Weeblykmharlan.weebly.com/.../engrformulasheet2012v2.1.docx · Web view1.0 Statistics Mode Place data in ascending order.Mode = most frequently occurring value(1.4)If two values occur
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Mode
Place data in ascending order.Mode = most frequently occurring value(1.4)
If two values occur with maximum frequency the data set is bimodal.If three or more values occur with maximum frequency the data set is multi-modal.
Mean (1.1a) (1.1b)µ = population mean = sample meanΣxi = sum of all data values (x1, x2, x3, …)N = size of populationn = size of sample
Standard Deviation (Population)(1.5a)
(Sample)(1.5b)σ = population standard deviations = sample standard deviationxi = individual data value ( x1, x2, x3, …)
= sample meanN = size of populationn = size of sample
Median
Place data in ascending order.If N is odd, median = central value(1.2)If N is even, median = mean of two central values N = size of population
Range (1.5)
Range = xmax - xmin (1.3)
xmax = maximum data valuexmin = minimum data value2.0 Probability
Independent Events
P (A and B and C) = PAPBPC(2.3)
P (A and B and C) = probability of independent events A and B and C occurring in sequence PA = probability of event A
Mutually Exclusive Events
P (A or B) = PA + PB(2.4)
P (A or B) = probability of either mutually exclusive event A or B occurring in a trialPA = probability of event A
Binomial Probability (order doesn’t matter)
(2.2)
Pk = binomial probability of k successes in n trialsp = probability of a successq = 1 – p = probability of failurek = number of successesn = number of trials
Conditional Probability
(2.5)
P (A|D) = probability of event A given event D P(A) = probability of event A occurringP(~A) = probability of event A not occurringP(D| ̶~A) = probability of event D given event A did not occur
1 J= 1 N·m1 N= 1 kg·m / s21 Pa = 1 N / m21 V= 1 W / A1 W= 1 J / s1 W= 1 V / A1 Hz= 1 s-11 F= 1 A·s / V1 H= 1 V·s / V
Mass and Weight
M = VDm(9.1)W = mg(9.2)W = VDw(9.3)V = volumeDm = mass densitym = massDw = weight densityg = acceleration due to gravity
Equations of Static Equilibrium
ΣFx = 0 ΣFy = 0 ΣMP = 0 (9.8) Fx = force in the x-directionFy = force in the y-directionMP = moment about point P
EDDBE CIMIED POE DE CEA AEElectricity
Ohm’s LawV = IR (9.32) P = IV (9.33)
RT (series) = R1 + R2+ ··· + Rn (9.34)
(9.35)Kirchhoff’s Current LawIT = I1 + I2 + ··· + In or (9.36)Kirchhoff’s Voltage Law VT = V1 + V2 + ··· + Vn or (9.37)V = voltageVT = total voltageI = currentIT = total currentR = resistanceRT = total resistanceP = power
Version 2.1
Numbers Less Than One Numbers Greater Than OnePower of 10 Prefix Abbreviation Power of 10 Prefix Abbreviation
10-1 deci- d 101 deca- da10-2 centi- c 102 hecto- h10-3 milli- m 103 kilo- k10-6 micro- µ 106 Mega- M10-9 nano- n 109 Giga- G10-12 pico- p 1012 Tera- T10-15 femto- f 1015 Peta- P10-18 atto- a 1018 Exa- E10-21 zepto- z 1021 Zetta- Z10-24 yocto- y 1024 Yotta- Y
Hazen-Williams Formula(16.1)hf = head loss due to friction (ft of H2O)L = length of pipe (ft)Q = water flow rate (gpm)C = Hazen-Williams constantd = diameter of pipe (in.)
Dynamic Headdynamic head = static head – head loss (16.2)static head = change in elevation between source and discharge (16.3)
(23.13) (23.14) (23.15) = eccentricityb = semi-minor axisa =semi-major axisT = orbital perioda = semi-major axisμ = gravitational parameterF = force of gravity between two bodiesG = universal gravitation constantM =mass of central bodym = mass of orbiting objectr = distance between center of two objects
Propulsion (23.5)(23.6)(23.7)(23.8)FN = net thrustW = air mass flowvo = flight velocityvj = jet velocityI = total impulseFave = average thrust forceΔt = change in time (thrust duration)Fnet = net forceFavg = average forceFg = force of gravityvf = final velocitya = accelerationΔt = change in time (thrust duration)
NOTE: Fave and Favg are easily confused.
Forces of Flight (23.1)(23.2)(23.3)(23.4)
CL = coefficient of liftCD = coefficient of dragL = liftD = dragA = wing areaρ = densityRe = Reynolds numberv = velocityl = length of fluid travelμ = fluid viscosityF = forcem = massg = acceleration due to gravityM = momentd = moment arm (distance from datum perpendicular to F)
Energy (23.9) (23.10) (23.11) (23.12)K = kinetic energym =massv = velocityU = gravitational potential energyG = universal gravitation constantM =mass of central bodym = mass of orbiting objectR = Distance center main body to center of orbiting objectE = Total Energy of an orbit