2 numbers in the middle, the median is the average of those 2 numbers.) Mode is the number in a data set that occurs most frequently. Left skewed Mean < Median < Mode -ve skewed, longer tails at lower values , most of values are at the right of Mean Right skewed Mode < Median < Mean , most of values are at the left of mean +ve skewed, longer tails at Higher values No Skew -symmetrical distribution: Mean = Median = Mode Standard Central tendency is the measure of four Mean, Median, Mode and Standard deviation deviation a measure of the average distance of all observations from the mean. Variance = Σ(X-Xav)2/N. Standard Deviation S = Square Root (X-Xav)2/N 1 std dev = 68% of the data set 2 std dev = 95.45% of the data set 3 std dev = 99.73% of the data set Sx = standard deviation, r = correlation coefficient Statistic and Statistic: Numerical value that describes data taken from a sample (a subset of the parameter population), we use F-test to measure the accuracy. Parameter: is to describe the characteristic of the population, it summaries data and the entire population Null Hypothesis No significant difference between the population, if any observed difference is due to sampling or experimental error H0= M1=M2 no difference between population Used in conjunction with 95% confidence means that there 95% chance of true Type I error-False reject the null hypothesis when its true (you should accept it), that there’s a difference +ve- Alfa between the means when there is no actual difference Type II error- Reject false null Hypothesis, no difference in mean, where there is actual difference False –ve-Beta accept the null hypothesis when its false (you should reject it) Coefficient Relative standard deviation RSD, measure of the dispersion of probability distribution or variation CV frequency distribution and define the ration of SD to the mean Coefficient of S/Xmean = % variation-CV Cumulative error Is used to calculate the upper confidence limit and lower confidence limit for air sampling, due to common errors: calibration, lab, instrument measurement, and correction errors during sampling calculation as sample size increases the result and assessment of mean enhanced Precision and Accuracy: how close the measurement is to the actual or accepted value-F-test accuracy Precision: the value of SD of repeated measurement of the same true or accepted value with same measurement method Lower confidence Used by the OSHA officer to determine if the measured is exceed the PEL limit-LCL If LCL > PEL Noncompliance , PEL > LCL compliance, Overexposure TWA or PEL >1 and LCL