BCSP Supplied Equations for Mechanics

Mechanics

• F = μN, where F is frictional force, μ is coefficient of friction, and N is newtons
• F1D1 = F2D2, where F is force, and D is distance
• v = vo + at, where v is velocity, vo is original velocity, a is acceleration, and t is time
• s = vot + (1/2)at^2, where s is displacement of the object, vo is initial velocity, t is time, and a is acceleration
• v^2 = vo^2 + 2as, where v is final velocity, vo is initial velocity, a is acceleration, and s is displacement

Energy

• K.E. = (1/2)mv^2, where K.E. is kinetic energy, m is mass of the object, and v is speed of the object
• P.E. = mgh, where P.E. is potential energy, m is mass of the object, g is gravitation acceleration, and h is height above earth's surface
• P.E. = (1/2)kx^2, where P.E. is potential energy, k is spring constant, and x is amount of compression

Momentum

• ρ = mv, where ρ is momentum, m is mass, and v is velocity
• F = ma, where F is force, m is mass, and a is acceleration

Work and Energy

• W = mg, where W is work done, m is mass, and g is gravity
• W = Fs, where W is work done, F is force, and s is distance

Ergonomic

• Lifting Index (LI) = L / RWL, where LI is Lifting Index, L is object weight, and RWL is recommended weight limit
• RWL = LC × HM × VM × DM × AM × FM × CM, where RWL is recommended weight limit, and various multipliers (LC, HM, VM, DM, AM, FM, CM) are used to calculate it

Heat Stress and Relative Humidity

• Indoor (no solar load): 0.7 WB + 0.3 GT
• Outdoors (with solar heat load): 0.7 WB + 0.2 GT = 0.1 DB

Concentrations of Vapors and Gases

• ppm = (mg/m^3) × (24.45 / MW), where ppm is parts per million, mg/m^3 is measured mg/m^3 of the contaminant, and MW is molecular weight of the contaminant
• TLVm = (f1 / TLV1) + (f2 / TLV2) + … + (fn / TLVn), where TLVm is threshold limit value, f is fraction of chemical, and TLV is threshold limit value of the chemical
• LFLm = (f1 / LFL1) + (f2 / LFL2) + … + (fn / LFLn), where LFLm is lower flammability limit, f is fraction of chemical, and LFL is lower flammability limit

Ventilation

• Q = VA, where Q is volumetric flow rate, V is velocity of the air, and A is cross-sectional area of the duct
• V = 4005 Ce SPh, where V is velocity, Ce is coefficient of entry loss, and SPh is static pressure of the hood
• SPfan = SPout - SPin - VPin, where SPfan is static pressure of the fan, SPout is static pressure of the outlet, SPin is static pressure of the inlet, and VPin is velocity pressure of the inlet
• SPh = VP + he, where SPh is static pressure of the hood, VP is duct velocity pressure, and he is overall hood entry loss

Engineering Economy

• F = P(1 + i)^n, where F is future value of money, P is present value of money, i is interest rate, and n is number of years
• P = F(1 + i)^(-n), where P is present worth of money, F is future worth, i is interest rate, and n is number of years
• F = A((1 + i)^n - 1) / i, where F is future value of money, A is each payment, i is interest rate, and n is number of periods
• A = F(i(1 + i)^n) / ((1 + i)^n - 1), where A is yearly payment of loan, F is future value of loan, i is interest rate, and n is number of periods

Reliability

• Pf = 1 - R(t), where Pf is probability of failure, and R(t) is reliability
• R(t) = e^(-λt), where R(t) is reliability, t is time in which reliability is measured, and λ is number of failures divided by number of time units

Noise

• I = p^2 / (ρc), where I is sound intensity, p is sound pressure level, ρ is the density of the medium, and c is the speed of sound
• Lpt = 10 log (∑ 10^(Lpi/10)), where Lpt is combined sound pressure level, and Lpi is individual measured sound pressure level
• Lw = 10 log (W / Wo), where Lw is sound power level, W is acoustic power, and Wo is reference acoustic power
• Lp = 20 log (p / po), where Lp is sound pressure level, p is measured sound pressure level, and po is reference sound pressure level

Radiation

• Ionizing: I2 = I1 (d1 / d2)^2, where I is intensity of source, and d is distance from source
• Nonionizing: W = 16 P^4 / (π D^2 A), where W is power density, P is antenna power, D is diameter of antenna, and A is effective antenna area

Mechanics

• F = μN, where F is frictional force, μ is coefficient of friction, and N is newtons
• F1D1 = F2D2, where F is force, and D is distance
• v = vo + at, where v is velocity, vo is original velocity, a is acceleration, and t is time
• s = vot + (1/2)at^2, where s is displacement of the object, vo is initial velocity, t is time, and a is acceleration
• v^2 = vo^2 + 2as, where v is final velocity, vo is initial velocity, a is acceleration, and s is displacement

Energy

• K.E. = (1/2)mv^2, where K.E. is kinetic energy, m is mass of the object, and v is speed of the object
• P.E. = mgh, where P.E. is potential energy, m is mass of the object, g is gravitation acceleration, and h is height above earth's surface
• P.E. = (1/2)kx^2, where P.E. is potential energy, k is spring constant, and x is amount of compression

Momentum

• ρ = mv, where ρ is momentum, m is mass, and v is velocity
• F = ma, where F is force, m is mass, and a is acceleration

Work and Energy

• W = mg, where W is work done, m is mass, and g is gravity
• W = Fs, where W is work done, F is force, and s is distance

Ergonomic

• Lifting Index (LI) = L / RWL, where LI is Lifting Index, L is object weight, and RWL is recommended weight limit
• RWL = LC × HM × VM × DM × AM × FM × CM, where RWL is recommended weight limit, and various multipliers (LC, HM, VM, DM, AM, FM, CM) are used to calculate it

Heat Stress and Relative Humidity

• Indoor (no solar load): 0.7 WB + 0.3 GT
• Outdoors (with solar heat load): 0.7 WB + 0.2 GT = 0.1 DB

Concentrations of Vapors and Gases

• ppm = (mg/m^3) × (24.45 / MW), where ppm is parts per million, mg/m^3 is measured mg/m^3 of the contaminant, and MW is molecular weight of the contaminant
• TLVm = (f1 / TLV1) + (f2 / TLV2) + … + (fn / TLVn), where TLVm is threshold limit value, f is fraction of chemical, and TLV is threshold limit value of the chemical
• LFLm = (f1 / LFL1) + (f2 / LFL2) + … + (fn / LFLn), where LFLm is lower flammability limit, f is fraction of chemical, and LFL is lower flammability limit

Ventilation

• Q = VA, where Q is volumetric flow rate, V is velocity of the air, and A is cross-sectional area of the duct
• V = 4005 Ce SPh, where V is velocity, Ce is coefficient of entry loss, and SPh is static pressure of the hood
• SPfan = SPout - SPin - VPin, where SPfan is static pressure of the fan, SPout is static pressure of the outlet, SPin is static pressure of the inlet, and VPin is velocity pressure of the inlet
• SPh = VP + he, where SPh is static pressure of the hood, VP is duct velocity pressure, and he is overall hood entry loss

Engineering Economy

• F = P(1 + i)^n, where F is future value of money, P is present value of money, i is interest rate, and n is number of years
• P = F(1 + i)^(-n), where P is present worth of money, F is future worth, i is interest rate, and n is number of years
• F = A((1 + i)^n - 1) / i, where F is future value of money, A is each payment, i is interest rate, and n is number of periods
• A = F(i(1 + i)^n) / ((1 + i)^n - 1), where A is yearly payment of loan, F is future value of loan, i is interest rate, and n is number of periods

Reliability

• Pf = 1 - R(t), where Pf is probability of failure, and R(t) is reliability
• R(t) = e^(-λt), where R(t) is reliability, t is time in which reliability is measured, and λ is number of failures divided by number of time units

Noise

• I = p^2 / (ρc), where I is sound intensity, p is sound pressure level, ρ is the density of the medium, and c is the speed of sound
• Lpt = 10 log (∑ 10^(Lpi/10)), where Lpt is combined sound pressure level, and Lpi is individual measured sound pressure level
• Lw = 10 log (W / Wo), where Lw is sound power level, W is acoustic power, and Wo is reference acoustic power
• Lp = 20 log (p / po), where Lp is sound pressure level, p is measured sound pressure level, and po is reference sound pressure level

Radiation

• Ionizing: I2 = I1 (d1 / d2)^2, where I is intensity of source, and d is distance from source
• Nonionizing: W = 16 P^4 / (π D^2 A), where W is power density, P is antenna power, D is diameter of antenna, and A is effective antenna area

Mechanics

• F = μN, where F is frictional force, μ is coefficient of friction, and N is newtons
• F1D1 = F2D2, where F is force, and D is distance
• v = vo + at, where v is velocity, vo is original velocity, a is acceleration, and t is time
• s = vot + (1/2)at^2, where s is displacement of the object, vo is initial velocity, t is time, and a is acceleration
• v^2 = vo^2 + 2as, where v is final velocity, vo is initial velocity, a is acceleration, and s is displacement

Energy

• K.E. = (1/2)mv^2, where K.E. is kinetic energy, m is mass of the object, and v is speed of the object
• P.E. = mgh, where P.E. is potential energy, m is mass of the object, g is gravitation acceleration, and h is height above earth's surface
• P.E. = (1/2)kx^2, where P.E. is potential energy, k is spring constant, and x is amount of compression

Momentum

• ρ = mv, where ρ is momentum, m is mass, and v is velocity
• F = ma, where F is force, m is mass, and a is acceleration

Work and Energy

• W = mg, where W is work done, m is mass, and g is gravity
• W = Fs, where W is work done, F is force, and s is distance

Ergonomic

• Lifting Index (LI) = L / RWL, where LI is Lifting Index, L is object weight, and RWL is recommended weight limit
• RWL = LC × HM × VM × DM × AM × FM × CM, where RWL is recommended weight limit, and various multipliers (LC, HM, VM, DM, AM, FM, CM) are used to calculate it

Heat Stress and Relative Humidity

• Indoor (no solar load): 0.7 WB + 0.3 GT
• Outdoors (with solar heat load): 0.7 WB + 0.2 GT = 0.1 DB

Concentrations of Vapors and Gases

• ppm = (mg/m^3) × (24.45 / MW), where ppm is parts per million, mg/m^3 is measured mg/m^3 of the contaminant, and MW is molecular weight of the contaminant
• TLVm = (f1 / TLV1) + (f2 / TLV2) + … + (fn / TLVn), where TLVm is threshold limit value, f is fraction of chemical, and TLV is threshold limit value of the chemical
• LFLm = (f1 / LFL1) + (f2 / LFL2) + … + (fn / LFLn), where LFLm is lower flammability limit, f is fraction of chemical, and LFL is lower flammability limit

Ventilation

• Q = VA, where Q is volumetric flow rate, V is velocity of the air, and A is cross-sectional area of the duct
• V = 4005 Ce SPh, where V is velocity, Ce is coefficient of entry loss, and SPh is static pressure of the hood
• SPfan = SPout - SPin - VPin, where SPfan is static pressure of the fan, SPout is static pressure of the outlet, SPin is static pressure of the inlet, and VPin is velocity pressure of the inlet
• SPh = VP + he, where SPh is static pressure of the hood, VP is duct velocity pressure, and he is overall hood entry loss

Engineering Economy

• F = P(1 + i)^n, where F is future value of money, P is present value of money, i is interest rate, and n is number of years
• P = F(1 + i)^(-n), where P is present worth of money, F is future worth, i is interest rate, and n is number of years
• F = A((1 + i)^n - 1) / i, where F is future value of money, A is each payment, i is interest rate, and n is number of periods
• A = F(i(1 + i)^n) / ((1 + i)^n - 1), where A is yearly payment of loan, F is future value of loan, i is interest rate, and n is number of periods

Reliability

• Pf = 1 - R(t), where Pf is probability of failure, and R(t) is reliability
• R(t) = e^(-λt), where R(t) is reliability, t is time in which reliability is measured, and λ is number of failures divided by number of time units

Noise

• I = p^2 / (ρc), where I is sound intensity, p is sound pressure level, ρ is the density of the medium, and c is the speed of sound
• Lpt = 10 log (∑ 10^(Lpi/10)), where Lpt is combined sound pressure level, and Lpi is individual measured sound pressure level
• Lw = 10 log (W / Wo), where Lw is sound power level, W is acoustic power, and Wo is reference acoustic power
• Lp = 20 log (p / po), where Lp is sound pressure level, p is measured sound pressure level, and po is reference sound pressure level

Radiation

• Ionizing: I2 = I1 (d1 / d2)^2, where I is intensity of source, and d is distance from source
• Nonionizing: W = 16 P^4 / (π D^2 A), where W is power density, P is antenna power, D is diameter of antenna, and A is effective antenna area

Ventilation

• Hood entry loss (he) is calculated as: he = (1 - C) VP / e^2
• Coefficient of entry loss (Ce) is calculated as: Ce = he / SPh
• Ventilation rate (Q) is calculated as: Q = 403 x 10^6 x SG x ER x K / MW x C
• Velocity of air (V) is calculated as: V = 4005 VP
• Total pressure (TP) is calculated as: TP = SP + VP

Engineering Economy

• Future value of money (F) is calculated as: F = P(1 + i)^n
• Present value of money (P) is calculated as: P = F(1 + i)^(-n)
• Future value of money (F) is also calculated as: F = A((1 + i)^n - 1) / i
• Period payment amount (A) is calculated as: A = F((1 + i)^n - 1) / i(1 + i)^n
• Present worth of money (P) is also calculated as: P = A((1 + i)^n - 1) / i(1 + i)^n

Reliability

• Probability of failure (Pf) is calculated as: Pf = 1 - R(t)
• Reliability (R(t)) is calculated as: R(t) = e^(-λt)
• Probability of failure (Pf) is also calculated as: Pf = (1 - Ps)

Noise

• Sound intensity (I) is calculated as: I = p^2 / ρc

Mechanics

• Frictional force (F) is calculated as: F = μN
• Force (F) is also calculated as: F = F1D1 / D2
• Velocity (v) is calculated as: v = vo + at
• Displacement (s) is calculated as: s = vot + (1/2)at^2
• Kinetic energy (K.E.) is calculated as: K.E. = (1/2)mv^2
• Potential energy (P.E.) is calculated as: P.E. = mgh or P.E. = (1/2)kx^2
• Momentum (ρ) is calculated as: ρ = mv
• Force (F) is also calculated as: F = ma
• Work done (W) is calculated as: W = mg or W = Fs

Ergonomic (Revised NIOSH Lifting Equations)

• Lifting Index (LI) is calculated as: LI = L / RWL
• Recommended weight limit (RWL) is calculated as: RWL = LC × HM × VM × DM × AM × FM × CM

Heat Stress and Relative Humidity

• Indoor (no solar load) equation: 0.7WB + 0.3GT
• Outdoors (with solar heat load) equation: 0.7WB + 0.2GT = 0.1DB

Concentrations of Vapors and Gases

• ppm is calculated as: ppm = mg/m3 × 24.45 / MW
• Threshold limit value (TLV) is calculated as: TLVm = f1/TLV1 + f2/TLV2 + … + fn/TLVn
• Lower flammability limit (LFL) is calculated as: LFLm = f1/LFL1 + f2/LFL2 + … + fn/LFLn

Gas Laws

• PV = nRT
• P1V1 / T1 = P2V2 / T2

Ventilation

• Hood entry loss (he) is calculated as: he = (1 - C) VP / e^2
• Coefficient of entry loss (Ce) is calculated as: Ce = he / SPh
• Ventilation rate (Q) is calculated as: Q = 403 x 10^6 x SG x ER x K / MW x C
• Velocity of air (V) is calculated as: V = 4005 VP
• Total pressure (TP) is calculated as: TP = SP + VP

Engineering Economy

• Future value of money (F) is calculated as: F = P(1 + i)^n
• Present value of money (P) is calculated as: P = F(1 + i)^(-n)
• Future value of money (F) is also calculated as: F = A((1 + i)^n - 1) / i
• Period payment amount (A) is calculated as: A = F((1 + i)^n - 1) / i(1 + i)^n
• Present worth of money (P) is also calculated as: P = A((1 + i)^n - 1) / i(1 + i)^n

Reliability

• Probability of failure (Pf) is calculated as: Pf = 1 - R(t)
• Reliability (R(t)) is calculated as: R(t) = e^(-λt)
• Probability of failure (Pf) is also calculated as: Pf = (1 - Ps)

Noise

• Sound intensity (I) is calculated as: I = p^2 / ρc

Mechanics

• Frictional force (F) is calculated as: F = μN
• Force (F) is also calculated as: F = F1D1 / D2
• Velocity (v) is calculated as: v = vo + at
• Displacement (s) is calculated as: s = vot + (1/2)at^2
• Kinetic energy (K.E.) is calculated as: K.E. = (1/2)mv^2
• Potential energy (P.E.) is calculated as: P.E. = mgh or P.E. = (1/2)kx^2
• Momentum (ρ) is calculated as: ρ = mv
• Force (F) is also calculated as: F = ma
• Work done (W) is calculated as: W = mg or W = Fs

Ergonomic (Revised NIOSH Lifting Equations)

• Lifting Index (LI) is calculated as: LI = L / RWL
• Recommended weight limit (RWL) is calculated as: RWL = LC × HM × VM × DM × AM × FM × CM

Heat Stress and Relative Humidity

• Indoor (no solar load) equation: 0.7WB + 0.3GT
• Outdoors (with solar heat load) equation: 0.7WB + 0.2GT = 0.1DB

Concentrations of Vapors and Gases

• ppm is calculated as: ppm = mg/m3 × 24.45 / MW
• Threshold limit value (TLV) is calculated as: TLVm = f1/TLV1 + f2/TLV2 + … + fn/TLVn
• Lower flammability limit (LFL) is calculated as: LFLm = f1/LFL1 + f2/LFL2 + … + fn/LFLn

Gas Laws

• PV = nRT
• P1V1 / T1 = P2V2 / T2

Sound Intensity Calculations

• The equation for combined sound pressure level is: Lpt = 10 log ∑ 10^(Lpi/10)
• Lpt is the combined sound pressure level, and Lpi is the individual measured sound pressure level
• Sound power level (Lw) is calculated as: Lw = 10 log (W/Wo)
• Where W is the acoustic power, and Wo is the reference acoustic power (10^−12 W)

Sound Pressure Level

• Sound pressure level (Lp) is calculated as: Lp = 20 log (p/po)
• Where p is the measured sound pressure level, and po is the reference sound pressure level (0.00002 N/m2)

Time Allowed for Exposure

• The time allowed for exposure (T) is calculated as: T = (L - 90) / 5
• Where L is the sound pressure level (dB)

Dosage

• Dosage (D) is calculated as: D = 100 ∑ (Ci / Ti)
• Where Ci is the actual exposure time, and Ti is the allowed exposure time

Noise Reduction

• Noise reduction (dB) is calculated as: dB = 10 log (A2 / A1)
• Where A1 is the total number of absorption units before treatment, and A2 is the total number after treatment

Radiation

• Ionizing radiation intensity (I) is calculated as: I2 = I1 * (d1 / d2)^2
• Where I1 is the initial intensity, and d1 and d2 are the distances from the source
• Non-ionizing radiation power density (W) is calculated as: W = 16P / (πD^2 A)
• Where P is the antenna power, D is the diameter of the antenna, and A is the effective antenna area

Ventilation

• Actual ventilation rate (Q) is calculated as: Q = 403 * 10^6 * SG * ER * K / (MW * C)
• Where SG is the specific gravity of the volatile liquid, ER is the evaporation rate, K is the design distribution constant, MW is the molecular weight, and C is the desired concentration
• Velocity of air (V) is calculated as: V = 4005 * VP / (10 * x^2 + A)
• Where VP is the velocity pressure, x is the source distance from the hood opening, and A is the area

Engineering Economy

• Future value of money (F) is calculated as: F = P * (1 + i)^n
• Present worth of money (P) is calculated as: P = F / (1 + i)^n
• Annual payment (A) is calculated as: A = F * (i * (1 + i)^n) / ((1 + i)^n - 1)

Reliability

• Probability of failure (Pf) is calculated as: Pf = 1 - R(t)
• Reliability (R(t)) is calculated as: R(t) = e^(-λt)
• Where λ is the number of failures divided by the number of time units during which all items were exposed

Mechanics

• F = μN, where F is frictional force, μ is coefficient of friction, and N is newtons
• F1D1 = F2D2, where F is force, and D is distance
• v = vo + at, where v is velocity, vo is original velocity, a is acceleration, and t is time
• s = vot + (1/2)at^2, where s is displacement of the object, vo is initial velocity, t is time, and a is acceleration
• v^2 = vo^2 + 2as, where v is final velocity, vo is initial velocity, a is acceleration, and s is displacement

Energy

• K.E. = (1/2)mv^2, where K.E. is kinetic energy, m is mass of the object, and v is speed of the object
• P.E. = mgh, where P.E. is potential energy, m is mass of the object, g is gravitation acceleration, and h is height above earth's surface
• P.E. = (1/2)kx^2, where P.E. is potential energy, k is spring constant, and x is amount of compression

Momentum

• ρ = mv, where ρ is momentum, m is mass, and v is velocity
• F = ma, where F is force, m is mass, and a is acceleration

Work and Energy

• W = mg, where W is work done, m is mass, and g is gravity
• W = Fs, where W is work done, F is force, and s is distance

Ergonomic

• Lifting Index (LI) = L / RWL, where LI is Lifting Index, L is object weight, and RWL is recommended weight limit
• RWL = LC × HM × VM × DM × AM × FM × CM, where RWL is recommended weight limit, and various multipliers (LC, HM, VM, DM, AM, FM, CM) are used to calculate it

Heat Stress and Relative Humidity

• Indoor (no solar load): 0.7 WB + 0.3 GT
• Outdoors (with solar heat load): 0.7 WB + 0.2 GT = 0.1 DB

Concentrations of Vapors and Gases

• ppm = (mg/m^3) × (24.45 / MW), where ppm is parts per million, mg/m^3 is measured mg/m^3 of the contaminant, and MW is molecular weight of the contaminant
• TLVm = (f1 / TLV1) + (f2 / TLV2) + … + (fn / TLVn), where TLVm is threshold limit value, f is fraction of chemical, and TLV is threshold limit value of the chemical
• LFLm = (f1 / LFL1) + (f2 / LFL2) + … + (fn / LFLn), where LFLm is lower flammability limit, f is fraction of chemical, and LFL is lower flammability limit

Ventilation

• Q = VA, where Q is volumetric flow rate, V is velocity of the air, and A is cross-sectional area of the duct
• V = 4005 Ce SPh, where V is velocity, Ce is coefficient of entry loss, and SPh is static pressure of the hood
• SPfan = SPout - SPin - VPin, where SPfan is static pressure of the fan, SPout is static pressure of the outlet, SPin is static pressure of the inlet, and VPin is velocity pressure of the inlet
• SPh = VP + he, where SPh is static pressure of the hood, VP is duct velocity pressure, and he is overall hood entry loss

Engineering Economy

• F = P(1 + i)^n, where F is future value of money, P is present value of money, i is interest rate, and n is number of years
• P = F(1 + i)^(-n), where P is present worth of money, F is future worth, i is interest rate, and n is number of years
• F = A((1 + i)^n - 1) / i, where F is future value of money, A is each payment, i is interest rate, and n is number of periods
• A = F(i(1 + i)^n) / ((1 + i)^n - 1), where A is yearly payment of loan, F is future value of loan, i is interest rate, and n is number of periods

Reliability

• Pf = 1 - R(t), where Pf is probability of failure, and R(t) is reliability
• R(t) = e^(-λt), where R(t) is reliability, t is time in which reliability is measured, and λ is number of failures divided by number of time units

Noise

• I = p^2 / (ρc), where I is sound intensity, p is sound pressure level, ρ is the density of the medium, and c is the speed of sound
• Lpt = 10 log (∑ 10^(Lpi/10)), where Lpt is combined sound pressure level, and Lpi is individual measured sound pressure level
• Lw = 10 log (W / Wo), where Lw is sound power level, W is acoustic power, and Wo is reference acoustic power
• Lp = 20 log (p / po), where Lp is sound pressure level, p is measured sound pressure level, and po is reference sound pressure level

Radiation

• Ionizing: I2 = I1 (d1 / d2)^2, where I is intensity of source, and d is distance from source
• Nonionizing: W = 16 P^4 / (π D^2 A), where W is power density, P is antenna power, D is diameter of antenna, and A is effective antenna area

Mechanics

• F = μN, where F is frictional force, μ is coefficient of friction, and N is newtons
• F1D1 = F2D2, where F is force, and D is distance
• v = vo + at, where v is velocity, vo is original velocity, a is acceleration, and t is time
• s = vot + (1/2)at^2, where s is displacement of the object, vo is initial velocity, t is time, and a is acceleration
• v^2 = vo^2 + 2as, where v is final velocity, vo is initial velocity, a is acceleration, and s is displacement

Energy

• K.E. = (1/2)mv^2, where K.E. is kinetic energy, m is mass of the object, and v is speed of the object
• P.E. = mgh, where P.E. is potential energy, m is mass of the object, g is gravitation acceleration, and h is height above earth's surface
• P.E. = (1/2)kx^2, where P.E. is potential energy, k is spring constant, and x is amount of compression

Momentum

• ρ = mv, where ρ is momentum, m is mass, and v is velocity
• F = ma, where F is force, m is mass, and a is acceleration

Work and Energy

• W = mg, where W is work done, m is mass, and g is gravity
• W = Fs, where W is work done, F is force, and s is distance

Ergonomic

• Lifting Index (LI) = L / RWL, where LI is Lifting Index, L is object weight, and RWL is recommended weight limit
• RWL = LC × HM × VM × DM × AM × FM × CM, where RWL is recommended weight limit, and various multipliers (LC, HM, VM, DM, AM, FM, CM) are used to calculate it

Heat Stress and Relative Humidity

• Indoor (no solar load): 0.7 WB + 0.3 GT
• Outdoors (with solar heat load): 0.7 WB + 0.2 GT = 0.1 DB

Concentrations of Vapors and Gases

• ppm = (mg/m^3) × (24.45 / MW), where ppm is parts per million, mg/m^3 is measured mg/m^3 of the contaminant, and MW is molecular weight of the contaminant
• TLVm = (f1 / TLV1) + (f2 / TLV2) + … + (fn / TLVn), where TLVm is threshold limit value, f is fraction of chemical, and TLV is threshold limit value of the chemical
• LFLm = (f1 / LFL1) + (f2 / LFL2) + … + (fn / LFLn), where LFLm is lower flammability limit, f is fraction of chemical, and LFL is lower flammability limit

Ventilation

• Q = VA, where Q is volumetric flow rate, V is velocity of the air, and A is cross-sectional area of the duct
• V = 4005 Ce SPh, where V is velocity, Ce is coefficient of entry loss, and SPh is static pressure of the hood
• SPfan = SPout - SPin - VPin, where SPfan is static pressure of the fan, SPout is static pressure of the outlet, SPin is static pressure of the inlet, and VPin is velocity pressure of the inlet
• SPh = VP + he, where SPh is static pressure of the hood, VP is duct velocity pressure, and he is overall hood entry loss

Engineering Economy

• F = P(1 + i)^n, where F is future value of money, P is present value of money, i is interest rate, and n is number of years
• P = F(1 + i)^(-n), where P is present worth of money, F is future worth, i is interest rate, and n is number of years
• F = A((1 + i)^n - 1) / i, where F is future value of money, A is each payment, i is interest rate, and n is number of periods
• A = F(i(1 + i)^n) / ((1 + i)^n - 1), where A is yearly payment of loan, F is future value of loan, i is interest rate, and n is number of periods

Reliability

• Pf = 1 - R(t), where Pf is probability of failure, and R(t) is reliability
• R(t) = e^(-λt), where R(t) is reliability, t is time in which reliability is measured, and λ is number of failures divided by number of time units

Noise

• I = p^2 / (ρc), where I is sound intensity, p is sound pressure level, ρ is the density of the medium, and c is the speed of sound
• Lpt = 10 log (∑ 10^(Lpi/10)), where Lpt is combined sound pressure level, and Lpi is individual measured sound pressure level
• Lw = 10 log (W / Wo), where Lw is sound power level, W is acoustic power, and Wo is reference acoustic power
• Lp = 20 log (p / po), where Lp is sound pressure level, p is measured sound pressure level, and po is reference sound pressure level

Radiation

• Ionizing: I2 = I1 (d1 / d2)^2, where I is intensity of source, and d is distance from source
• Nonionizing: W = 16 P^4 / (π D^2 A), where W is power density, P is antenna power, D is diameter of antenna, and A is effective antenna area

Mechanics

• F = μN, where F is frictional force, μ is coefficient of friction, and N is newtons
• F1D1 = F2D2, where F is force, and D is distance
• v = vo + at, where v is velocity, vo is original velocity, a is acceleration, and t is time
• s = vot + (1/2)at^2, where s is displacement of the object, vo is initial velocity, t is time, and a is acceleration
• v^2 = vo^2 + 2as, where v is final velocity, vo is initial velocity, a is acceleration, and s is displacement

Energy

• K.E. = (1/2)mv^2, where K.E. is kinetic energy, m is mass of the object, and v is speed of the object
• P.E. = mgh, where P.E. is potential energy, m is mass of the object, g is gravitation acceleration, and h is height above earth's surface
• P.E. = (1/2)kx^2, where P.E. is potential energy, k is spring constant, and x is amount of compression

Momentum

• ρ = mv, where ρ is momentum, m is mass, and v is velocity
• F = ma, where F is force, m is mass, and a is acceleration

Work and Energy

• W = mg, where W is work done, m is mass, and g is gravity
• W = Fs, where W is work done, F is force, and s is distance

Ergonomic

• Lifting Index (LI) = L / RWL, where LI is Lifting Index, L is object weight, and RWL is recommended weight limit
• RWL = LC × HM × VM × DM × AM × FM × CM, where RWL is recommended weight limit, and various multipliers (LC, HM, VM, DM, AM, FM, CM) are used to calculate it

Heat Stress and Relative Humidity

• Indoor (no solar load): 0.7 WB + 0.3 GT
• Outdoors (with solar heat load): 0.7 WB + 0.2 GT = 0.1 DB

Concentrations of Vapors and Gases

• ppm = (mg/m^3) × (24.45 / MW), where ppm is parts per million, mg/m^3 is measured mg/m^3 of the contaminant, and MW is molecular weight of the contaminant
• TLVm = (f1 / TLV1) + (f2 / TLV2) + … + (fn / TLVn), where TLVm is threshold limit value, f is fraction of chemical, and TLV is threshold limit value of the chemical
• LFLm = (f1 / LFL1) + (f2 / LFL2) + … + (fn / LFLn), where LFLm is lower flammability limit, f is fraction of chemical, and LFL is lower flammability limit

Ventilation

• Q = VA, where Q is volumetric flow rate, V is velocity of the air, and A is cross-sectional area of the duct
• V = 4005 Ce SPh, where V is velocity, Ce is coefficient of entry loss, and SPh is static pressure of the hood
• SPfan = SPout - SPin - VPin, where SPfan is static pressure of the fan, SPout is static pressure of the outlet, SPin is static pressure of the inlet, and VPin is velocity pressure of the inlet
• SPh = VP + he, where SPh is static pressure of the hood, VP is duct velocity pressure, and he is overall hood entry loss

Engineering Economy

• F = P(1 + i)^n, where F is future value of money, P is present value of money, i is interest rate, and n is number of years
• P = F(1 + i)^(-n), where P is present worth of money, F is future worth, i is interest rate, and n is number of years
• F = A((1 + i)^n - 1) / i, where F is future value of money, A is each payment, i is interest rate, and n is number of periods
• A = F(i(1 + i)^n) / ((1 + i)^n - 1), where A is yearly payment of loan, F is future value of loan, i is interest rate, and n is number of periods

Reliability

• Pf = 1 - R(t), where Pf is probability of failure, and R(t) is reliability
• R(t) = e^(-λt), where R(t) is reliability, t is time in which reliability is measured, and λ is number of failures divided by number of time units

Noise

• I = p^2 / (ρc), where I is sound intensity, p is sound pressure level, ρ is the density of the medium, and c is the speed of sound
• Lpt = 10 log (∑ 10^(Lpi/10)), where Lpt is combined sound pressure level, and Lpi is individual measured sound pressure level
• Lw = 10 log (W / Wo), where Lw is sound power level, W is acoustic power, and Wo is reference acoustic power
• Lp = 20 log (p / po), where Lp is sound pressure level, p is measured sound pressure level, and po is reference sound pressure level

Radiation

• Ionizing: I2 = I1 (d1 / d2)^2, where I is intensity of source, and d is distance from source
• Nonionizing: W = 16 P^4 / (π D^2 A), where W is power density, P is antenna power, D is diameter of antenna, and A is effective antenna area

This quiz covers the fundamental equations in mechanics, including frictional force, force and distance, and velocity and acceleration. Test your understanding of these essential concepts.