Errors can occur in writing equations to solve problems in classical physics. Many of these errors can be prevented by performing a dimensionality check on the equations. All physical quantities have a fundamental dimension that is independent of the units of measurement. The basic physical dimensions are: length, mass, time, electrical charge, temperature and luminous intensity. There are a number of systems of units for measuring physical dimensions. The MKS system is based on meter, kilogram, second measurement. The CGS system is based on centimeter, gram, second measurement. The English system is based on feet, pound, second measurement. A few physical dimensions and the associated measurement unit in these three systems are : Physical Quantity Unit System Dimension MKS CGS English length meter centimeter feet mass kilogram gram pound mass time second second second force newton dyne poundal energy joule erg B.t.u. The checking of a physical equation has two aspects. The first is to check the dimensionality. The dimensionality is independent of the unit system. The second is to check that a consistent system of units is used in the equation. An example of a dimensionality check is using the basic equation F=ma to determine that force has the dimension mass x length / time squared, then 2 check if F=mv /r is dimensionally correct. The check is performed by expanding the dimensions, e.g. mass x (length/time) x (length/time) / length. Combining terms and reducing yields mass x length / time squared. This agrees with the dimensions expected for force from the basic equation F=ma. As expected, centripetal force has the same dimensionality as the force from Newton's second law of motion. The table below is organized to present the physical quantity name with associated information. The second column is one of the typical symbols used for the physical quantity. The third column is the dimension of the physical quantity expressed in terms of the fundamental dimensions. The fourth column is the name of the unit in the MKS measurement system. The fifth column is the typical MKS unit equation. An independent table presents conversion factors from the MKS measurement system to other measurement systems. Physics developed over a period of many years by many people from a variety of disciplines. Thus, there is ambiguity and duplication of symbols.

PHYSICAL QUANTITY SYMBOL DIMENSION MEASUREMENT UNIT UNIT EQUATION _________________ ______ _________ ________________ ______________ length s L meter m mass m M kilogram Kg time t T second sec electric charge q Q coulomb c luminous intensity I C candle cd o temperature T K degree kelvin K angle theta none radians none

PHYSICAL QUANTITY SYMBOL DIMENSION MEASUREMENT UNIT UNIT EQUATION _________________ ______ _________ ________________ ______________ 2 2 area A L square meter m 3 3 volume V L stere m velocity v L/T meter per second m/sec angular velocity omega 1/T radians per second 1/sec 2 2 acceleration a L/T meter per square m/sec second 2 2 angular acceleration alpha 1/T radians per 1/sec square second 2 2 force F ML/T newton Kg m/sec 2 2 2 2 energy E ML /T joule Kg m /sec work W " heat Q " 2 2 2 2 torque T ML /T newton meter Kg m /sec 2 3 power P ML /T watt joule/sec 3 3 density D M/L kilogram per Kg/m cubic meter 2 2 pressure P M/LT newton per Kg/m sec elastic modulus square meter momentum p ML/T newton second Kg m/sec impulse 2 2 inertia I ML /T joule second Kg m /sec luminous flux phi C lumen (4Pi candle cd sr for point source) 2 2 illumination E C/L lumen per cd sr/m square meter 2 2 2 2 o entropy S ML /T K joule per degree Kg m /sec K 3 3 volume rate of flow Q L /T cubic meter m /sec per second 2 2 kinematic viscosity nu L /T square meter m /sec per second dynamic viscosity mu M/LT newton second Kg/m sec per square meter 2 2 2 2 specific weight gamma M/L T newton Kg/m sec per cubic meter

PHYSICAL QUANTITY SYMBOL DIMENSION MEASUREMENT UNIT UNIT EQUATION _________________ ______ _________ ________________ ______________ electric current I Q/T ampere c/sec 2 2 2 2 emf,voltage,potential E ML /T Q volt Kg m /sec c 2 2 2 2 electric resistance R ML /TQ ohm Kg m /sec c 2 3 2 3 conductivity sigma TQ /ML mho per meter sec c /Kg m 2 2 2 2 2 2 capacitance C T Q /ML farad sec c /Kg m 2 2 2 2 inductance L ML /Q henry Kg m /c 2 2 current density J Q/TL ampere per c/sec m square meter 3 3 charge density rho Q/L coulomb per c/m cubic meter magnetic flux, B M/TQ weber per Kq/sec c magnetic induction square meter magnetic intensity H Q/LT ampere per meter c/m sec magnetic vector potential A ML/TQ weber/meter Kg m/sec c 2 2 electric field intensity E ML/T Q volt/meter or Kg m/sec c newton per coulomb 2 2 electric displacement D Q/L coulomb per c/m square meter 2 2 permeability mu ML/Q henry per meter Kg m/c 2 2 3 2 2 3 permittivity, epsi T Q /ML farad per meter sec c /Kg m dielectric constant -1 frequency f Pi/T hertz sec -1 angular frequency omega 1/T radians per second sec wave length lambda L meters m

The dimension of any physical quantity can be written as a b c d e f L M T Q C K where a,b,c,d,e and f are integers such as -4, -3, -2 , -1, 0, 1, 2, 3, 4 and L is length, M is mass, T is time, Q is charge, C is luminous intensity and K is temperature. An exponent of zero means the dimension does not apply to the physical quantity. The normal rules of algebra for exponents apply for combining dimensions. In order to add or subtract two physical quantities the quantities must have the same dimension. The resulting physical quantity has the same dimensions. Physical quantities with the same dimension in different systems of units can be added or subtracted by multiplying one of the quantities by a units conversion factor to obtain compatible units. The multiplication of two physical quantities results in a new physical quantity that has the sum of the exponents of the dimensions of the initial two quantities. The division of one physical quantity by another results in a new physical quantity that has the dimension of the exponents of the first quantity minus the exponents of the second quantity. Taking the square root of a physical quantity results in a new physical quantity having a dimension with exponents half of the initial dimension. Raising a physical quantity to a power results in a new physical quantity having a dimension with the exponents multiplied by the power. e.g. v has dimension L/T 2 2 2 2 -2 then v has dimension L /T or L T The derivative of a physical quantity with respect to another physical quantity results in a new physical quantity with the exponents of the first dimension minus the exponents of the other dimension. e.g. v has dimension L/T, t has dimension T, 2 then dv/dt has dimension L/T of acceleration The integral of a physical quantity over the range of another physical quantity results in a new physical quantity that has a dimension with the sum of the exponents of the two quantities. e.g. v has dimension L/T, t has dimension T, then integral v dt has dimension L

This section is organized to be consistent with the discussion of physical quantities and equations of physics. The definition of the six fundamental units of physical quantities is presented for the MKS system of units. The definition of some derived units is then presented in the MKS system. The definitions in other systems of units follow the MKS definitions. This is followed by a table of conversion factors between the MKS system and other systems of units. The MKS system based on the meter, kilogram second was augmented to allow force and energy from electrical quantities to be measured in one rationalized system of units. The system was proposed by Giorgi in 1904. It was adopted by the IEC in 1935 to take effect on January 1, 1940. The electrical to mechanical conversion was chosen to be based on the permeability of free space to be -7 4Pi x 10 henry per meter.

Meter, fundamental unit of length, defined as the distance between two o specified lines on a specific bar of platinum-iridium at 0 C at standard atmospheric pressure supported at two neutral points 0.285 meter from the center of the bar. The bar is kept at the International Bureau of Weights and Measures near Paris France. Centimeter, cgs unit of length, defined as 1/100 meter. Feet, English unit of length, defined as 0.3048 meter in U.S. Inch, English unit of length, defined as 0.00254 meter in U.S. -10 Angstrom, unit of length, defined as 10 meter. Kilogram, fundamental unit of mass, defined as the mass of a specific cylinder of platinum - iridium kept at the International Bureau of Weights and Measures. Gram, cgs unit of mass, defined as 1/1000 kilogram. Pound, English unit of mass, the avoirdupois pound is defined to be 0.4535924277 kilogram in the U.S. The apothecary or troy pound is 5760/7000 of the avoirdupois pound. Second, fundamental unit of time, defined as one 86,400th part of a mean solar day. Presently measured by an atomic clock based on the rate of nuclear decay. Coulomb, fundamental unit of charge, defined as the charge required to obtain one newton of force between two such charges at a distance of one meter. Candle, fundamental unit of luminous intensity, defined as the source intensity of 1/60 centimeter square opening of the standard light source of a glowing cavity with temperature equal to that of solidifying platinum. A point source of one candle radiates one lumen per steradian. Degrees kelvin, fundamental unit of temperature, defined as zero where the molecular activity of gases cease. The scale is based on zero degrees centigrade (Celsius) for the freezing point of water and 100 degrees centigrade at the boiling point of water. Zero degrees centigrade is 273.16 degrees kelvin. Radians, fundamental unit of angle, defined as the angle formed by a length of circular arc being equal to the radius creating the arc.

Newton, unit of force, defined as the force required to accelerate a mass of 1 kilogram at 1 meter per second per second when acting continuously. Dyne, cgs unit of force, defined as the force required to accelerate a mass -5 of 1 gram at at 1 centimeter per second per second. One dyne is 10 newton. Poundal, English unit of force, defined as the force required to accelerate a mass of 1 pound at 1 foot per second per second. One poundal is -10 7.23300 10 newton. A poundal based on earth's gravitation is 32.174 pounds avoirdupois. Joule, unit of energy, defined as work done by 1 newton acting through a distance of one meter. Erg, cgs unit of energy, defined as work done by 1 dyne acting through a -7 distance of one centimeter. One erg is 10 joule. Kilogram calorie, large calorie, unit of energy, is the heat required to raise the temperature of 1 kilogram of water from 1 degree centigrade at a stated temperature. i.e. Kg Cal(22 C). The mean kilogram calorie is defined as 1/100 of the heat required to raise the temperature of 1 kilogram of water o o from 0 C to 100 C. The small calorie is the gram calorie equal to 1/1000 of a large calorie. One mean kilogram calorie is 0.000238889 joule . British thermal unit, B.t.u , unit of energy, the heat required to raise the temperature of 1 pound of water 1 degree Fahrenheit at a stated o temperature. i.e. B.t.u.(39 F). The mean British thermal unit is defined as 1/180 of the heat required to raise the temperature of 1 pound of water from o o 32 F to 212 F. One mean B.t.u. is 0.00009480 joule. Mole, kilogram molecule, is the number of kilograms of a substance that corresponds to its molecular weight divided by 1000. In the cgs system of units a mole, gram molecule, is the number of grams of a substance that corresponds to its molecular weight. The mass of a single molecule in kilograms is the kilogram molecule divided by Avogadro's number. For atoms the molecular weight is the atomic weight. Steradian, sr, is the ratio of the area of the intercepted surface of a sphere to the radius of the sphere squared. 4Pi steradians means the total area of the sphere is intercepted. Watt, unit of power, defined as work done at a constant rate of one joule per second. Horsepower ( mechanical ), English unit of power, defined as work done at a rate of 550 foot-pounds per second. One mechanical horsepower is 745.705 watt. Horsepower ( electrical ), English unit of power, by definition exactly 760 watt. Ampere, unit of electric current, defined as the current that will flow through a circuit with a resistance of one ohm when one volt is applied. The international standard is defined as the current which will deposit silver at a rate of 0.00111800 gram per second. One international ampere is about 0.999835 absolute ampere. International electrical units are based on physical standards whose specifications are slightly in error. Instruments made after January 1, 1948 are calibrated in absolute units. Notes: The singular form of units is used with the exception of foot and feet. Proper names appearing in units and constants are not capitalized. References: Conversion Factors and Tables by Zimmerman and Lavine Electric and Magnetic Fields by Stephen Attwood Elements of Physics by Shortley and Williams

to get MKS units from other units to get other units from MKS units value value value value in MKS = in other x constant in other = in MKS x constant units units units units length meter = angstrom x 1.0E-10 angstrom = meter x 1.0E10 meter = mil x 0.254E-4 mil = meter x 39370.07874 meter = centimeter x 0.01 centimeter = meter x 100 meter = inch x 0.0254 inch = meter x 39.37007874 meter = feet x 0.3048 feet = meter x 3.280839895 meter = yard x 0.9144018288 yard = meter x 1.0936111 meter = fathom x 1.8288036 fathom = meter x meter = rod x 5.0292099 rod = meter x 0.19883839 meter = chain(surveyor) x 20.12 chain(surveyor) = meter x 66 ft meter = chain(engineer) x 30.48006 chain(engineer) = meter x 100 ft meter = furlong x 0.2011684E+3 furlong = meter x 0.49709597E-2 meter = mile(statute) x 1.6093472E+3 mile(statute) = meter x 0.6213699E-3 * meter = mile(nautical) x 1.8532487E+3 mile(nautical) = meter x 0.539593E-3 meter = league(land) x 4.82804E+3 league(land) = meter x meter = league(marine) x 5.5596E+3 league(marine) = meter x meter = light year x 9.459936E+15 light year = meter x mass kilogram = gram x 0.001 gram = kilogram x 1000 kilogram = grain(troy) x 0.6480E-4 grain(troy) = kilogram x kilogram = pennyweight(troy) x 1.5552E-3 pennyweight(troy) = kilogram x 24 grains kilogram = carat(troy) x 0.2E-3 3086 grains kilogram = scruple x 1.296E-3 scruple = kilogram x kilogram = dram(avdp) x 1.772E-3 dram(avdp) = kilogram x kilogram = ounce(avdp) x 0.02834952 ounce(avdp) = kilogram x 35.27 kilogram = ounce(troy) x 0.031103481 ounce(troy) = kilogram x 32.15 kilogram = pound(troy) x 0.37324177 pound(troy) = kilogram x 2.6792285 kilogram = pound(avdp) x 0.45359244 pound(avdp) = kilogram x 2.204622341 * kilogram = ton(short) x 907.18486 ton(short) = kilogram x 2000lbs * kilogram = ton(long) x 1016.047 ton(long) = kilogram x 0.9842064E-3 kilogram = ton(metric) x 1000 ton(metric) = kilogram x 0.001 time second = minute x 60 minute = second x second = hour x 3600 hour = second x second = day x 0.86400E+5 day = second x second = fortnight x 1.2096E+6 fortnight = second x second = month x 2.628E+6 month = second x second = year x year = second x electric charge coulomb = electron charge x electron charge = coulomb x 1.60193E-19 coulomb = faraday x faraday = coulomb x 96.480 coulomb = ampere hours x ampere hours = coulomb x 3600 temperature o o o oL K = C + 273.16 C = K - 273.16 o o oL K = F = ( K - 273.16) x 1.8 + 32.0 angle radian = second(angular) x 4.84814E-6 second(angular) = radian x radian = minute(angular) x 0.000290888 minute(angular) = radian x radian = degree(angular) x 0.0174533 degree(angular) = radian x radian = revolution x 6.2831853 revolution = radian x radian = bam x area square meter = square centimeter square centimeter = square meter x 1.0E-4 x 10,000 square meter = square inch square inch = square meter x x square meter = square feet square feet = square meter x 0.09290341 x square meter = square yard square yard = square meter x x square meter = square mile(statute) square mile(statute) = square meter x x square meter = acre x 4046.873 acre = square meter x square meter = circular mil x circular mil = square meter x 1.97352E+6 square meter = hectare x 1.0E+4 hectare = square meter x square meter = township x 93.24E+6 township = square meter x square meter = barn x 1.0E-28 volume cubic cubic cubic cubic meter = centimeter x 1.0E-6 centimeter = meter x 1.0E+6 cubic cubic cubic cubic meter = inch x 0.16387162E-4 inch = meter x cubic meter = cubic feet x 0.028317017 cubic feet = cubic meter x cubic meter = cubic yard x cubic yard = cubic meter x cubic cubic cubic cubic meter = mile(statute) x mile(statute) = meter x cubic meter = liter x 0.001 liter = cubic meter x 1000 cubic meter = fluid ounce x 0.295737E-4 fluid ounce = cubic meter x 0.33814E+7 cubic meter = cup x cubic cubic meter = pint(liquid) x 0.4731798E-3 pint(liquid) = meter x 21113.4 cubic meter = quart(liquid) x quart(liquid) = cubic meter x cubic meter = gallon x 0.003785 gallon = cubic meter x cubic meter = barrel x 1/0.1589873 barrel = cubic meter x 0.1589873 cubic meter = pint(dry) x 0.03524/64 cubic meter = quart(dry) x 0.03524/32 cubic meter = peck x 0.03524/4 cubic meter = bushel x 0.03524 bushel = cubic meter x cubic meter = keg x (less than 10 gal) cubic meter = cord x 3.625 barrel = gallon x 31.5 (food) x 42 (petroleum) velocity meter per second = centimeters per second x meter per second = kilometer per hour x meter per second = inches per second x meter per second = feet per second x meter per second = miles per second x meter per second = inches per minute x meter per second = feet per minute x meter per second = miles per hour x meter per second = knots x acceleration meter per second squared = centimeter per second squared x meter per second squared = feet per second squared x meter per second squared = miles per hour squared x force newton = dyne x 1.0E-5 newton = poundal x 7.23300E-10 newton = pound x 7.23300E-10/32.17 g energy joule = erg x 1.0E-7 joule = gram calorie x 0.238889E-6 joule = kilogram calorie x 0.238889E-3 joule = gram calorie x 0.238889E-6 joule = B.t.u x 0.9480E-4 joule = foot pounds x 1.356 joule = kilowatt hour x 3.6E+6 joule = horsepower hours x 2.684E+6 power watt = kilogram calorie per second x watt = kilogram calorie per minute x watt = horsepower(mechanical) x 745.705 watt = horsepower(electrical) x 760 watt = horsepower(metric) 1.014 ? watt = horsepower(boiler) x 9.804E+3 33,520 Btu per hour watt = B.t.u per minute x 17.57 watt = B.t.u per hour x 17.57*60 watt = foot pound per minute x 0.2260E-3 33000 HP watt = foot pound per second x 1.356 550 HP density kilogram per cubic meter = pound per cubic foot pressure pascal = newton per square meter x 1 pascal = pounds per square foot x pascal = ton per square foot x pascal = atmosphere(standard) x 1.013250E5 pascal = feet of water x pascal = inches of mercury pascal = millimeters of mercury x 1/133.3 pascal = bar x 1.0E5 pascal = millibar x pascal = torr x torque newton meter = foot pound x flow rate cubic meter per second = gallon per minute x 0.6309E-8 cubic meter per second = cubic feet per minute x 0.4719E-3 specific heat, entropy o oL joule per kilogram K = B.t.u. per pound F x 4.187E+3 dynamic viscosity poise = dyne second per square centimeter kinematic viscosity stoke = square centimeter per second electric current ampere = abampere x 10 ampere = statampere x 0.333333E-9 magnetic flux B magnetic induction magnetomotive force magnetic field strength H dielectric constant permittivity constant rotation rate radians per second = revolutions per second x radians per second = revolutions per minute x

There are a number of physical constants that are used in equations to solve problems in physics. Errors may occur because the dimensionality and/or units of the physical constant are not known. The table below presents some physical constants with their typical symbol, dimension, nominal value and unit of measure in the MKS system. PHYSICAL CONSTANT SYMBOL DIMENSION MKS VALUE UNIT _________________ ______ _________ _________ ____ 3 3 air density, normal rho M/L 1.293 Kg/m conditions air molecule, mass m M 4.81E-26 Kg a air molecule, w M 0.028952 Kg/mole kilogram molecular weight 2 2 atmospheric pressure A M/LT 1.01325 newton/m Avogadro's number N none 6.023E+23 molecules in molecules in a mole a mole 2 2 o Boltzmann's constant k ML /T K 1.380E-23 joule/ K 2 2 electron volt e ML /T 1.60210E-10 joule 3 2 2 2 2 electrostatic constant k ML /T Q 8.987E+9 nt m/coulomb reciprocal permittivity m/farad elementary charge e Q 1.6021892E-19 coulomb electron mass m M 9.1066E-31 Kg e faraday f L/T 9.648456E+4 coulomb/mole 2 2 o gas constant of a mole R ML /T K 8.3144 joule/ K 2 2 gravity (earth) g L/T 9.80665 m/sec hydrogen atom mass m M 1.6734E-27 Kg h hydrogen atom w M 1.0079E-3 Kg/mole kilogram atomic weight 2 2 impedance of free space Z ML /TQ 120Pi ohm 0 mechanical equivalent J none 4186.05 joule/ of heat Kg calorie 2 2 3 permittivity (vacuum) epsi T Q /ML 8.854E-12 farad/meter 0 2 permeability (vacuum) mu ML/Q 4Pi E-7 henry/meter 0 Pi, ratio of circumference Pi none 3.14159265 radians to diameter 2 Planck's constant h ML /T 6.624E-34 joule second speed of light (vacuum) c L/T 2.99792458E+8 meter/second speed of sound (air) s L/T 331.45 meter/second 2 2 2 2 universal gravitational G L /MT 6.6720E-12 nt m /Kg constant Note: some constants are related to combinations of other constants : electrostatic constant = 1/ 4Pi permittivity (vacuum) speed of light = 1/ sqrt( permittivity x permeability ) impedance of free space Z = sqrt( permeability / permittivity ) 0

SOME EQUATIONS OF PHYSICS F = m a force equals mass times acceleration, Newton's second law of motion 2 F = m v /r force equals mass times velocity squared over radius, centripetal force of a mass traveling in a circle 2 F = G m m /s gravitational force between mass and mass at distance s 1 2 1 2 with universal gravitational constant G 2 g = G m /r acceleration due to gravity on earth earth earth 2 F = k Q Q /s electrical force between charge and charge at distance s 1 2 1 2 with electrostatic constant k . If there is a dielectric then multiply by the non dimensional dielectric constant. F = 1/2Pi mu I I /s 1 2 electrical force between two parallel wires carrying currents I and I with a spacing s with permeability 1 2 mu. This is the force for one meter of wire length. 2 F = B H s electrical force in a magnetic field equals the magnetic flux times the magnetic intensity applied to an area 2 F = E D s electrical force in an electric field equals the electric field intensity times the electric displacement applied to an area s = v t distance equals velocity times time (linear) v = a t velocity equals acceleration times time (linear) 2 s = s + v t + 1/2 a t 0 0 linear distance equals initial distance plus initial velocity times time plus one half acceleration times time squared 2 v = sqrt( v + 2as) f 0 the final velocity equals the square root of the initial velocity squared plus two times the acceleration times the distance traveled v = sqrt( s g ) the critical velocity for any object to orbit at a c distance s from the source of gravitational field g theta = omega t angle equals angular velocity times time (rotational) omega = alpha t angular velocity equals angular acceleration times time (rotational) 2 theta = theta + omega t + 1/2 alpha t 0 0 angular rotation equals initial angle plus initial angular velocity times time plus one half angular acceleration times time squared 2 w = sqrt(w + 2 alpha * angle) f 0 the final angular velocity equals the square root of the initial angular velocity squared time twice the angular acceleration times the angle traveled E = I R voltage equals current through a resistor times the resistance I = C (E - E )/(t - t ) 2 1 2 1 the current through a capacitor equals the capacitance times the change in voltage over the change in time E = L (I - I )/(t - t ) 2 1 2 1 the voltage across an inductor equals the inductance times the change in current over the change in time C = epsi A/s the capacitance in farad of a parallel plate capacitor equals the permittivity times the area divided by the spacing. L = n mu r (ln 8r/d - 7/4) the inductance in henry of n turns of wire with diameter d closely wrapped in a coil of radius r with permeability mu is approximately given by this equation. H = 1/2 I / r the magnetic intensity at the center of a current loop equals 1/2 the current divided by the radius of the loop B = mu H the magnetic flux equals the permeability times the magnetic intensity D = epsi E the electric displacement equals the permittivity times the electric field intensity P = E I power equals an electrical potential causing a current P = F s power equals a force applied over a distance 2 L E = m c energy from converting a mass to energy ( c = speed of light) 2 L E = 1/2 m v kinetic energy of a mass traveling at a velocity E = m g s potential energy of a mass in a gravitational field at a height s E = 1/2 B H V energy of a magnetic field in the volume V with magnetic flux B and magnetic intensity H. This is usually an integral of an incremental volume times B times H in the incremental volume. E = 1/2 D E V energy of an electric field in the volume V with electric displacement D and electric field intensity E. This is usually an integral of an incremental volume times D times E in the incremental volume. 2 E = 1/2 C V energy stored in a capacitor with capacitance C having a voltage V 2 E = 1/2 L I energy stored in an inductor with inductance L having a current I T = F s torque equals the force applied at radius s T = I alpha torque equals the rotational inertia times the angular acceleration 2 E = P V = R T = N k T = 1/3 N m v ideal gas law rms These relations are for one mole (kilogram molecule) of an ideal gas at an absolute pressure P, volume V, gas constant R, Avogadro's number N, Boltzmann's constant k, temperature T in degrees kelvin, gas molecule mass m, root mean square speed of the molecules v in meters per second. Each section of the equation rms represents energy in joule. 2 2 P + 1/2 rho v + rho g z = P + 1/2 rho v + rho g z 1 1 1 2 2 2 This equation relates pressure P, velocity v and relative height z for a non compressible fluid in a pipe, observed at location 1 and location 2. rho is the density of the fluid and g is the gravitational constant. 2 L = C rho v A / 2 LL the lift force equals the dimensionless coefficient of lift times the air density times the velocity squared times the surface area divided by 2. 2 D = C rho v A / 2 D the drag force equals the dimensionless coefficient of drag times the air density times the velocity squared times the surface area divided by 2. nu = mu / rho the kinematic viscosity equals the dynamic viscosity over the density in a fluid P = Q (p - p ) 1 2 the power, P, required to drive a volume rate of flow, Q, from pressure p to pressure p . 1 1 o o C = K - 273.16 degrees centigrade equals degrees kelvin minus 273.16 o oL F = ( K -273.16) x 9/5 + 32 degrees Fahrenheit as a function of degrees kelvin

Last updated 9/8/01