Engineering Formula Sheet

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Project Lead The Way, Inc. Copyright 2010 Engineering Formula Sheet - Page 1 Engineering Formula Sheet Circular Shapes FormulasVariables C = Circumference C d = t- = 3.14 d = Diameter 2A r = t- A = Area r = Radius Electrical Systems FormulasVariables V = Voltage V = IRI = Current R = Resistance Right Triangle Ratios FormulasVariables oppositeSinhypotenuseu = adjacentCoshypotenuseu = = Angle oppositeTanadjacentu = Simple Machines FormulasVariables =REFAMAF AMA = Actual Mechanical Advantage FR = Resistance force FE = Effort force ERDIMAD= IMA = Ideal Mechanical Advantage DR = Resistance Distance DE = Effort Distance = LELeverIMALR LE = Length from fulcrum to effort LR = Length from fulcrum to resistance Wheel and Axle=WArIMArrw = Wheel radius ra = Axle radius Pulley IMA = Total number of strands supporting the load Inclined Plane LMAH=L = Slope lengthH = HeightWedge= LIMAH L = Base lengthH = Height =CScrewIMAPitch C = Circumference 1PitchTPI= Pitch = Screw pitch TPI = Threads per inch Project Lead The Way, Inc. Copyright 2010 Engineering Formula Sheet - Page 2 Properties of Materials FormulasVariables OFA= = Stress F = Axial force OLo=Ao = Cross-sectional area = Strain OOFLA E= = Deformation Lo = Original length E= E = Modulus of Elasticity ( )( )E 2 1 O2 1 OF F LA= Fluids FormulasVariables FPA=P = Pressure F = Force 1 21 2V VT T=A = Area V = Volume ( ) ( )1 1 2 2P V P V = Gear Ratios FormulasVariables inoutGRe=e GR = Gear ratio in = Driver gear, rpm out = Driven gear, rpm outinNGRN=Nin = Number of teeth on driver Nout = Number of teeth on driven din = Diameter of driver out out out inin in out inN dN dt e= = =e t dout = Diameter of driven in = Torque of driver, ft-lbs out = Torque of driven, ft-lbs Kinematics FormulasVariables ( )-g2iV * Sin 2Xu=X= Range Vi = Initial velocity ( )gixVSin 2=u g = Acceleration due to gravity = Initial trajectory angle from the horizontal ix iV V cos = u Vix = Initial horizontal velocity = uiy iV V sinViy = Initial vertical velocity Project Lead The Way, Inc. Copyright 2010 Engineering Formula Sheet - Page 3 Statics FormulasVariables = M Fd M = Moment about a point F = Force d = Perpendicular distance XF 0 X( right ) X( left ) E = = E + E = Sum of X = Force in x-direction Y = Force in y-direction ( ) ( )YF 0 Y up Y down E = = E + ECCW = Counter-clockwise moment M0 CCW CW E = = E +E CW = Clockwise moment R M J + = 2J = Number of joints M = Number of members R = Number of reaction forces Rectangular Sections =XXI3bh12 IXX = Moment of inertia about x-x axis b = Base dimension h = Height Work and Power FormulasVariables WF D = W = Work F = Force D = Distance WPt=P = Power W = Work t = Time = P V IV = Volts I = Current QPt=A P = Rate of heat transfer Q = Energy transfer t = Difference in time TP kALA=k = Thermal conductivity A = Area of thermal conductivity L = Thickness T = Difference in temperature PUA T = A U = Thermal transmittance (U-factor) 1UR=R = Resistance to heat flow (R-value)