Refrigeration - 4 http://www.engproguides.com
2.0 KEY EQUATIONS Evaporator Net Refrigeration Effect
๐๐๐๐ก ๐๐๐๐๐๐๐๐๐๐ก๐๐๐ ๐๐๐๐๐๐ก [๐ต๐ก๐ข] = (๐ป1 โ ๐ป4) ๏ฟฝ๐ต๐ก๐ข๐๐
๏ฟฝ โ (๐ ๐๐๐๐๐ ๐น๐๐๐ค ๐ ๐๐ก๐) ๏ฟฝ๐๐๐๐๐
๏ฟฝ โ (60) ๏ฟฝ๐๐๐โ๐
๏ฟฝ
๐ป1 = ๐๐๐๐ฃ๐๐๐ ๐๐ฃ๐๐๐๐๐๐ก๐๐ ๐๐๐กโ๐๐๐๐ฆ ๏ฟฝ๐ต๐ก๐ข๐๐
๏ฟฝ ; ๐ป4 = ๐๐๐ก๐๐๐๐๐ ๐๐ฃ๐๐๐๐๐๐ก๐๐ ๐๐๐กโ๐๐๐๐ฆ [๐ต๐ก๐ข๐๐
]
Compressor Work
๐๐๐๐๐๐๐๐ ๐ ๐๐ [๐ต๐ก๐ข] = (๐ป2 โ ๐ป1) ๏ฟฝ๐ต๐ก๐ข๐๐
๏ฟฝ โ (๐ ๐๐๐๐๐ ๐น๐๐๐ค ๐ ๐๐ก๐) ๏ฟฝ๐๐๐๐๐
๏ฟฝ โ (60) ๏ฟฝ๐๐๐โ๐
๏ฟฝ
๐ป2 = ๐๐๐๐ฃ๐๐๐ ๐๐๐๐๐๐๐ ๐ ๐๐ ๐๐๐กโ๐๐๐๐ฆ ๏ฟฝ๐ต๐ก๐ข๐๐
๏ฟฝ ; ๐ป1 = ๐๐๐ก๐๐๐๐๐ ๐๐๐๐๐๐๐ ๐๐ ๐๐๐กโ๐๐๐๐ฆ [๐ต๐ก๐ข๐๐
]
Net Condenser Effect
๐๐๐๐ก ๐๐๐๐๐๐๐ ๐๐ ๐๐๐๐๐๐ก [๐ต๐ก๐ข] = (๐ป2 โ ๐ป4) ๏ฟฝ๐ต๐ก๐ข๐๐
๏ฟฝ โ (๐ ๐๐๐๐๐ ๐น๐๐๐ค ๐ ๐๐ก๐) ๏ฟฝ๐๐๐๐๐
๏ฟฝ โ (60) ๏ฟฝ๐๐๐โ๐
๏ฟฝ
๐ป2 = ๐๐๐ก๐๐๐๐๐ ๐๐๐๐๐๐๐ ๐๐ ๐๐๐กโ๐๐๐๐ฆ ๏ฟฝ๐ต๐ก๐ข๐๐
๏ฟฝ ; ๐ป4 = ๐๐๐๐ฃ๐๐๐ ๐๐๐๐๐๐๐ ๐๐ ๐๐๐กโ๐๐๐๐ฆ [๐ต๐ก๐ข๐๐
]
Net Condenser Effect Function of Compressor Work and Net Refrigeration Effect
๐๐๐๐ก ๐๐๐๐๐๐๐ ๐๐ ๐๐๐๐๐๐ก [๐ต๐ก๐ข] = ๐๐๐๐๐๐๐๐ ๐ ๐๐ [๐ต๐ก๐ข] + ๐๐๐๐ก ๐๐๐๐๐๐๐๐๐๐ก๐๐๐ ๐๐๐๐๐๐ก [๐ต๐ก๐ข]
Coefficient of Performance
๐ถ๐๐ = ๐๐๐ข๐ก
๐๐๐=๐๐๐๐ก ๐๐๐๐๐๐๐๐๐๐ก๐๐๐ ๐๐๐๐๐๐ก [๐ต๐ก๐ข]
๐๐๐๐๐๐๐๐ ๐ ๐๐ [๐ต๐ก๐ข]
Refrigeration Room Ventilation Rate
๐[๐ถ๐น๐] = 100๐๐บ0.5, where G = lbs of refrigerant.
Steam - 3 http://www.engproguides.com
2.0 KEY EQUATIONS AND TERMS
Relationship of Enthalpy of Vaporization, Enthalpy of Saturated Vapor and Liquid Water
โ๐ = โ๐ + โ๐๐
โ๐ = ๐๐๐กโ๐๐๐๐ฆ ๐๐ ๐ ๐๐ก๐ข๐๐๐ก๐๐ ๐ฃ๐๐๐๐[๐ต๐ก๐ข๐๐๐
] โ๐ = ๐๐๐กโ๐๐๐๐ฆ ๐๐ ๐ ๐๐ก๐ข๐๐๐ก๐๐ ๐๐๐๐ข๐๐ โ๐๐ = ๐๐๐กโ๐๐๐๐ฆ ๐๐ ๐ฃ๐๐๐๐๐๐ง๐๐ก๐๐๐
โ ๐๐๐ ๐๐๐กโ๐๐๐๐๐๐ ๐๐ก ๐๐๐๐ ๐ก๐๐๐ก ๐ก๐๐๐๐๐๐๐ก๐ข๐๐ & ๐๐๐๐ ๐ ๐ข๐๐ Enthalpy of Wet Steam (Mixed Region) as a Function of Steam Quality
โ๐๐๐ฅ = โ๐ + ๐ฅ โ โ๐๐ โ๐๐๐ฅ = ๐๐๐กโ๐๐๐๐ฆ ๐๐ ๐ค๐๐ก ๐ ๐ก๐๐๐ (๐๐๐ฅ ๐๐ ๐๐๐๐ข๐๐ & ๐ฃ๐๐๐๐)
๐ฅ = ๐ ๐ก๐๐๐ ๐๐ข๐๐๐๐ก๐ฆ,๐๐๐๐ฆ๐๐ ๐ ๐๐๐๐๐ก๐๐๐, % ๐ฃ๐๐๐๐ Relationship of Entropy of Vaporization, Entropy of Saturated Vapor and Liquid Water
๐ ๐ = ๐ ๐ + ๐ ๐๐ ๐ ๐ = ๐๐๐ก๐๐๐๐ฆ ๐๐ ๐ ๐๐ก๐ข๐๐๐ก๐๐ ๐ฃ๐๐๐๐[ ๐ ๐ = ๐๐๐ก๐๐๐๐ฆ ๐๐ ๐ ๐๐ก๐ข๐๐๐ก๐๐ ๐๐๐๐ข๐๐ ๐ ๐๐ = ๐๐๐ก๐๐๐๐ฆ ๐๐ ๐ฃ๐๐๐๐๐๐ง๐๐ก๐๐๐
Entropy of Wet Steam (Mixed Region) as a Function of Steam Quality
๐ ๐๐๐ฅ = ๐ ๐ + ๐ฅ โ ๐ ๐๐ ๐ ๐๐๐ฅ = ๐๐๐ก๐๐๐๐ฆ ๐๐ ๐ค๐๐ก ๐ ๐ก๐๐๐ (๐๐๐ฅ ๐๐ ๐๐๐๐ข๐๐ & ๐ฃ๐๐๐๐)
๐ฅ = ๐ ๐ก๐๐๐ ๐๐ข๐๐๐๐ก๐ฆ,๐๐๐๐ฆ๐๐ ๐ ๐๐๐๐๐ก๐๐๐, % ๐ฃ๐๐๐๐
Heat Available from Condensing Steam
๐ = ๏ฟฝฬ๏ฟฝ โ โ๐๐
๏ฟฝฬ๏ฟฝ = ๐๐๐ ๐ ๐๐๐๐ค ๐๐๐ก๐ [๐๐๐โ๐
]
๐ = ๐๐๐๐๐๐ฆ [๐ต๐ก๐ขโ๐
]
Throttling: Irreversible Adiabatic [Constant Enthalpy] or Isenthalpic
โ๐๐๐๐ก๐๐๐ = โ๐๐๐๐๐
Steam - 4 http://www.engproguides.com
Tank Heating/Cooling: Isometric [Constant Volume]
๐ฃ๐๐๐๐ก๐๐๐ = ๐ฃ๐๐๐๐๐
๐ฃ = ๐ ๐๐๐๐๐๐๐ ๐ฃ๐๐๐ข๐๐ [๐๐ก3
๐๐]
Turbine Expansion: Isentropic [Constant Entropy] or Reversible Adiabatic
๐ ๐๐๐๐ก๐๐๐ = ๐ ๐๐๐๐๐
Compressor: Isentropic [Constant Entropy] or Reversible Adiabatic
๐ ๐๐๐๐ก๐๐๐ = ๐ ๐๐๐๐๐
Boiler Heating: Isobaric [Constant Pressure]
๐๐๐๐๐ก๐๐๐ = ๐๐๐๐๐๐ ๐ = ๐๐๐๐ ๐ ๐ข๐๐ [๐๐ ๐๐]
Heat Exchanger (Boiling or Condensing): Isothermal [Constant Temperature]
๐๐๐๐๐ก๐๐๐ = ๐๐๐๐๐๐
Boiler Efficiency
๐๐๐๐๐๐๐ =(๏ฟฝฬ๏ฟฝ๐๐๐๐๐ค๐๐ก๐๐) โ (๐ป๐ ๐ก๐๐๐,๐๐ข๐ก โ ๐ป๐๐๐๐๐ค๐๐ก๐๐,๐๐)
๏ฟฝฬ๏ฟฝ๐๐ข๐๐ โ ๐ป๐ป๐
Convert Feed-Water Flowrate in GPM to Steam Flowrate in lbs/hr
1๐๐๐๐๐๐ ๐๐ ๐ค๐๐ก๐๐
๐๐๐๐ข๐ก๐โ [
1 ๐๐ก3
7.48 ๐๐๐๐๐๐โ
62.4 ๐๐๐๐ก3
โ60 ๐๐๐๐ข๐ก๐โ๐๐ข๐
] = 500๐๐๐ โ๐
Simplified Steam Heating Coil: Steam to Water Heat Transfer
๏ฟฝฬ๏ฟฝ๐ ๐ก๐๐๐ โ โ๐๐ = 500 โ ๐บ๐๐๐ค๐๐ก๐๐ โ โ๐
Steam - 5 http://www.engproguides.com
Simplified Steam Heating Coil: Steam to Air Heat Transfer
๏ฟฝฬ๏ฟฝ๐ ๐ก๐๐๐ โ โ๐๐ = 1.08 โ ๐ถ๐น๐๐๐๐ โ โ๐
Psychrometrics - 4 http://www.engproguides.com
2.0 KEY TERMS
1 Dry Bulb Temperature
Dry bulb temperature indicates the amount of energy independent of the amount of water in the air.
Measured with a thermometer.
๐ผ๐๐๐๐ = [โ]
2 Wet Bulb Temperature
Wet bulb temperature indicates the amount of water in the air. Measured
with a sling psychrometer or hygrometer. ๐ผ๐๐๐๐ = [โ]
3 Dew Point
The temperature at which moist air must be cooled to, in order for water to
condense out of the air. ๐ผ๐๐๐๐ = [โ]
4 Humidity Ratio Humidity ratio or specific humidity is the measure of the amount of water in air.
๐๐๐๐ก๐ = [๐๐ ๐๐ ๐พ๐๐๐๐ ๐ฝ๐๐๐๐๐๐๐ ๐๐ ๐ซ๐๐ ๐จ๐๐
]
5 Relative Humidity
Relative Humidity indicates the amount of water in the air relative to the total
amount of water the air can hold. Units = [%]
Psychrometrics - 5 http://www.engproguides.com
6 Sensible Heat
Sensible heat indicates the amount of dry heat. It indicates the amount of
energy either absorbed or released to change the dry bulb temperature of the
air. ๐ผ๐๐๐๐ = [
๐ฉ๐๐๐๐ ๐๐ ๐๐๐
]
7 Latent Heat
Latent heat indicates the amount of energy in the air due to moisture. It is
the amount of heat released when water in the air condenses out or the amount of heat absorbed by water in
order to vaporize the water. ๐ผ๐๐๐๐ = [
๐ฉ๐๐๐๐ ๐๐ ๐๐๐
]
8 Enthalpy
Enthalpy is an indication of the total amount of energy in the air, both
sensible and latent. ๐ผ๐๐๐๐ = [
๐ฉ๐๐๐๐ ๐๐ ๐๐๐
]
Exam Tip #1: Do not spend enormous amounts of time trying to interpolate the exact value on the psychrometric chart.
The psychrometric chart is provided as part of the NCEES exam, but the chart is small and unclear compared to the ones typically used in practice. It is the opinion of the writer that this fact should indicate to the test taker that it is not important to get the values to the nearest 0.0001 (exaggeration) because it is impossible. In addition, the exam writer would not provide possible multiple choice answers that are fairly close together because of the confusion that would arise.
Exam Tip #2: During the exam, do not write on anything that is not part of the exam, including your own psychrometric chart. This may result in disqualification.
Psychrometrics - 6 http://www.engproguides.com
3.0 KEY EQUATIONS
Sensible Heat Equation
๐๐ ๐๐๐ ๐๐๐๐ = 1.08 โ โ๐๐ท๐ต โ ๐ถ๐น๐
๐๐ ๐๐๐ ๐๐๐๐ = ๐ ๐๐๐ ๐๐๐๐ โ๐๐๐ก [๐ต๐ก๐ขโ๐
] โ๐๐ท๐ต = ๐๐๐๐๐๐๐๐๐๐ ๐๐ ๐๐๐ฆ ๐๐ข๐๐ ๐ก๐๐๐๐๐๐๐ก๐ข๐๐ ๐๐๐ก๐ค๐๐๐ ๐๐๐ก๐๐๐๐๐ ๐๐๐ ๐๐๐๐ฃ๐๐๐
๐ถ๐น๐ = ๐ฃ๐๐๐ข๐๐๐ก๐๐๐ ๐๐๐๐ค ๐๐๐ก๐, ๐๐ข๐๐๐ ๐๐๐๐ก ๐๐๐ ๐๐๐๐ข๐ก๐
Latent Heat Equation
๐ธ๐๐๐๐๐๐ = ๐.๐๐ โ โ๐พ๐ฎ๐น โ ๐ช๐ญ๐ด
๐๐๐๐ก๐๐๐ก = ๐๐๐ก๐๐๐ก โ๐๐๐ก [๐ต๐ก๐ขโ๐
]
โ๐พ๐ฎ๐น = ๐โ๐๐๐๐ ๐๐ โ๐ข๐๐๐๐๐ก๐ฆ ๐๐๐ก๐๐ [๐๐๐๐๐ ๐๐ ๐ค๐๐ก๐๐ ๐ฃ๐๐๐๐
๐๐ ๐๐ ๐๐๐ฆ ๐๐๐]
๐ถ๐น๐ = ๐ฃ๐๐๐ข๐๐๐ก๐๐๐ ๐๐๐๐ค ๐๐๐ก๐, ๐๐ข๐๐๐ ๐๐๐๐ก ๐๐๐ ๐๐๐๐ข๐ก๐ Latent Heat Equation
๐ธ๐๐๐๐๐๐ = ๐,๐๐๐ โ โ๐พ๐ณ๐ฉ โ ๐ช๐ญ๐ด
๐๐๐๐ก๐๐๐ก = ๐๐๐ก๐๐๐ก โ๐๐๐ก [๐ต๐ก๐ขโ๐
]
โ๐พ๐๐ = ๐โ๐๐๐๐ ๐๐ โ๐ข๐๐๐๐๐ก๐ฆ ๐๐๐ก๐๐ [๐๐๐ ๐๐ ๐ค๐๐ก๐๐ ๐ฃ๐๐๐๐
๐๐ ๐๐ ๐๐๐ฆ ๐๐๐]
๐ถ๐น๐ = ๐ฃ๐๐๐ข๐๐๐ก๐๐๐ ๐๐๐๐ค ๐๐๐ก๐, ๐๐ข๐๐๐ ๐๐๐๐ก ๐๐๐ ๐๐๐๐ข๐ก๐ Total Heat Equation
๐ธ๐๐๐๐๐ = ๐.๐ โ (โ๐) โ ๐ช๐ญ๐ด
๐๐ก๐๐ก๐๐ = ๐ก๐๐ก๐๐ โ๐๐๐ก [๐ต๐ก๐ขโ๐
] โ๐ = ๐โ๐๐๐๐ ๐๐ ๐๐๐กโ๐๐๐๐ฆ ๐๐๐ก๐ค๐๐๐ ๐๐๐ก๐๐๐๐๐ ๐๐๐ ๐๐๐๐ฃ๐๐๐ ๐ถ๐น๐ = ๐ฃ๐๐๐ข๐๐๐ก๐๐๐ ๐๐๐๐ค ๐๐๐ก๐, ๐๐ข๐๐๐ ๐๐๐๐ก ๐๐๐ ๐๐๐๐ข๐ก๐
Air Mixing Equation - Dry Bulb
๐ป๐๐๐,๐ซ๐ฉ = ๐ป๐,๐ซ๐ฉ โ %๐ + ๐ป๐,๐ซ๐ฉ โ %๐ ๐ป๐๐๐,๐ซ๐ฉ = ๐๐๐ฅ๐๐ ๐๐๐ ๐๐๐ฆ ๐๐ข๐๐ ๐ก๐๐๐๐๐๐๐ก๐ข๐๐ ๐ป๐,๐ซ๐ฉ = ๐๐๐ ๐ ๐ก๐๐๐๐ 1 ๐๐๐ฆ ๐๐ข๐๐ ๐ก๐๐๐๐๐๐๐ก๐ข๐๐
%๐ = ๐๐๐ ๐ ๐ก๐๐๐๐ 1 ๐๐๐๐๐๐๐ก ๐๐ฆ ๐๐๐ ๐ ๐ป๐,๐ซ๐ฉ = ๐๐๐ ๐ ๐ก๐๐๐๐ 2 ๐๐๐ฆ ๐๐ข๐๐ ๐ก๐๐๐๐๐๐๐ก๐ข๐๐
%๐ = ๐๐๐ ๐ ๐ก๐๐๐๐ 2 ๐๐๐๐๐๐๐ก ๐๐ฆ ๐๐๐ ๐
Psychrometrics - 7 http://www.engproguides.com
Air Mixing Equation - Dry Bulb
๐ป๐๐๐,๐ซ๐ฉ =๐ป๐,๐ซ๐ฉ โ ๐ช๐ญ๐ด๐ + ๐ป๐,๐ซ๐ฉ โ ๐ช๐ญ๐ด๐
๐ช๐ญ๐ด๐ + ๐ช๐ญ๐ด๐
๐ช๐ญ๐ด๐ = ๐๐๐ ๐ ๐ก๐๐๐๐ 1 ๐ฃ๐๐๐ข๐๐๐ก๐๐๐ ๐๐๐๐ค ๐๐๐ก๐ ๐ช๐ญ๐ด๐ = ๐๐๐ ๐ ๐ก๐๐๐๐ 2 ๐ฃ๐๐๐ข๐๐๐ก๐๐๐ ๐๐๐๐ค ๐๐๐ก๐
Air Mixing Equation - Enthalpy
๐๐๐๐ = ๐๐,๐ซ๐ฉ โ %๐ + ๐๐,๐ซ๐ฉ โ %๐ ๐๐๐๐ = ๐๐๐ฅ๐๐ ๐๐๐ ๐๐๐กโ๐๐๐๐ฆ ๐๐ = ๐๐๐ ๐ ๐ก๐๐๐๐ 1 ๐๐๐กโ๐๐๐๐ฆ
%๐ = ๐๐๐ ๐ ๐ก๐๐๐๐ 1 ๐๐๐๐๐๐๐ก ๐๐ฆ ๐๐๐ ๐ ๐๐ = ๐๐๐ ๐ ๐ก๐๐๐๐ 2 ๐๐๐กโ๐๐๐๐ฆ
%๐ = ๐๐๐ ๐ ๐ก๐๐๐๐ 2 ๐๐๐๐๐๐๐ก ๐๐ฆ ๐๐๐ ๐ Air Mixing Equation - Enthalpy
๐๐๐๐ =๐๐ โ ๐ช๐ญ๐ด๐ + ๐๐ โ ๐ช๐ญ๐ด๐
๐ช๐ญ๐ด๐ + ๐ช๐ญ๐ด๐
Relative Humidity as a Function of Humidity Ratio and Partial Pressures
๐น๐ฏ =๐๐๐๐บ๐จ๐ป
๐ ๐๐๐% โ ๐พ๐
๐พ๐บ๐จ๐ป๐ ๐๐๐%
๐น๐ฏ = ๐๐๐๐๐ก๐๐ฃ๐ โ๐ข๐๐๐๐๐ก๐ฆ
๐๐ = ๐๐๐๐ก๐๐๐ ๐๐๐๐ ๐ ๐ข๐๐ ๐๐ ๐ค๐๐ก๐๐ ๐ฃ๐๐๐๐ ๐๐ ๐กโ๐ ๐๐๐ ๐ ๐ก๐๐๐๐ ๐๐บ๐จ๐ป = ๐ ๐๐ก๐ข๐๐๐ก๐๐ ๐ฃ๐๐๐๐ ๐๐๐๐ ๐ ๐ข๐๐ ๐๐ ๐ค๐๐ก๐๐ ๐๐ก ๐กโ๐ ๐ก๐๐๐๐๐๐๐ก๐ข๐๐ ๐๐ ๐๐ข๐๐ ๐ก๐๐๐
๐พ๐ = โ๐ข๐๐๐๐๐ก๐ฆ ๐๐๐ก๐๐ ๐๐ ๐กโ๐ ๐๐๐ ๐ ๐ก๐๐๐๐ ๐พ๐บ๐จ๐ป = โ๐ข๐๐๐๐๐ก๐ฆ ๐๐๐ก๐๐ ๐๐ ๐กโ๐ ๐๐๐ ๐ ๐ก๐๐๐๐ ๐๐ก ๐ ๐๐ก๐ข๐๐๐ก๐๐๐ ๐๐ก ๐กโ๐ ๐ก๐๐๐๐๐๐๐ก๐ข๐๐ ๐๐ ๐๐ข๐๐ ๐ก๐๐๐
Heat Transfer - 4 http://www.engproguides.com
2.0 IMPORTANT TERMS & EQUATIONS
Convert U-Factor to R-Value
๐ =1๐
๐ = โ๐๐๐ก ๐ก๐๐๐๐ ๐๐๐ ๐๐๐๐๐๐๐๐๐๐๐ก [๐ต๐ก๐ข
โ๐ โ ๐๐ก2 โ โ ]
๐ = ๐กโ๐๐๐๐๐ ๐๐๐ ๐๐ ๐ก๐๐๐๐ [โ๐ โ ๐๐ก2 โ โ
๐ต๐ก๐ข ]
Addition of R-Values
๐ ๐ก๐๐ก๐๐ = ๐ 1 + ๐ 2 + ๐ 3 โฆ + ๐ ๐
Addition of U-Factors
1๐๐ก๐๐ก๐๐
=1๐1
+1๐2
+1๐3
โฆ +1๐๐
Thermal Conductivity Units
๐ =๐ต๐ก๐ข
โ๐ โ ๐๐ก โ โ
Convert Thermal Conductivity to R-Value and U-Factor
๐ =๐ก๐
๐ก = ๐กโ๐๐๐๐๐๐ ๐ ๐๐ ๐๐๐ก๐๐๐๐๐ [๐๐ก]
๐ = ๐กโ๐๐๐๐๐ ๐๐๐๐๐ข๐๐ก๐๐ฃ๐๐ก๐ฆ [๐ต๐ก๐ข
โ๐ โ ๐๐ก โ โ
๐ =๐๐ก
Heat Transfer Equation
๐ = ๐ โ ๐ด โ โ๐
๐ = ๐๐ฃ๐๐๐๐๐ โ๐๐๐ก ๐ก๐๐๐๐ ๐๐๐ ๐๐๐๐๐๐๐๐๐๐๐ก[๐ต๐ก๐ข
โ๐ โ ๐๐ก2 โ โ ]
๐ด = ๐๐๐๐ ๐๐ โ๐๐๐ก ๐ก๐๐๐๐ ๐๐๐ [๐๐ก2] โ๐ = ๐ก๐๐๐๐๐๐๐ก๐ข๐๐ ๐๐๐๐๐๐๐๐๐๐ ๐๐๐ก๐ค๐๐๐ โ๐๐ก ๐๐๐ ๐๐๐๐ ๐๐๐๐๐ ๐๐ โ๐๐๐ก ๐ก๐๐๐๐ ๐๐๐ [โ]
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Log Mean Temperature Difference (LMTD)
๐ฟ๐๐๐ท =โ๐๐ โ โ๐๐
ln (โ๐๐โ๐๐)
โ๐๐ = ๐ก๐๐๐๐๐๐๐ก๐ข๐๐ ๐๐๐๐๐๐๐๐๐๐ ๐๐ก ๐๐๐ก๐๐๐๐๐ โ๐๐ = ๐ก๐๐๐๐๐๐๐ก๐ข๐๐ ๐๐๐๐๐๐๐๐๐๐ ๐๐ก ๐๐ฅ๐๐ก
Counter-flow Heat Exchanger
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Parallel-flow Heat Exchanger
Conduction Heat Transfer Equation
๐ =๐ โ ๐ด โ (๐โ๐๐ก โ ๐๐๐๐๐)
๐ก
๐คโ๐๐๐ ๐ = ๐๐ข๐๐๐ก๐๐ก๐ฆ ๐๐ โ๐๐๐ก ๐ก๐๐๐๐ ๐๐๐๐๐ ๏ฟฝ๐ต๐ก๐ขโ๐
๏ฟฝ
๐ = ๐กโ๐๐๐๐๐ ๐๐๐๐๐ข๐๐ก๐๐ฃ๐๐ก๐ฆ ๐๐ ๐๐๐ก๐๐๐๐๐ ๏ฟฝ๐ต๐ก๐ข
โ๐ โ ๐๐ก โ โ๏ฟฝ
๐โ๐๐ก โ ๐๐๐๐๐ = ๐ก๐๐๐๐๐๐๐ก๐ข๐๐ ๐๐๐๐๐๐๐๐๐๐ ๐๐๐ก๐ค๐๐๐ ๐๐๐๐๐๐๐ ๐๐๐ ๐๐ข๐ก๐๐๐๐๐ [โ] ๐ก = ๐กโ๐๐๐๐๐๐ ๐ ๐๐ ๐๐๐ก๐๐๐๐๐ [๐๐ก] ๐ด = ๐๐๐๐ ๐๐ โ๐๐๐ก ๐ก๐๐๐๐ ๐๐๐ [๐๐ก2]
Convective Heat Transfer Equation
๐ = โ โ ๐ด โ โ๐
โ = ๐๐๐๐ฃ๐๐๐ก๐๐ฃ๐ โ๐๐๐ก ๐ก๐๐๐๐ ๐๐๐ ๐๐๐๐๐๐๐๐๐๐๐ก[๐ต๐ก๐ข
โ๐ โ ๐๐ก2 โ โ ]
๐ด = ๐๐๐๐ ๐๐ โ๐๐๐ก ๐ก๐๐๐๐ ๐๐๐ [๐๐ก2] โ๐ = ๐ก๐๐๐๐๐๐๐ก๐ข๐๐ ๐๐๐๐๐๐๐๐๐๐ ๐๐๐ก๐ค๐๐๐ โ๐๐ก ๐๐๐ ๐๐๐๐ ๐๐๐๐๐ ๐๐ โ๐๐๐ก ๐ก๐๐๐๐ ๐๐๐ [โ]
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Radiative Heat Transfer Equation
๐ = โ๐๐๐ โ ๐ด โ โ๐
โ๐๐๐ = ๐๐๐๐๐๐ก๐๐๐ โ๐๐๐ก ๐ก๐๐๐๐ ๐๐๐ ๐๐๐๐๐๐๐๐๐๐๐ก[๐ต๐ก๐ข
โ๐ โ ๐๐ก2 โ โ ]
๐ด = ๐๐๐๐ ๐๐ โ๐๐๐ก ๐ก๐๐๐๐ ๐๐๐ [๐๐ก2] โ๐ = ๐ก๐๐๐๐๐๐๐ก๐ข๐๐ ๐๐๐๐๐๐๐๐๐๐ ๐๐๐ก๐ค๐๐๐ โ๐๐ก ๐๐๐ ๐๐๐๐ ๐๐๐๐๐ ๐๐ โ๐๐๐ก ๐ก๐๐๐๐ ๐๐๐ [โ]
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2.0 KEY EQUATIONS AND TERMS
Mechanical Horsepower of a Fan
๐๐ป๐ =๐ถ๐น๐ โ ๐๐๐[๐๐.๐ค๐]
6,356
๐๐ป๐ = ๐๐๐โ๐๐๐๐๐๐ โ๐๐๐ ๐ ๐๐๐ค๐๐ [๐ป๐] ๐ถ๐น๐ = ๐๐๐๐๐๐๐ค
๐๐๐ = ๐ก๐๐ก๐๐ ๐ ๐ก๐๐ก๐๐ ๐๐๐๐ ๐ ๐ข๐๐ [๐๐.๐ค๐] Convert Mechanical Horsepower to Brake Horsepower
๐ต๐ป๐ = ๐๐ป๐ โ (1
๐๐๐ ๐๐๐๐๐๐๐๐๐๐ฆ)
Convert Brake Horsepower to Electric Horsepower
๐ป๐ = ๐ต๐ป๐ โ ๏ฟฝ1
๐๐๐ก๐๐ ๐๐๐๐๐๐๐๐๐๐ฆ๏ฟฝ
Velocity Pressure as a Function of Air Velocity
๐๐ =๐น๐๐4005
[๐๐.๐ค๐]
๐น๐๐ = ๐๐๐ ๐ฃ๐๐๐๐๐๐ก๐ฆ ๐๐ ๐๐๐๐ก ๐๐๐ ๐๐๐๐ข๐ก๐ ๐๐ = ๐ฃ๐๐๐๐๐๐ก๐ฆ ๐๐๐๐ ๐ ๐ข๐๐ [๐๐.๐ค๐]
Simplified Sensible Heat Equation
๐ ๏ฟฝ๐ต๐ก๐ขโ๏ฟฝ = 1.08 โ ๐ถ๐น๐ โ โ๐[โ]
โ ๐๐๐ ๐๐๐๐๐๐ก๐๐๐๐ ๐๐ก 70โ ๐๐๐ 1 ๐๐ก๐.
Friction loss due to length of duct
๐น๐๐ข๐๐ก[๐๐.๐ค๐] = ๐ฟ[๐๐ก] โ ๐[๐๐.๐ค๐100 ๐๐ก
]
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Fan Affinity Laws
๐ช๐จ๐บ๐ฌ ๐: ๐ต๐๐๐ = ๐ต๐๐๐
๐ถ๐น๐๐๐๐ค = ๏ฟฝ๐ ๐๐๐๐๐ค
๐ ๐๐๐๐๐๏ฟฝ1๐ถ๐น๐๐๐๐
๐๐๐๐ค = ๏ฟฝ๐ ๐๐๐๐๐ค
๐ ๐๐๐๐๐๏ฟฝ2๐๐๐๐
๐ต๐ป๐๐๐๐ค = ๏ฟฝ๐ ๐๐๐๐๐ค
๐ ๐๐๐๐๐๏ฟฝ3๐ต๐ป๐๐๐๐
Fan Affinity Laws
๐ช๐จ๐บ๐ฌ ๐: ๐น๐ท๐ด๐๐๐ = ๐น๐ท๐ด๐๐๐
๐ถ๐น๐๐๐๐ค = ๏ฟฝ๐๐๐๐ค๐๐๐๐
๏ฟฝ1๐ถ๐น๐๐๐๐
๐๐๐๐ค = ๏ฟฝ๐๐๐๐ค๐๐๐๐
๏ฟฝ2๐๐๐๐
๐ต๐ป๐๐๐๐ค = ๏ฟฝ๐๐๐๐ค๐๐๐๐
๏ฟฝ3๐ต๐ป๐๐๐๐
Bypass Factor Equation for Coils
๐ต๐ฆ๐๐๐ ๐น๐๐๐ก๐๐ =โ๐๐๐ก๐๐๐๐๐ ๐๐๐๐ โ โ๐๐๐๐ฃ๐๐๐ ๐๐๐๐
โ๐๐๐ก๐๐๐๐๐ ๐๐๐๐ โ โ๐๐๐๐๐๐๐ก๐ข๐ ๐๐๐ค ๐๐๐๐๐ก
where h is equal to the enthalpy
Bypass Factor Equation for Coils
๐ต๐ฆ๐๐๐ ๐น๐๐๐ก๐๐ =๐๐๐๐ก๐๐๐๐๐ ๐๐๐๐ โ ๐๐๐๐๐ฃ๐๐๐ ๐๐๐๐
๐๐๐๐ก๐๐๐๐๐ ๐๐๐๐ โ ๐๐๐๐๐๐๐๐ก๐ข๐ ๐๐๐ค ๐๐๐๐๐ก
where T is equal to the dry bulb temperature
Bypass Factor Equation for Coils
๐ต๐ฆ๐๐๐ ๐น๐๐๐ก๐๐ =๐๐๐๐ก๐๐๐๐๐ ๐๐๐๐ โ ๐๐๐๐๐ฃ๐๐๐ ๐๐๐๐
๐๐๐๐ก๐๐๐๐๐ ๐๐๐๐ โ ๐๐๐๐๐๐๐๐ก๐ข๐ ๐๐๐ค ๐๐๐๐๐ก
where W is equal to the humidity ratio
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Moisture Transfer Equation
๐ป = 60 โ ๐ โ ๐ โ (๐๐๐ฅ๐๐ก โ ๐๐๐๐ก๐๐)
๐ = ๐กโ๐ โ๐ข๐๐๐๐๐ก๐ฆ ๐๐๐ก๐๐ ๐๐๐ก๐๐๐๐๐ ๐๐ ๐๐๐๐ฃ๐๐๐ ๐กโ๐ ๐ ๐ฆ๐ ๐ก๐๐[๐๐ ๐๐ ๐ค๐๐ก๐๐]
[๐๐ ๐๐ ๐๐๐ฆ ๐๐๐]
๐ = ๐๐๐๐ ๐๐ก๐ฆ ๐๐ ๐๐๐ [๐๐๐๐ก3
]
๐ = ๐๐๐ ๐๐๐๐ค ๐๐๐ก๐ [๐๐ก3
๐๐๐]
๐ป = ๐๐๐๐ ๐ก๐ข๐๐ ๐ก๐๐๐๐ ๐๐๐๐๐๐ [๐๐โ๐
]
Energy Recovery Device Efficiency Equations
๐๐ ๐๐๐ ๐๐๐๐ =๐๐ ๐๐๐ ๐๐๐๐,๐๐๐ก๐ข๐๐
๐๐ ๐๐๐ ๐๐๐๐,๐๐๐ฅ
๐๐๐๐ก๐๐๐ก =๐๐๐๐ก๐๐๐ก,๐๐๐ก๐ข๐๐
๐๐๐๐ก๐๐๐ก,๐๐๐ฅ
๐๐ก๐๐ก๐๐ =๐๐ก๐๐ก๐๐,๐๐๐ก๐ข๐๐๐๐ก๐๐ก๐๐,๐๐๐ฅ
Energy Recovery Device Determine Actual Sensible Heat Transferred
๐๐ ๐๐๐ ๐๐๐๐,๐๐๐ก๐ข๐๐ = 1.08 โ ๐ถ๐น๐๐๐ข๐ก๐๐๐๐ โ (๐๐๐ข๐ก๐๐๐๐ โ ๐๐ ๐ข๐๐๐๐ฆ) ๐๐ ๐๐๐ ๐๐๐๐,๐๐๐ก๐ข๐๐ = 1.08 โ ๐ถ๐น๐๐๐๐ก๐ข๐๐ โ (๐๐๐๐ก๐ข๐๐ โ ๐๐๐ฅโ๐๐ข๐ ๐ก)
Energy Recovery Device Determine Maximum Possible Sensible Heat Transferred
๐๐ ๐๐๐ ๐๐๐๐,๐๐๐ฅ = 1.08 โ ๐ถ๐น๐๐๐๐ โ (๐๐๐ข๐ก๐๐๐๐ โ ๐๐๐๐ก๐ข๐๐)
Energy Recovery Device Determine Actual Latent Heat Transferred
๐๐๐๐ก๐๐๐ก,๐๐๐ก๐ข๐๐ = 4,770 โ ๐ถ๐น๐๐๐ข๐ก๐๐๐๐ โ (๐๐๐ข๐ก๐๐๐๐ โ๐๐ ๐ข๐๐๐๐ฆ) ๐๐๐๐ก๐๐๐ก,๐๐๐ก๐ข๐๐ = 4,770 โ ๐ถ๐น๐๐๐๐ก๐ข๐๐ โ (๐๐๐๐ก๐ข๐๐ โ๐๐๐ฅโ๐๐ข๐ ๐ก)
Energy Recovery Device Determine Maximum Possible Latent Heat Transferred
๐๐๐๐ก๐๐๐ก,๐๐๐ฅ = 4,770 โ ๐ถ๐น๐๐๐๐ก๐ข๐๐ โ (๐๐๐ข๐ก๐๐๐๐ โ๐๐๐๐ก๐ข๐๐)
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Energy Recovery Device Determine Actual Enthalpy Transferred
๐๐ก๐๐ก๐๐,๐๐๐ก๐ข๐๐ = 4.5 โ ๐ถ๐น๐๐๐ข๐ก๐๐๐๐ โ (โ๐๐ข๐ก๐๐๐๐ โ โ๐ ๐ข๐๐๐๐ฆ) ๐๐ ๐ก๐๐ก๐๐,๐๐๐ก๐ข๐๐ = 4.5 โ ๐ถ๐น๐๐๐๐ก๐ข๐๐ โ (โ๐๐๐ก๐ข๐๐ โ โ๐๐ฅโ๐๐ข๐ ๐ก)
Energy Recovery Device Determine Maximum Possible Enthalpy Transferred
๐๐ก๐๐ก๐๐,๐๐๐ฅ = 4.5 โ ๐ถ๐น๐๐๐ข๐ก๐๐๐๐ โ (โ๐๐ข๐ก๐๐๐๐ โ โ๐๐๐ก๐ข๐๐)
Darcy Weisbach Equation
โ =๐๐ฟ๐ฃ2
2๐ท๐ [๐ท๐๐๐๐ฆ ๐๐๐๐ ๐๐๐โ ๐ธ๐๐ข๐๐ก๐๐๐]
๐คโ๐๐๐ โ = ๐๐ก ๐๐ โ๐๐๐; ๐ = ๐ท๐๐๐๐ฆ ๐๐๐๐๐ก๐๐๐ ๐๐๐๐ก๐๐; ๐ฃ = ๐ฃ๐๐๐๐๐๐ก๐ฆ ๏ฟฝ๐๐ก๐ ๐๐
๏ฟฝ,
๐ท = ๐๐๐๐๐ ๐๐๐๐๐๐ก๐๐ [๐๐ก],๐ = ๐๐๐๐ฃ๐๐ก๐ฆ [32.2๐๐ก๐ ๐๐2
]
Darcy Weisbach Equation
โ =๐๐ฟ๐ฃ2
2๐ท๐ [๐ท๐๐๐๐ฆ ๐๐๐๐ ๐๐๐โ ๐ธ๐๐ข๐๐ก๐๐๐]
๐คโ๐๐๐ โ = ๐๐ก ๐๐ โ๐๐๐; ๐ = ๐ท๐๐๐๐ฆ ๐๐๐๐๐ก๐๐๐ ๐๐๐๐ก๐๐; ๐ฃ = ๐ฃ๐๐๐๐๐๐ก๐ฆ ๏ฟฝ๐๐ก๐ ๐๐
๏ฟฝ,
๐ท = ๐๐๐๐๐ ๐๐๐๐๐๐ก๐๐ [๐๐ก],๐ = ๐๐๐๐ฃ๐๐ก๐ฆ [32.2๐๐ก๐ ๐๐2
]
Positive Suction Head Equation
๐ท๐๐๐๐ = ยฑ๐ท๐๐๐๐ โ ๐ท๐๐๐๐ + ๐ท๐๐๐ Pressure Drop due to Velocity Equation [Pump]
๐ฝ๐
๐๐[๐๐ก ๐๐ โ๐๐๐]; ๐ฃ๐๐๐๐๐๐ก๐ฆ ๐๐
๐๐ก๐ ๐๐
;
๐๐๐๐ฃ๐๐ก๐ฆ = 32.2๐๐ก
sec2
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Pump Affinity Laws
๐1
๐2 =๐ท1
๐ท2 ; ๐๐ ๐ ๐๐๐๐ ๐๐ โ๐๐๐ ๐๐๐๐ ๐ก๐๐๐ก
๐1
๐2 =๐1
๐2 ; ๐๐ ๐๐๐๐๐๐ก๐๐ ๐๐ โ๐๐๐ ๐๐๐๐ ๐ก๐๐๐ก
Pump Affinity Laws
๐ป1๐ป2
=๐ท12
๐ท22; ๐๐ ๐ ๐๐๐๐ ๐๐ โ๐๐๐ ๐๐๐๐ ๐ก๐๐๐ก
๐ป1๐ป2
=๐12
๐22; ๐๐ ๐๐๐๐๐๐ก๐๐ ๐๐ โ๐๐๐ ๐๐๐๐ ๐ก๐๐๐ก
Pump Affinity Laws
๐1๐2
=๐ท13
๐ท23; ๐๐ ๐ ๐๐๐๐ ๐๐ โ๐๐๐ ๐๐๐๐ ๐ก๐๐๐ก
๐1๐2
=๐13
๐23; ๐๐ ๐๐๐๐๐๐ก๐๐ ๐๐ โ๐๐๐ ๐๐๐๐ ๐ก๐๐๐ก
Heat Transfer Between Pipe to Outer Surface
๐๐๐๐๐ ๐ก๐ ๐๐ข๐ก๐๐ ๐ ๐ข๐๐๐๐๐ =๐[ ๐ต๐ก๐ข โ ๐๐โ โ ๐๐ก2 โ โ]
๐[๐๐]โ ๐ด[๐๐ก2] โ (๐๐๐ข๐ก๐๐ ๐ ๐ข๐๐๐๐๐ โ ๐๐๐๐๐)[โ]
Where k is equal to the conductivity of the insulation and X is equal to the thickness of the
insulation. K can vary depending on the temperature of the pipe. Heat Transfer Between Pipe Surface and Air
๐๐๐ข๐ก๐๐ ๐ ๐ข๐๐๐๐๐ ๐ก๐ ๐๐๐ = โ[๐ต๐ก๐ข
๐๐ก2 โ โ โ โ] โ ๐ด[๐๐ก2] โ (๐๐๐๐๐๐๐๐ก โ ๐๐๐ข๐ก๐๐ ๐ ๐ข๐๐๐๐๐)[โ]
Where h is equal to the surface coefficient of the insulation. This value is a measure of how well
the surface of the material in question is at conducting heat to the ambient air. The value can increase for higher wind speeds and varying surface and air temperatures.
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Cooling Tower Range
๐ ๐๐๐๐ = ๐๐ค๐๐ก๐๐,๐๐ [โ] โ ๐๐ค๐๐ก๐๐,๐๐ข๐ก [โ] Cooling Tower Apprach
๐ด๐๐๐๐๐๐โ = ๐๐ค๐๐ก๐๐,๐๐ข๐ก [โ] โ ๐๐๐๐ ๐๐,๐๐ต [โ] Cooling Tower Effectiveness
๐ธ๐๐๐๐๐ก๐๐ฃ๐๐๐๐ ๐ =๐ ๐๐๐๐
๐ ๐๐๐๐ + ๐ด๐๐๐๐๐๐โ
Cooling Tower Evaporation Rate
. 000943 โ ๐๐๐๐๐๐๐ ๐ก๐๐ค๐๐ ๐๐๐๐ค ๐๐๐ก๐ ๏ฟฝ๐๐๐๐๐๐
๏ฟฝ โ ๏ฟฝ๐๐ค๐๐ก๐๐,๐ผ๐ โ ๐๐ค๐๐ก๐๐,๐๐ข๐ก๏ฟฝ = ๐๐ฃ๐๐๐๐๐๐ก๐๐๐ ๐๐๐ก๐ ๏ฟฝ๐๐๐๐๐๐
๏ฟฝ
Combining the Sound Levels of Multiple Sources
๐ฟ๐ด = 10 โ log10(10๐ท๐ต1100 + 10
๐ท๐ต2100 + 10
๐ท๐ต3100 + 10
๐ท๐ต4100 + 10
๐ท๐ต5100 + 10
๐ท๐ต6100 + ๐ฃ10
๐ท๐ต7100 + 10
๐ท๐ต8100)
Sound Level at a Distance from a Point Source (Spherical Propagation)
๐ฟ๐๐ = ๐ฟ๐๐๐ข๐๐ โ 20 โ log10 ๐ฅ โ 1 ๐ฟ๐๐ = ๐๐๐ข๐๐ ๐๐๐ฃ๐๐ ๐๐ก ๐ ๐๐๐ ๐ก๐๐๐๐ ๐๐ ๐ฅ [๐ท๐ต] ๐ฟ๐๐๐ข๐๐ = ๐๐๐ข๐๐ ๐๐๐ฃ๐๐ ๐๐ ๐๐๐ข๐๐๐๐๐๐ก [๐ท๐ต] ๐ฅ = ๐๐๐ ๐ก๐๐๐๐ ๐๐๐๐ ๐๐๐ข๐๐๐๐๐๐ก [๐๐กโฒ]
Sound Level at a Distance from a Point Source (Half-Spherical Propagation)
๐ฟ๐๐ = ๐ฟ๐๐๐ข๐๐ โ 20 โ log10 ๐ฅ + 2
Sound Level at a Distance from a Point Source (Quarter-Spherical Propagation)
๐ฟ๐๐ = ๐ฟ๐๐๐ข๐๐ โ 20 โ log10 ๐ฅ + 5
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Sound Level at a Distance from a Point Source (Eighth-Spherical Propagation)
๐ฟ๐๐ = ๐ฟ๐๐๐ข๐๐ โ 20 โ log10 ๐ฅ + 8
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2.0 EQUATIONS/TERMS Ohmโs Law
๐ผ =๐๐
๐ผ = ๐๐ข๐๐๐๐๐ก [๐๐๐๐ ] ๐ = ๐ฃ๐๐๐ก๐๐๐ [๐ฃ๐๐๐ก๐ ] ๐ = ๐๐๐ ๐๐ ๐ก๐๐๐ก๐๐ [๐๐๐๐ ]
Resistors in series
๐ ๐๐,๐ ๐๐๐๐๐ = ๐ 1 + ๐ 2 + ๐ 3 + ๐ ๐ Resistors in parallel
1๐ ๐๐
=1๐ 1
+1๐ 2
+1๐ 3
+1๐ ๐
Power Equations
๐ = ๐ผ โ ๐
๐ =๐2
๐
๐ = ๐ผ2 โ ๐
Pump Water Horsepower Equations
๐๐๐๐โ ๐ค๐๐๐,๐๐ข๐๐[๐ป๐] =โ๐๐ก โ ๐๐๐๐ โ (๐๐บ)
3956;
๐ = ๐ฃ๐๐๐ข๐๐๐ก๐๐๐ ๐๐๐๐ค ๐๐๐ก๐ [๐๐๐๐๐๐๐ ๐๐๐ ๐๐๐๐ข๐ก๐]
โ = ๐๐๐๐ ๐ ๐ข๐๐ [๐๐๐๐ก ๐๐ โ๐๐๐] ๐ = ๐๐๐ค๐๐ [โ๐๐๐๐ ๐๐๐๐ค๐๐] ๐๐บ = ๐ ๐๐๐๐๐๐๐ ๐๐๐๐ฃ๐๐ก๐ฆ
๐๐๐๐โ ๐ค๐๐๐,๐๐ข๐๐,[๐ป๐] =๐๐๐ ๐ โ ๐๐๐๐ โ (๐๐บ)
1,714;
๐ = ๐๐๐๐ ๐ ๐ข๐๐ [๐๐ ๐]
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Fan Mechanical Horsepower Equation
๐๐๐๐โ ๐ค๐๐๐,๐๐๐[๐ป๐] =๐๐๐๐ โ ๐๐๐๐ ๐ค๐
6356;
๐๐๐๐ = ๐ฃ๐๐๐ข๐๐๐ก๐๐๐ ๐๐๐๐ค ๐๐๐ก๐ ๐๐ ๐๐๐ [๐๐ข๐๐๐ ๐๐๐๐ก ๐๐๐ ๐๐๐๐ข๐ก๐] ๐๐๐๐ ๐ค๐ = ๐ก๐๐ก๐๐ ๐๐๐๐ ๐ ๐ข๐๐ [๐๐๐โ๐๐ ๐ค๐๐ก๐๐ ๐๐๐ข๐๐] ๐๐๐๐โ ๐ค๐๐๐,๐๐๐[๐ป๐] = ๐๐๐ ๐๐๐โ๐๐๐๐๐๐ โ๐๐๐ ๐๐๐๐ค๐๐
Pump or Fan Brake Horsepower Equation
๐๐๐๐/๐๐ข๐๐[๐ป๐] =๐๐๐๐โ ๐ค๐๐๐[๐ป๐]]
๐๐๐๐/๐๐ข๐๐;
Motor Horsepower Equation
๐๐๐๐ก๐๐ =๐๐๐๐โ ๐ค๐๐๐[๐ป๐]]
๐๐๐๐ก๐๐;
Electrical Power Supplied to Motor
๐๐ ๐ข๐๐๐๐๐๐ ๐ก๐ ๐๐๐ก๐๐[๐ป๐] =๐๐๐๐ก๐๐[๐ป๐]
๐๐น
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Conversion Formula Factor Value
Present Value to Future Value ๐น๐ = ๐๐ ๐ฅ (1 + ๐)๐ Multiply PV by (F/P, i, n)
Future Value to Present Value ๐๐ =๐น๐
(1 + ๐)๐
Multiply FV by (P/F, i, n)
Present Value to Annual Value ๐ด = ๐๐ โ (๐ โ (1 + ๐)๐
(1 + ๐)๐ โ 1)
Multiply PV by (A/P, i, n)
Annual Value to Present Value ๐๐ = ๐ด โ (1 โ (1 + ๐)โ๐
๐)
Multiply A by (P/A, i, n)
Future Value to Annual Value ๐ด = ๐น๐(๐
(1 + ๐)๐ โ 1)
Multiply FV by (A/F, i, n)
Annual Value to Future Value ๐น๐ = ๐ด โ ((1 + ๐)๐ โ 1
๐)
Multiply A by (F/A, i, n)