COOLING & HEATING EQUATIONS

SENSIBLE HEAT FACTOR or RATIO (SHR)

SUPPLY AIR FLOW RATE

AIR BALANCE EQUATIONS

CALCULATION OF HEATING, COOLING DEGREE DAYS

FUEL CONSUMPTION BY HEATING, COOLING UNITS

AIR CHANGE RATE EQUATIONS

ESTIMATING AIR LEAKAGE

VENTILATION FORMULA

ESTIMATING AIR VOLUME FOR HOODS AND ITS PRESSURE

DUCTWORK EQUATIONS

FAN EQUATIONS

PUMP EQUATIONS

CHILLER HEAT LOAD & WATER FLOW

FRICTION LOSS IN WATER PIPES

COOLING TOWERS

CONTROL VALVE SIZING

HEAT EXCHANGERS

HUMIDIFICATION & DEHUMIDIFICATION

EXPANSION TANKS

TONS OF REFRIGERATION (TR)

ENERGY EFFICIENCY TERMS OF REFRIGERATION SYSTEMS

DECIBEL CALCULATION

STEAM & CONDENSATE EQUATIONS

RELIEF VALVE SIZING

STEEL PIPE EQUATIONS

FLOW COEFFICIENT (Cv) - Formulas for Liquids, Steam and Gases

ELECTRICITY

### ELECTRICITY

• 1 HP (motor) = 0.746 KW (operating energy)

• 5 HP x 0.746 KW/HP x 3413 BTUH/KW = 12,700 BTUH = 1 Ton of Cooling

• Watts = Volts x Amps

• Efficiency = 746 x Output Horsepower (HP) / Input Watts

• KW (1 Phase) = Volts x Amps x Power Factor / 1000

• KW (3 Phase) = Volts x Amps x 1.732 x Power Factor / 1000

• KVA (3 Phase) = 1.732 x Volts x Amps /1000

• BHP (3 Phase) = 1.732 x Volts x Amps x Power Factor x Device Efficiency / 746

• Motor HP = BHP / Motor Efficiency

DFP x RPMFP = DMP x RPMMP

BL = [(DFP + DMP) x 1.5708] + (2 x L)

Where

• DFP = Fan Pulley Diameter

• DMP = Motor Pulley Diameter

• RPMFP = Fan Pulley RPM

• RPMMP = Motor Pulley RPM

• BL = Belt Length

• L = Center-to-Center Distance of Fan and Motor Pulleys

• 5 HP x 0.746 KW/HP x 3413 BTUH/KW = 12,700 BTUH = 1 Ton of Cooling

• Watts = Volts x Amps

• Efficiency = 746 x Output Horsepower (HP) / Input Watts

• KW (1 Phase) = Volts x Amps x Power Factor / 1000

• KW (3 Phase) = Volts x Amps x 1.732 x Power Factor / 1000

• KVA (3 Phase) = 1.732 x Volts x Amps /1000

• BHP (3 Phase) = 1.732 x Volts x Amps x Power Factor x Device Efficiency / 746

• Motor HP = BHP / Motor Efficiency

**Motor Drive Formulas**DFP x RPMFP = DMP x RPMMP

BL = [(DFP + DMP) x 1.5708] + (2 x L)

Where

• DFP = Fan Pulley Diameter

• DMP = Motor Pulley Diameter

• RPMFP = Fan Pulley RPM

• RPMMP = Motor Pulley RPM

• BL = Belt Length

• L = Center-to-Center Distance of Fan and Motor Pulleys

### FLOW COEFFICIENT (Cv) - Formulas for Liquids, Steam and Gases

The flow coefficient ( CV ) - is important for proper design of control valves, which provides flow comparison of different sizes and types of valve of different manufacturer’s. Cv is generally determined experimentally and express the flow capacity - GPM (gallons per minute) of water that a valve will pass for a pressure drop of 1 lb/in2 (psi). The flow factor (Kv) - is also in common use, but express the capacity in SI-units.

Specific formulas used to estimate Cv for different fluids is indicated below:

Flow Coefficient - Cv - for Liquids

For liquids the flow coefficient - CV - expresses the flow capacity in gallons per minute (GPM) of 600F water with a pressure drop of 1 psi (lb/in2).

**Flow expressed by volume**

C = Q x (SG / ▲p)1/2

Where

• Q = water flow (US gallons per minute)

• SG = specific gravity (1 for water)

• ▲p = pressure drop (psia)

**Flow is expressed by weight**

CV = w / (500 x (▲p x SG)1/2 )

Where

• w = water flow (lb/h)

• SG = specific gravity (1 for water)

• ▲p = pressure drop (psia)

F

**low Coefficient - Cv - for Saturated Steam**

Since steam and gases are compressible fluids, the formula must be altered to accommodate changes in the density.

**Critical (Choked) Pressure Drop**

At choked flow the critical pressure drop the outlet pres sure - p0 - from the control valve is less than 58% of the inlet pressure - pi . The flow coefficient can be expressed as:

CV = m / 1.61 pi

Where

• m = steam flow (lb/h)

• pi = inlet s team absolute pressure (psia)

• po = outlet steam absolute pressure (psia)

**Non Critical Pressure Drop**

For non critical pressure drop the outlet pressure - po - from the control valve is greater than 58% of the inlet pressure - pI . The flow coefficient can be expressed as:

Cv = m /3.2 ((pI - po) x po)1/2

**Flow Coefficient - Cv- for Air and other Gases**

For critical pressure drop the outlet pressure - po - from the control valve is less than 53% of the inlet pressure - pI . The flow coefficient can be expressed as:

Cv = Q x [SG (T + 460)]1/2 / 660pI

Where

• Q = free gas per hour, standard cubic feet per hour (Cu-foot/h)

• SG = specific gravity of flowing gas gas relative to air at 14.7 psia and 600F

• T = flowing air or gas temperature (°F)

• pI = inlet gas absolute press ure (psia)

For non critical pressure drop the outlet pressure - po - from the control valve is greater than 53% of the inlet pressure - pI . The flow coefficient can be expressed as:

CV = Q x [SG (T + 460)]1/2 / [1360 (▲p x pO ) ]1/2

Where

• ▲p = (pI - pO )

• pO = outlet gas absolute pressure (psia)

### STEEL PIPE EQUATIONS

A = 0.785 x ID2

WP = 10.6802 x T x (OD - T)

WW = 0.3405 x ID2

OSA = 0.2618 x OD

ISA = 0.2618 x ID

A M = 0.785 x (OD2 - ID2 )

Where

• A = Cross-Sectional Area (Sq- inches)

• WP = Weight of Pipe per Foot (Lbs)

• WW = Weight of Water per Foot (Lbs)

• T = Pipe Wall Thickness (Inches)

• ID = Inside Diameter (Inches)

• OD = Outside Diameter (Inches)

• OSA = Outside Surface Area per Foot (Sq-ft)

• ISA = Inside Surface Area per Foot (Sq-ft)

• AM = Area of the Metal (Sq-inches)

WP = 10.6802 x T x (OD - T)

WW = 0.3405 x ID2

OSA = 0.2618 x OD

ISA = 0.2618 x ID

A M = 0.785 x (OD2 - ID2 )

Where

• A = Cross-Sectional Area (Sq- inches)

• WP = Weight of Pipe per Foot (Lbs)

• WW = Weight of Water per Foot (Lbs)

• T = Pipe Wall Thickness (Inches)

• ID = Inside Diameter (Inches)

• OD = Outside Diameter (Inches)

• OSA = Outside Surface Area per Foot (Sq-ft)

• ISA = Inside Surface Area per Foot (Sq-ft)

• AM = Area of the Metal (Sq-inches)

### RELIEF VALVE SIZING

Liquid System Relief Valves and Spring Style Relief Valves:

A = (GPM x (G)1/2 ) / [28.14 x KB x KV x ( ▲P)1/2 ]

Liquid System Relief Valves and Pilot Operated Relief Valves:

A = (GPM x (G)1/2 ) / [36.81 x KV x (▲P)1/2 ]

Steam System Relief Valves:

A = W / (51.5 x K x P x KSH x KN x KB )

Gas and Vapor System Relief Valves (Lb/Hr.):

A = (W x (TZ)1/2 ) / [C x K x P x KB x (M)1/2 ]

Gas and Vapor System Relief Valves (SCFM):

A = (SCFM x (TGZ)1/2 ) / (1.175 x C x K x P x KB )

Where

• A = Minimum Required Effective Relief Valve Discharge Area (Sq- inches)

• GPM = Required Relieving Capacity at Flow Conditions (Gallons per Minute)

• W = Required Relieving Capacity at Flow Conditions (Lbs / hr)

• SCFM = Required Relieving Capacity at Flow Conditions (Standard Cubic Feet per Minute)

• G = Specific Gravity of Liquid, Gas, or Vapor at Flow Conditions Water = 1.0 for most HVAC applications; Air = 1.0

• C = Coefficient Determined from Expression of Ratio of Specific Heats; C = 315 if Value is Unknown

• K = Effective Coefficient of Discharge; K = 0.975

• KB = Capacity Correction Factor Due to Back Pressure; KB = 1.0 for Atmospheric Discharge Systems

• KV = Flow Correction Factor Due to Viscosity; KV = 0.9 to 1.0 for most HVAC Applications with Water

• KN = Capacity Correction Factor for Dry Saturated Steam at Set Pressures above 1500 Psia and up to 3200 Psia; KN = 1.0 for most HVAC Applications

• KSH = Capacity Correction Factor Due to the Degree of Superheat; KSH = 1.0 for Saturated Steam

• Z = Compressibility Factor; Z = 1.0 If Value is Unknown

• P = Relieving Pressure (Psia); P = Set Pressure (Psig) + Over Pressure (10% Psig) + Atmospheric Pressure (14.7 Psia)

• P = Differential Pressure (Psig); P = Set Pressure (Psig) + Over Pressure (10% Psig) - Back Pressure (Psig)

• T = Absolute Temperature (°R = °F. + 460)

• M = Molecular Weight of the Gas or Vapor

**Notes:**

1) When multiple relief valves are used, one valve shall be set at or below the maximum allowable working pressure, and the remaining valves may be set up to 5 percent over the maximum allowable working pressure.

2) When sizing multiple relief valves, the total area required is calculated on an overpressure of 16 percent or 4 Psi, whichever is greater.

3) For superheated steam, the correction factor values listed below may be used:

• Superheat up to 400 °F: 0.97 (Range 0.979–0.998)

• Superheat up to 450 °F: 0.95 (Range 0.957–0.977)

• Superheat up to 500 °F: 0.93 (Range 0.930–0.968)

Relief Valve Vent Line Maximum Length

L = (9 x P21 x D5) / C2 = (9 x P22 x D5) / (16 x C2)

Where

• P1 = 0.25 x [(PRESSURE SETTING x 1.1) + 14.7]

• P2 = [(PRESSURE SETTING x 1.1) + 14.7]

• L = Maximum Length of Relief Vent Line (Feet)

• D = Inside Diameter of Pipe (Inches)

• C = Minimum Discharge of Air (Lbs/Min)

### STEAM & CONDENSATE EQUATIONS

Some common steam and condensate equations can be expressed as Steam Heating

ms = H / 960

Where

• ms = steam mass flow rate (Lbs /hr)

• H = heat flow rate (Btu/hr)

Steam Heating Liquid Flow

Ms = QL x 500 x SGL x CPL x ▲T / L S

Where

• Ms = steam mass flow rate (Lbs /hr)

• QL = volume flow liquid (GPM)

• SGL = specific heat capacity of the liquid (Btu/lb °F)

• CPL = specific gravity of the fluid

• ▲T = temperature difference liquid (°F)

• L S =latent heat of steam at steam design pressure (Btu/lb)

ms = QG x 60 x ρG x CPG x ▲TG / LS

Where

• ms = steam mass flow rate (lbs /hr)

• QG = volume flow gas (CFM)

• ρG = density of the gas (lb/ft3 )

• CPG = specific gravity of the gas (Air CPG = 0.24 Btu/Lb)

• ▲TG = temperature difference gas (0F)

• LS = latent heat of steam at steam design pressure (Btu/lb)

▲P = [(0.01306 x W2 x (1+ 3.6/ID)] / (3600 x D x ID5)

W = 60 x {(P x D x ID5) / [0.01306 x (1+3.6 / ID)]}1/2

W = 0.41667 x V x AINCHES x D = 60 x V x AFEET x D

V = 2.4 x W/ AINCHES x D = W / (60 x AFEET x D)

Where

• ▲P = Pressure Drop per 100 Feet of Pipe (Psig/100 feet)

• W = Steam Flow Rate (Lbs /Hr)

• ID = Actual Inside Diameter of Pipe (Inches)

• D = Average Density of Steam at System Pres sure (Lbs/Cu-ft)

• V = Velocity of Steam in Pipe (Feet/Minute)

• AINCHES = Actual Cross Sectional Area of Pipe (Sq-inches)

• AFEET = Actual Cross Sectional Area of Pipe (Sq-ft)

FS = (Hss – Hsc) / HLC x 100

WCR = FS / 100 x W

Where

• FS = Flash Steam (Percentage %)

• Hss = Sensible Heat at Steam Supply Pressure (Btu/Lb)

• Hsc = Sensible Heat at Condensate Return Pressure (Btu/Lb)

• HLC = Latent Heat at Condensate Return Pressure (Btu/Lb)

• W = Steam Flow Rate (Lbs/Hr)

• WCR = Condensate Flow based on percentage of Flash Steam created during condensing

process (Lbs/hr)

Use this flow rate in steam equations above to determine condensate return pipe size.

ms = H / 960

Where

• ms = steam mass flow rate (Lbs /hr)

• H = heat flow rate (Btu/hr)

Steam Heating Liquid Flow

Ms = QL x 500 x SGL x CPL x ▲T / L S

Where

• Ms = steam mass flow rate (Lbs /hr)

• QL = volume flow liquid (GPM)

• SGL = specific heat capacity of the liquid (Btu/lb °F)

• CPL = specific gravity of the fluid

• ▲T = temperature difference liquid (°F)

• L S =latent heat of steam at steam design pressure (Btu/lb)

**Steam Heating Air or Gas Flow**ms = QG x 60 x ρG x CPG x ▲TG / LS

Where

• ms = steam mass flow rate (lbs /hr)

• QG = volume flow gas (CFM)

• ρG = density of the gas (lb/ft3 )

• CPG = specific gravity of the gas (Air CPG = 0.24 Btu/Lb)

• ▲TG = temperature difference gas (0F)

• LS = latent heat of steam at steam design pressure (Btu/lb)

**Steam Pipe Sizing Equations**▲P = [(0.01306 x W2 x (1+ 3.6/ID)] / (3600 x D x ID5)

W = 60 x {(P x D x ID5) / [0.01306 x (1+3.6 / ID)]}1/2

W = 0.41667 x V x AINCHES x D = 60 x V x AFEET x D

V = 2.4 x W/ AINCHES x D = W / (60 x AFEET x D)

Where

• ▲P = Pressure Drop per 100 Feet of Pipe (Psig/100 feet)

• W = Steam Flow Rate (Lbs /Hr)

• ID = Actual Inside Diameter of Pipe (Inches)

• D = Average Density of Steam at System Pres sure (Lbs/Cu-ft)

• V = Velocity of Steam in Pipe (Feet/Minute)

• AINCHES = Actual Cross Sectional Area of Pipe (Sq-inches)

• AFEET = Actual Cross Sectional Area of Pipe (Sq-ft)

**Steam Condensate Pipe Sizing Equations**FS = (Hss – Hsc) / HLC x 100

WCR = FS / 100 x W

Where

• FS = Flash Steam (Percentage %)

• Hss = Sensible Heat at Steam Supply Pressure (Btu/Lb)

• Hsc = Sensible Heat at Condensate Return Pressure (Btu/Lb)

• HLC = Latent Heat at Condensate Return Pressure (Btu/Lb)

• W = Steam Flow Rate (Lbs/Hr)

• WCR = Condensate Flow based on percentage of Flash Steam created during condensing

process (Lbs/hr)

Use this flow rate in steam equations above to determine condensate return pipe size.

### DECIBEL CALCULATION

Decibel is a logarithmic unit used to describe the ratio of the signal level - power, sound pressure,voltage, intensity, etc. Decibel is a logarithmic unit used to describe the ratio of the signal level -power, sound pressure, intensity or several other things.The decibel can be expressed as:

Decibel = 10 log (P / Pref)

Where

• P = signal power (W)

• Pref = reference power (W)

The sound power and sound power level is commonly used to specify the emitted noise or sound from technical equipment as fans, pump and other machines.

The logarithmic decibel scale is convenient when calculating resulting sound power levels and sound pressure levels for two or more sound or noise sources.

Lwt = 10 log (n N / N0) = 10 log (N / N0) + 10 log (n)

= Lws + 10 log (n)

Where

• Lwt = Total sound power level (dB)

• Lws = Sound power level from each single source (dB)

• N = sound power (W)

• N0 = 10-12 - reference sound power (W)

• n = number of sources

Note: Adding two identical sources will increase the total sound power level with 3 dB (10 log (2)).

The resulting sound pressure level when adding equal sound pressure can be expressed as:

Lpt = Lps + 20 log (n)

Where

• Lpt = total sound pres sure (dB)

• Lps = Sound pressure level from each single source (dB)

• n = number of sources

The sound power level from more than one source can be calculated as:

Lwt = 10 log ((N1 + N2 ... + Nn) / N0)

Decibel = 10 log (P / Pref)

Where

• P = signal power (W)

• Pref = reference power (W)

**Note!**Doubling the signal level increases the decibel with 3 dB (10 log (2)).**Adding Equal Sound Power Sources**The sound power and sound power level is commonly used to specify the emitted noise or sound from technical equipment as fans, pump and other machines.

The logarithmic decibel scale is convenient when calculating resulting sound power levels and sound pressure levels for two or more sound or noise sources.

Lwt = 10 log (n N / N0) = 10 log (N / N0) + 10 log (n)

= Lws + 10 log (n)

Where

• Lwt = Total sound power level (dB)

• Lws = Sound power level from each single source (dB)

• N = sound power (W)

• N0 = 10-12 - reference sound power (W)

• n = number of sources

Note: Adding two identical sources will increase the total sound power level with 3 dB (10 log (2)).

**Adding Equal Sound Pressure Levels**The resulting sound pressure level when adding equal sound pressure can be expressed as:

Lpt = Lps + 20 log (n)

Where

• Lpt = total sound pres sure (dB)

• Lps = Sound pressure level from each single source (dB)

• n = number of sources

**Adding Sound Power from Sources at different Levels**The sound power level from more than one source can be calculated as:

Lwt = 10 log ((N1 + N2 ... + Nn) / N0)

### ENERGY EFFICIENCY TERMS OF REFRIGERATION SYSTEMS

**KW per ton**

The term kW/ton is common used for large commercial and industrial air-conditioning, heat pump and refrigeration systems. The term is defined as the ratio of the rate of energy consumption in kW to the rate of heat removal in tons at the rated condition. The lower the kW/ton the more efficient is the system.

KW/ton = Pc / Hr

Where

• Ps = energy consumption (k W)

• Hr = heat removed (ton)

**Coefficient of Performance-COP**

The Coefficient of Performance - COP - is the basic unit less parameter used to report the efficiency of refrigerant bas ed s ystems. The Coefficient of Performance - COP - is the ratio between useful energy acquired and energy applied and can be expressed as:

COP = Hu / Ha

Where

• COP = Coefficient of performance

• Hu = Useful energy acquired (Btu)

• Ha = Energy applied (Btu)

COP can be used to define either cooling efficiency or heating efficiency as for a heat pump.

‹ For cooling, COP is defined as the ratio of the rate of heat removal to the rate of energy input to the compressor.

‹ For heating, COP is defined as the ratio of rate of heat delivered to the rate of energy input to the compressor.

COP can be used to define the efficiency at a single standard or non-standard rated condition or a weighted average seasonal condition. The term may or may not include the energy consumption of auxiliary systems such as indoor or outdoor fans, chilled water pumps, or cooling tower systems. For purposes of comparison, the higher the COP the more efficient the system.

COP can be treated as an efficiency where COP of 2.00 = 200% efficient for unitary heat pumps, ratings at two standard outdoor temperatures of 47°F and 17°F (8.3°C and -8.3°C) are typically used.

**Energy Efficiency Ratio – EER**

The Energy Efficiency Ratio - EER - is a term generally used to define the cooling efficiency of unitary air-conditioning and heat pump systems. The efficiency is determined at a single rated condition specified by the appropriate equipment standard and is defined as the ratio of net cooling capacity - or heat removed in Btu/h (not in tons) - to the total input rate of electric energy applied - in watt hour (not in kW). The units of EER are Btu/W-hr.

EER = Hc /Pa

Where

• EER = Energy efficient ratio (Btu/W-hr)

• Hc = net cooling capacity (Btu/hr)

• Pa = applied energy (Watts)

This efficiency term typically includes the energy requirement of auxiliary systems such as the indoor and outdoor fans and the higher the EER the more efficient is the system. Energy efficiency ratio is further categorized as Energy efficiency ratio (EER) and Seasonal energy efficiency ratio (SEER):

‹ The cooling equipment systems such as room air conditioners, heat pumps etc used in residential and small commercial buildings often express cooling system efficiency in terms of the Energy Efficiency Ratio (EER).

‹ The central air-conditioning equipment used in large residential and commercial buildings expresses cooling system efficiency in terms of the Seasonal Energy Efficiency Ratio (SEER).

Recommended selection of room air conditioners is EER of at least 9.0 for mild climates and over 10 for hot climates and for central air conditioning system it is tested to be as high as 17 units. The U.S. Government's minimum efficiency level is 10 SEER for split systems and 9.7 for packaged units.

**Efficiency - Heating Systems**

Turndown Ratio = Maximum Firing Rate: Minimum Firing Rate (i.e., 5:1, 10:1, 25:1)

Overall Thermal Efficiency = (Gross Btu Output / Gross Btu Input) x 100%

• Overall Thermal Efficiency Range 75%–90%

Combustion Efficiency = {(Btu Input – Btu Stack Loss) / Btu Input} x 100%

• Combustion Efficiency Range 85%–95%

### TONS OF REFRIGERATION (TR)

A ton of refrigeration is the amount of heat removed by an air c onditioning system that would melt 1 ton of ice in 24 hours.

1TR = 12,000 Btu/hr

One ton of refrigeration is equal to heat extraction @ of 200 BTUs per minute, 12,000 Btu per hour or 3025.9 Kcal/hr. This is based on the latent heat of fusion for ice which is 144 Btu per pound

1TR = 12,000 Btu/hr

One ton of refrigeration is equal to heat extraction @ of 200 BTUs per minute, 12,000 Btu per hour or 3025.9 Kcal/hr. This is based on the latent heat of fusion for ice which is 144 Btu per pound

### HUMIDIFICATION & DEHUMIDIFICATION

**HUMIDIFICATION**

GRreqd = (WGR/ SpV) Room air – (WGR / SpV) Supply Air

Lbreqd = (Wlb / SpV) Room air – (Wlb / SpV) Supply Air

Qsteam = (Qair x GRreqd x 60) / 7000

Qsteam = Qair x Lbreqd x 60

Where

• GRreqd = Grains of Moisture Required (Gr H2O per Cu-ft of air)

• Lbreqd = Pounds of Moisture Required (Lb H2O per Cu-ft of air)

• Qair = Air Flow Rate (CFM)

• Qsteam = Steam Flow Rate (Lb per hour)

• SpV = Specific Volume of Air (Cu-ft per lb of dry air)

• ▲Wlb = Specific Humidity (lb-H2O per lb of dry air)

• ▲WGr = Specific Humidity (Gr. H2O per lb of dry air)

**Humidifier Sensible Heat Gain**

H = (0.244 x Q x ▲T) + (L x 380)

Where

• H = Sensible Heat Gain (Btu/Hr)

• Q = Steam Flow (Lb-Steam/Hr)

• ▲T = Steam Temperature - Supply Air Temperature (°F)

• L = Length of Humidifier Manifold (ft)

A measure of the capacity of a dehumidifier is expressed in lbs per hour of moisture removal and is estimated by equation:

MRC = [Qair x (60 min/hr / Vs] x (GPPin - GPPout )) / 7000 grains/lb

Where,

• MRC = Moisture removal capacity (in Lb /hr)

• Qair = Volumetric rate of air (CFM)

• Vs = Specific volume of air (Cu-ft / lb)

• GPPin = Grains of moisture per pound of dry air in the inlet air stream

• GPPout = Grains of moisture per pound of dry air in the outlet air stream

The difference in (GPPin – GPPout) represents the grain "depression" or removal across the

dehumidifier.

Where

• H = Sensible Heat Gain (Btu/Hr)

• Q = Steam Flow (Lb-Steam/Hr)

• ▲T = Steam Temperature - Supply Air Temperature (°F)

• L = Length of Humidifier Manifold (ft)

**DEHUMIDIFIER EQUATIONS**A measure of the capacity of a dehumidifier is expressed in lbs per hour of moisture removal and is estimated by equation:

MRC = [Qair x (60 min/hr / Vs] x (GPPin - GPPout )) / 7000 grains/lb

Where,

• MRC = Moisture removal capacity (in Lb /hr)

• Qair = Volumetric rate of air (CFM)

• Vs = Specific volume of air (Cu-ft / lb)

• GPPin = Grains of moisture per pound of dry air in the inlet air stream

• GPPout = Grains of moisture per pound of dry air in the outlet air stream

The difference in (GPPin – GPPout) represents the grain "depression" or removal across the

dehumidifier.

### HEAT EXCHANGERS

Range = EWT – LWT

Approach = EWTHS - LWTCS

Where

• EWT = Entering Water Temperature (°F)

• LWT = Leaving Water Temperature (°F)

• EWTHS = Entering Water Temperature – Hot Side (°F)

• LWTCS = Leaving Water Temperature – Cold Side (°F)

**Logarithmic Mean Temperature Difference – LMTD**

In a heat transfer process, the temperature difference varies with position and time. The determination of the mean temperature difference in a heat transfer process depends upon the direction of fluid flow involved in the process. The primary and secondary fluid in a heat exchanger process may:

1) flow in the same direction - parallel flow/co-current flow

2) in the opposite direction - counter current flow

3) or perpendicular to each other - cross flow

When the secondary fluid passes over the heat transfer surface, the highest rate of heat transfer occurs at the inlet and progressively decays with higher secondary fluid temperature along its way to the outlet. The rise in secondary temperature is non-linear and is best represented by a logarithmic calculation. For this purpose the mean temperature difference chosen is termed the Logarithmic Mean Temperature Difference or LMTD and can be expressed as:

LMTD = (TD2 - TD1) / ln (TD2 / TD1)

Where

• LMTD = Logarithmic Mean Temperature Difference 0F

• TD1 = TP1 – TS2 - Entering primary fluid and leaving secondary fluid temperature difference °F

• TD2 = TP2 – TS1 - Leaving primary fluid and entering secondary fluid temperature difference °F

**Arithmetic Mean Temperature Difference – AMTD**An easier but less accurate way to calculate the mean temperature difference is to consider the Arithmetic Mean Temperature Difference or AMTD and can be expressed as:

AMTD = (TP1 + TP2 ) / 2 - (TS1 + TS2 ) / 2

Where

• AMTD = Arithmetic Mean Temperature Difference 0F

• TP1 = primary inlet temperature 0F

• TP2 = primary outlet temperature 0F

• TS1 = secondary inlet temperature 0F

• TS2 = secondary outlet temperature 0F

A linear increase in the secondary fluid temperature makes it easier to do manual calculations. AMTD will in general give a satisfactory approximation for the mean temperature difference. When heat is transferred as a result of a change of phase in condensation or evaporation heat exchangers, the temperature of the primary or secondary fluid remains constant. For example, with saturation of steam the primaryfluid temperature can be tak en as a constant because heat is

transferred as a result of a change of phase only. The equation can then be simplified by setting

TP1 = TP2 or TS1 = TS2 0F

Thus in the equation above, the temperature profile in the primary fluid is not dependent on the direction of flow.

### CONTROL VALVE SIZING

A control valve is the single most important element in any fluid handling s ystem. The basic plan in sizing a valve is to determine the flow coefficient (Cv) of a valve.

Rangeability factor (RF) = Maximum flow / minimum controllable flow

The rangeability factor is measured under laboratory conditions, with a constant differential pressure applied across the valve. Rangeability is a characteristic of the valve itself and it depends on its design and tolerances.

Turndown Ratio (TR) = Maximum flow (installed) / minimum controllable flow

The higher the turndown ratio is, the better the controllability will be.

Valve Authority: As a control valve closes, the pressure drop across the valve increases so thatwhen the valve is completely closed, the differential pressure drop across the valve matches the pressure drop from the supply to the return line. This pressure drop is known as P-max. When the valve is completely open, the pressure drop across the valve is at its lowest point and is referred to P-min. The ratio (N) P min ÷ P max is the valve authority.

The increase in pres sure drop across the valve as it closes is important to note. Valves are rated based on a constant pressure drop. As the pressure drop shifts, the performance of the valve changes. The method to minimize the change in valve performance is to maintain the Valve Authority (N) above 0.5. Authority is related to turndown.

Turndown ratio = Rangeability X (Authority)0.5

**Rangeability Factor:**This describes the ability of a valve to stay on its theoretical characteristic at the bottom end near the closed position. This is the minimum value that should be considered if good control on light load is to be achieved. The ratio between the full flow and the minimum controllable flow is the rangeability factor.Rangeability factor (RF) = Maximum flow / minimum controllable flow

The rangeability factor is measured under laboratory conditions, with a constant differential pressure applied across the valve. Rangeability is a characteristic of the valve itself and it depends on its design and tolerances.

**Turndown Ratio:**This is the ratio between the maximum normal flow and the minimum controllable flow. It is substantially less than the range ability if the valve is oversized, either by error or deliberately to allow for an occasional peak load.Turndown Ratio (TR) = Maximum flow (installed) / minimum controllable flow

The higher the turndown ratio is, the better the controllability will be.

Valve Authority: As a control valve closes, the pressure drop across the valve increases so thatwhen the valve is completely closed, the differential pressure drop across the valve matches the pressure drop from the supply to the return line. This pressure drop is known as P-max. When the valve is completely open, the pressure drop across the valve is at its lowest point and is referred to P-min. The ratio (N) P min ÷ P max is the valve authority.

The increase in pres sure drop across the valve as it closes is important to note. Valves are rated based on a constant pressure drop. As the pressure drop shifts, the performance of the valve changes. The method to minimize the change in valve performance is to maintain the Valve Authority (N) above 0.5. Authority is related to turndown.

Turndown ratio = Rangeability X (Authority)0.5

### COOLING TOWERS

Cooling towers are rated in terms of approach and range.

The approach is the difference in temperature between the cooled-water temperature and the entering-air wet bulb temperature.

Approach = LWT – WBT

The range is the temperature difference between the water inlet and exit states.

Range = EWT – LWT

Where

• EWT = Entering hot water temperature (°F)

• LWT = Leaving cold water temperature (°F)

• WBT = Ambient wet bulb temperature (Design WB, °F)

**Water Circulation through Cooling Tower**

Q = H / (Range X 500)

Where

• H = Cooling tower heat rejection in Btu/hr

• Q = Water flow rate in GPM

**Cooling Tower Water Balance**

The amount of water that enters as make-up must be equal to the total water that exits the system

or

MR = water lost through evaporation (ER) + bleed (BR) + drift (DR)}

Where

• MR = Makeup water requirement in GPM

• DR = Typical drift rate in GPM

• ER = Evaporation rate in GPM

• BR = Bleed rate in GPM

The evaporation rate of cooling tower is

ER = Q X Range / 1,000

The drift loss is roughly 0.2 to 0.5%

DR = 0.002% X Q

When we ignore the insignificant drift losses

Then, MR = ER + BR …… (eq.1)

Recognizing that in order to keep off from making scale, all of the solids that enter as make- up must exit as bleed, it follows that:

MR = COC x BR …… (eq.2)

And that:

MR = ER [(COC)/ (COC -1)] ……. (eq.3)

Combine (eq.2) and (eq.3) to get:

BR = ER / (COC -1)

Where

• COC = Cycles of concentration.

Ideally the COC is maximized to 5 to 7 by addition of water treatment chemicals.

**Cooling Tower Efficiency**

Since the cooling towers are based on the principles of evaporative cooling, the maximum cooling tower efficiency depends on the wet bulb temperature (WBT) of the air. The cooling tower efficiency can be expressed as:

Efficiency = (EWT - LWT) x 100 / (EWT - WBT)

Where

• Efficiency = cooling tower efficiency - common range between 70 - 75%

• EWT = inlet temperature of water to the tower (0F)

• LWT = outlet temperature of water from the tower (0F)

• WBT = wet bulb temperature of air (0F)

The temperature difference between inlet and outlet water (EWT - LWT) is normally in the range 10 – 150 C. The water consumption - the make up water - of a cooling tower is about 0.2-0.3 liter perminute per ton of refrigeration.

Cooling towers use the principle of evaporative cooling in order to cool water. They can achieve water temperatures below the dry bulb temperature (DBT) of the air used to cool it. They are in general smaller and cheaper for the same cooling load than other cooling systems.

A cooling tower ton is defined as:

1 cooling tower ton = 15,000 Btu/hr (3782 kCal /hr)

This is roughly 25% more than chiller ton because the heat of compress ion of the refrigeration compressor is added to the condenser/cooling tower.

Efficiency = (EWT - LWT) x 100 / (EWT - WBT)

Where

• Efficiency = cooling tower efficiency - common range between 70 - 75%

• EWT = inlet temperature of water to the tower (0F)

• LWT = outlet temperature of water from the tower (0F)

• WBT = wet bulb temperature of air (0F)

The temperature difference between inlet and outlet water (EWT - LWT) is normally in the range 10 – 150 C. The water consumption - the make up water - of a cooling tower is about 0.2-0.3 liter perminute per ton of refrigeration.

Cooling towers use the principle of evaporative cooling in order to cool water. They can achieve water temperatures below the dry bulb temperature (DBT) of the air used to cool it. They are in general smaller and cheaper for the same cooling load than other cooling systems.

**Cooling Tower Tons**A cooling tower ton is defined as:

1 cooling tower ton = 15,000 Btu/hr (3782 kCal /hr)

This is roughly 25% more than chiller ton because the heat of compress ion of the refrigeration compressor is added to the condenser/cooling tower.

### FRICTION LOSS IN WATER PIPES

Friction loss in water pipes can be obtained by using the empirical Hazen-Williams equation

**Hazen-Williams Equation**

f = 0.2083 (100/C)1.852 Q1.852/ d4.8655

Where

• f = friction head loss in feet of water per 100 feet of pipe

• C = Hazen-Williams roughness constant

• Q = volume flow (gal/min)

• d = inside diameter (inches)

Note that the Hazen-Williams formula is empirical and lack s physical basis. Be aware that the roughness constants are based on "normal" condition with approximately 3 ft/sec.

**Darcy-Weisbach equation and Head Loss**

The Darcy-Weisbach equation is valid for fully developed, steady, incompressible flow. The friction factor or coefficient -depends on the flow - if it is laminar, transient or turbulent (the Reynolds Number) - and the roughness of the tube or duct. The friction coefficient can be calculated by the Colebrook e Equation or by using the Moody Diagram.

Alternatively the Darcy-Weisbach equation can be expressed as head loss:

H loss = λ (L / dn) [v2/ (2 x g)]

Where

• H loss H = head loss (ft)

• λ = friction coefficient

• L = length of duct or pipe (ft)

• g = acceleration of gravity (32.2 ft/s2 )

• dn = The hydraulic diameter - dh - is used for calculating the dimensionless Reynolds

Number (Re) to determine if the flow is turbulent or laminar.

The Reynolds Number (Re) is important in analyzing any type of flow when there is substantial velocity gradient - shear. The Reynolds Number indicates the relative significance of the viscous effect compared to the inertia effect. The Reynolds number is proportional to inertial force divided by viscous force. The flow is

‹ laminar if Re <> 4000

Reynolds Number can be expressed as:

Re = D x v x ρ / µ

Where

• D = characteristic length (For a pipe or duct the characteristic length is the pipe or duct diameter, in m)

• v = velocity (m/s)

• ρ = density (kg/m3 )

• µ = dynamic (absolute) viscosity (Ns/m2 )

Hydraulic Diameter: The hydraulic diameter is not the same as the geometrical diameter in non- circular ducts or pipes and can be calculated from the generic equation:

dh = 4 A / P

Where:

• dh = hydraulic diameter (in)

• A = area section of the pipe (in2 )

• P = wetted perimeter of the pipe (in)

Friction Coefficient (λ) for fully developed laminar flow the roughness of the duct or pipe can be neglected. The friction coefficient depends only the Reynolds Number -Re - and can be expressed as:

λ= 64 / Re

Where

• Re = the dimensionless Reynolds number

### CHILLER HEAT LOAD & WATER FLOW

The flow rate necessary to deliver the full output of the heat source at a specific temperature drop can be found using equation below:

Q = H / (8.01 x ρ x c x ▲T)

Where:

• Q= Water volume flow rate (GPM)

• H = Heat load (Btu/hr)

• ▲T = Intended temperature drop (°F)

• ρ = Fluid's density at the average system temperature (lb/ft3)

• c = the fluid's specific heat at the average system temperature (Btu/lb/°F)

• 8.01 = a constant

In small to medium size hydronic systems, the product of (8.01 x ρ x c) can be taken as 500 for

water, 479 for 30% glycol, and 450 for 50% glycol. The total heat removed by air condition chilled-

water installation can thus be expressed as

H = 500 x Q x ▲T

Where

• H = total heat removed (Btu/h)

• Q = water flow rate (gal/min)

• ▲T = temperature difference ( 0F)

**Evaporator Flow Rate**

The evaporator water flow rate can be expressed as

Qe = Htons x 24 / T

Where

• Qe = Evaporator water flow rate (GPM)

• Htons = Air conditioning cooling load (tons)

• T = Temperature differential between inlet and outlet (°F)

**Condenser Flow Rate**

The condenser water flow rate can be expressed as

Qc = Htons x 30 / ▲T

Where

• Qc = Condenser water flow rate (GPM)

• Htons = Air conditioning cooling load (tons)

• ▲T = Temperature differential between inlet and outlet (°F)

Note the equation above assumes 25% heat of compression.

**CONDENSATE GENERATION**

Condensate generation in an air condition system where specific humidity before and after are known can be expressed as

Q Cond = Q air x W Lb / (SpV x 8.33)

Q Cond = Q air x W GR / (SpV x 8.33 x 7000)

Where

• Q Cond = Air Conditioning condensate generated (GPM)

• Q air = Air Flow Rate through the air-handling unit cooling c oil (Cu-ft / minute)

• SpV = Specific Volume of Air (Cu-ft per lb of dry air)

• W Lb = Specific Humidity diff. between inlet and outlet of air stream across coil (lb-H2O per

lb of dry air)

• W GR = Specific Humidity diff. between inlet and outlet of air stream acros s coil (Gr. H2O per lb of dry air)

**FLOW RATES IN HEATING SYSTEMS**

The volumetric flow rate in a heating system can be expressed by the basic equation:

Q = H / (Cp x ρ x ▲T)

Where

• Q = volumetric flow rate (GPM)

• H = heat flow rate (Btu/hr)

• CP = specific heat capacity (Btu/lb-°F)

• ρ = density (lb/ft3 )

• ▲T = temperature difference (°F)

The basic equation can be expressed for water with temperature 600F flow rate as:

Q = H (7.48 gal/ft3 ) / ((1 Btu/lb- 0F) (62.34 lb/ft3 ) (60 min/h)▲T)

Or

Q = h / (500 x ▲T)

Where

• Q = Water flow rate (GPM)

• H = Heat flow rate (Btu/hr)

• ▲T = Temperature difference (0F) (usually 20ºF)

For more exact volumetric flow rates for hot water the properties of hot water should be used.

Water Mass Flow Rate Water mas s flow can be express ed as:

m = h / ((1.2 Btu/lb- 0F) x ▲T)

Where

• m = mass flow (lb/hr)

### PUMP EQUATIONS

**Pump Energy Consumption**

The energy consumption of the pumps depends on two factors:

Pump BHP = GPM x TDH x SG / (3960 x Efficiency)

Pump BHP = GPM x PSI x SG / (1713 x Efficienc y)

Where

• BHP = brake horse power

• Q = water flow, gallons per minute (GPM)

• TDH = Total Dynamic Head, ft

• SG = Specific Gravity, for water it is 1

• Efficiency = Pump efficiency from its pump curves for the water flow and TDH

Power consumption, KWH = KW input x operating hours

The KW input will depend on the motor efficiency and pump power requirement. (1 KW = 0.746 HP)

**Pump Motor Horsepower**

Motor HP = BHP / Motor Ef f

Where

• BHP = Break Horsepower

• Motor Ef f = Motor drive efficiency usually 80-95%

**Pump Affinity Laws**

Effect on centrifugal pumps of change of speed or impeller diameter

Capacity varies directly as the speed or impeller diameter (GPM x rpm x D)

Head varies as the square of speed or impeller diameter (GPM x rpm2 x D2)

BHP varies as the cube of the speed or impeller diameter (BHP x rpm3 x D3)

**Specific Gravity**

Specific gravity is direct ratio of any liquid’s weight to the weight of water at 62 deg F. Water at 62 deg F weighs 8.33 lbs per gallon and is designated as 1.0 specific gravity. By definition, the specific gravity of a fluid is: SG = PF / PW

Where PF is the fluid density and PW is water density at standard conditions.

Example Specific Gravity of HCl = Weight of HCl / Weight of Water = 10.0 / 8.34 = 1.2

**Head and Pressure**

To start, head is not equivalent to pressure. Since the pump is a dynamic device, it is convenient to consider the head generated rather than the pressure. The term “Head” is usually expressed in feet whereas pressure is usually expressed in pounds per square inch. The relations hip between two is

PSI = Head (feet) x Specific Gravity / 2.31

Ve

**locity Head**

VH = V2 /2g

Where

• VH = Velocity head in ft

• V = Velocity in ft/s

• g = Acceleration due to gravity (32.17 ft/s2 )

**Bernoulli's equation**

The pump generates the same head of liquid whatever the density of the liquid being pumped. In the following equation (Bernoulli's equation) each of the terms is a head term: elevation head h, pressure head p and v elocity head v2 /2g. Head is equal to specific energy, of which the units are lbf-ft/lbf. Therefore, the elevation head is actually the specific potential energy, the pressure head, the

specific pressure energy and the velocity head is the specific kinetic energy (specific means per unit weight).

h + p/y + v2 /2g = E = Constant

Where

• h: elevation in ft;

• p: pres sure lb/sq-in;

• y: fluid specific weight

• v: velocity in ft/s

• g: acceleration due to gravity (32.17 ft/s2);

• E: specific energy or energy per unit mass.

Note: A centrifugal pump develops head not pressure. All pressure figures should be converted to feet of head taking into considerations the specific gravity.

**Pump NPSH**

To determine the NPSH available, the following formula may be used

NPSHA = HA ± HS - HF - HVP

Where

• NPSHA = Net Positive Suction Available at Pump expressed in feet of fluid

• NPSHR = Net Positive Suction Required at Pump (Feet)

• HA = Absolute pressure on the surface of the liquid where the pump takes suction, expressed in feet. This could be atmospheric pressure or vessel pressure (pressurized tank). It is a positive factor (34 Feet for Water at Atmospheric Pressure)

• HS =Static elevation of the liquid above or below the centerline of the impeller, expressed in feet. Static suction head is positive factor while static suction lift is a negative factor.

• HF = Friction and velocity head loss in the piping, also expressed in feet. It is a negative factor.

• HVP = Absolute vapor pressure of the fluid at the pumping temperature, expressed in feet of liquid. It is a negative pressure.

The Net Positive Suction Head (N.P.S.H.) is the pressure head at the suction flange of the pump less the vapour pressure converted to fluid column height of the fluid. The N.P.S.H. is always positive since it is expressed in terms of absolute fluid column height. The value, by which the pressure in the pump suction exceeds the liquid vapour pressure and is expressed as a head of liquid and referred to as Net Positive Suction Head Available – (NPSHA). This is a characteristic of the suction system design. The value of NPSH needed at the pump suction to prevent the pump from cavitating is known as NPSH Required – (NPSHR). This is a characteristic of the pump design.

**Note**that NPSHA > NPSHR i.e. the N.P.S.H. available must always be greater than the N.P.S.H. required for the pump to operate properly.

**Pump Specific Speed**

Equation below gives the value for the pump specific speed;

Ns = (Nr x Q) / (H)3/4

Where

• Ns = Specific speed

• Q = Flow in US gallons per minute (GPM)

• Nr = Pump speed, RPM

• H = Head, ft

Specific speed is a dimensionless quantity. Specific speed is indicative of the shape and characteristics of an impeller. Impeller form and proportions vary with specific speed but not the size. It can be seen that there is a gradual change

in the profiles from radial to axial flow configuration. Studies indicate that a pump efficiency at the best efficiency point (BEP) depends mainly on the specific speed, and a pump with specific speed of 1500 is more efficient then the one with specific speed of 1000.

### FAN EQUATIONS

**Output Power**

BHP = Q x SP / (6356 x Fan Ef f.)

Where

• BHP = Break Horsepower

• Pt = Total pressure, in-WG

• Q = Air flow rate in CFM

• SP = Static pressure in-WG

• FAN EFF = Fan efficiency usually in 65–85% range

**Fan Motor Horsepower**

Motor HP = BHP / MotorEFF

Where

• BHP = Break Horsepower

• MotorEFF = Motor drive efficienc y usually 80-95%

**Tip Speed**

Ts = 3.14 x D x N

Where

• Ts = Fan tip speed, FPM

• D = Fan diameter, ft

• N = Fan speed, RPM

**V-belt Length Formula**

Once a sheave combination is selected we can calculate approximate belt length. Calculate the approximate V-belt length using the following formula:

L = 2C + 1.57 * (D+d) + (D-d)2/ 4C

Where

• L = Pitch Length of Belt

• C = Center Distance of Sheaves

• D = Pitch Diameter of Large Sheave

• d = Pitch Diameter of Small Sheave

### DUCTWORK EQUATIONS

**Velocity in Duct**

Velocity in duct can be expressed as

V = Q / A = 144 x Q / a x b

Where

• V = air velocity in ft per minute (FPM)

• Q = air flow through duct in cubic ft per minute (CFM)

• A = cross-section of duct in sq-ft

**For rectangular ducts**

• a = Width of duct side (inches)

• b = Height of other duct side (inches)

**Equivalent Round Duct Size for a Rectangular Duct**

Equivalent round duct size for a rectangular duct can be expressed as

Deq = 1.3 x (a x b)0.625 / (a +b)0.25

Where

• Deq = equivalent diameter

• a = one dimension of rectangular duct (inches )

• b = adjacent side of rectangular duct (inches)

**Equations for Flat Oval Ductwork**

P= ((3.14XDS) + 2 x (DL – DS)) / 12

Deq = (1.55 x A0.625)/p0.625

A=((((DL –DS) x DS) + (3.14 x DS2)/4))/144

Where

• DL = Major Axis Dimens ion (Inches)

• DS = Minor Axis Dimension (Inc hes)

• A = Cross-Sectional Area (Sq-ft)

• P = Perimeter or Surface Area (Sq-ft per linear feet)

• Deq = Equivalent Round Duct Diameter

**Duct Air Pressure Equations**

TP = SP + VP

Where

• TP = Total Pressure

• SP = Static Pressure, friction losses

• VP = Velocity Pressure, dynamic losses

**Velocity Pressure**

VP = (V / 4005)2

Where

• VP = Velocity pressure

• V = Air velocity in FPM

### ESTIMATING AIR VOLUME FOR HOODS AND ITS PRESSURE

**Enclosed Hoods**For enclosed hoods, the exhaust volumetric flow rate can be calculated by the equation:

Q = V x A

Where

• Q = Volumetric flow rate (CFM)

• V = Average flow velocity (FPM)

• A = Flow cross-sectional area (Sq-ft)

The inflow velocity is usually around 100 FPM.

**Non-enclosed Hoods**For non enclosed hoods, the capture velocity and the air velocity at the point of contaminant release must be equal and be directed so that the contaminant enters the hood. This results in different volumetric flow rate equations for different type of hoods. For un-flanged round and rectangular openings, the required flow rate equation is:

Q = V x [(10X x 10X) + A]

Where

• Q = Flow rate (CFM)

• V = Capture velocity (FPM)

• X = Centre line distance from the hood face to the point of contaminant generation (ft)

• A = Hood face area (Sq-ft)

L = Long dimension of the slot (ft)

**For slot hoods,**the required flow rte is predicted by an equation for openings between 0.5 to 2” in

width:

Q = 3.7 x L x V x X

Where

• Q = Flow rate (CFM)

• V = Capture velocity (FPM)

• X = Centre line distance from the hood face to the point of contaminant generation (ft)

• L = Long dimension of the slot (ft)

If a flange is installed around the hood opening, the required flow rate for plain openings is reduced to 75 percent of that for the corresponding un-flanged opening. The flange size should be approx imately equal to four times the area divided by the perimeter of the face hood. For flanged slots with aspect rations less than 0.15 and flanges greater than three times the slot width, the equation is

Q = 2.6 x L x V x X

A baffle is sold barrier that prevents airflow from unwanted areas in front of the hood. For hoods that Include baffles, the DallaValle half hood equation is used to approximate the required flow rate:

Q = v x [(5X x 5X) + A]

**HOOD SYSTEM PRESSURE**The hood converts duct static pressure to velocity pressure. The hood's ability to convert static pressure to velocity pressure is given by the coefficient of entry (Ce), as follows:

Ce = (VP/SPh )0.5 = [1/ (1+K)] 0.5

Where

• K = Loss factor

• VP = Velocity pressure in duct

• SPh = Absolute static pressure about 5 duct diameters down the duct from the hood

### VENTILATION FORMULA

**NATURAL VENTILATION**The equation below is used in calculating ventilation (or infiltration) due to the stack effect.

Q = C x A x [h x (ti – to )] / ti

In this equation:

• Q = Air Flow Rate (CFM)

• C = constant of proportionality = 313 (This assumes a value of 65 percent of the maximum theoretical flow, due to limited effectiveness of actual openings. With less favorable conditions, due to indirect paths from openings to the stack, etc., the effectiveness drops to 50 percent, and C = 240.)

• A = area of cross-section through stack or outlets in sq ft. (Note: Inlet area must be at least equal to this amount)

• ti = (higher) temperature inside (°F), within the height h

• to = (lower) temperature outside (°F)

• h = height difference between inlets and outlets (ft)

**OUTDOOR AIR**The equation for calculating outdoor quantities using carbon dioxide measurements is:

Outdoor air (in percent) = (Cr – Cs) x 100 / (Cr – Co)

Where:

Cs= ppm of carbon dioxide in the mixed air (if measured at an air handler) or in supply air (if measured in a room)

Cr= ppm of carbon dioxide in the return air

Co= ppm of carbon dioxide in the outdoor air

The auto-controller ensures that the increased ventilation is supplied only when required or needed for higher occupancies. This benefit in the energy cost s avings because of reduced cooling and heating of outdoor air during reduced occupancy rates.

**DILUTION VENTILATION**Dilution ventilation is most often used to advantage to control the vapours from organic liquids such as the less toxic solvents. To determine the correct volume flow rate for dilution (Qd), it is neces sary to estimate the evaporation rate of the contaminant (qd) according to the following equation:

qd = 387 (lbs) / (MW) x (T) x (ρ)

Where

• qd = Evaporation rate in CFM

• 387 = Volume in cubic feet formed by the evaporation of one lb-mole of a substance, e.g. a solvent

• MW = Molecular weight of the emitted material

• lbs = Pounds of evaporated material

• T = Time of evaporation in minutes

• ρ = density c orrection factor

The appropriate dilution volume flow rate for toxics is:

Qd = qd x Km x 106 / Ca

Where

• Qd = Volume flow rate of air, in CFM

• qd = Evaporation rate in CFM

• Km = Mixing factor to account for poor or random mixing (note Km = 2 to 5; Km = 2 is optimum)

• Ca = Accessible airborne concentration of the material

### ESTIMATING AIR LEAKAGE

Leakage through the fixed openings should be restricted as much as possible. The amount of expected leakage can be calculated from the following:

Lv = 4005 x (Rp)1/2

L = 4005 x A x (Rp ) 1/2

Where

• Lv = Leakage velocity in FPM

• L = Air leak age in CFM

• Rp = Room pressure in in-WG

• A = Opening area

Assuming 0.05 in-WG room pressures has an opening of 2 sq-ft opening

Leakage velocity = 0.223 x 4005

= 895 feet per minute

With a total of 2 square feet opening size

Leakage air volume = 2 x 895 = 1800 CFM

Lv = 4005 x (Rp)1/2

L = 4005 x A x (Rp ) 1/2

Where

• Lv = Leakage velocity in FPM

• L = Air leak age in CFM

• Rp = Room pressure in in-WG

• A = Opening area

Assuming 0.05 in-WG room pressures has an opening of 2 sq-ft opening

Leakage velocity = 0.223 x 4005

= 895 feet per minute

With a total of 2 square feet opening size

Leakage air volume = 2 x 895 = 1800 CFM

### AIR CHANGE RATE EQUATIONS

AIR CHANGE RATE EQUATIONS

The most generic method used to calculate ventilation air requirements is based on complete changes of air in a structure or room in a given time period. To determine the airflow required to adequately ventilate an area, calculate the Room Volume to be ventilated Width x Length x Height = ft3 (cubic feet) and than calculate the Air Volume requirement by multiplying the Room Volume by the Air Change Rate per hour.

ACH = Cu-ft / min x 60 min/hr / room volume

CFM = ACH x room volume / 60 min/hr

Where

• ACH = Air Change Rate per Hour

• CFM = Air Flow Rate (Cubic Feet per Minute)

• Room volume = Space Volume (Cubic Feet)

The most generic method used to calculate ventilation air requirements is based on complete changes of air in a structure or room in a given time period. To determine the airflow required to adequately ventilate an area, calculate the Room Volume to be ventilated Width x Length x Height = ft3 (cubic feet) and than calculate the Air Volume requirement by multiplying the Room Volume by the Air Change Rate per hour.

ACH = Cu-ft / min x 60 min/hr / room volume

CFM = ACH x room volume / 60 min/hr

Where

• ACH = Air Change Rate per Hour

• CFM = Air Flow Rate (Cubic Feet per Minute)

• Room volume = Space Volume (Cubic Feet)

### FUEL CONSUMPTION BY HEATING, COOLING UNITS

**FUEL CONSUMPTION BY HEAING UNITS**The amount of fuel required for annual heating can be calculated using the formula:

F = H / (e x FHC)

Where

• F = Quantity of fuel consumed (in gallon, MCF, kW, etc.) per year for heating

• H = Annual heating load in BTUH

• e = efficiency of the heating unit in decimal fraction (coefficient of performance in case of a heat pump)

• FHC = fuel heat content Btu per gal or kW

**FUEL CONSUMPTION BY COOLING UNITS**The amount of fuel required for annual cooling can be calculated us ing the formula:

F = C / (SEER x 1000)

Where

• F = Electrical energy required in kWh per year for cooling

• C = Annual cooling load in Btu

• SEER = Seasonal Energy Efficiency Ratio of the cooling unit (Quantity of heat removed in BTUH for an input of 1 watt)

**Fuel Cost**USD ($) = F x cost per unit (unit being gallon, mcf, kW, etc.)

### CALCULATION OF HEATING, COOLING DEGREE DAYS

**CALCULATION OF HEATING DEGREE DAYS**Heating Degree Days (HDD) for a particular climate is obtained by subtracting each day's mean outdoor dry bulb temperature from the balance point temperature; this result is the number of HDDs for that day. For example, if the maximum and minimum outdoor dry bulb temperatures of a place were 80°F and 20°F respectively, and the balance point temperature were 65°F, then HDD of the place for that particular day would have been 65-[(80+20)/2] = 15. If the mean outdoor dry bulb temperature is equal to or higher than the balance point temperature, then the HDD would be equal

to 0.

**Degree Days and Annual Heating loss**A preliminary estimate of annual heating load, using degree day method, can be obtained by the following formula:

H = PHL x 24 x HDD /▲T

Where

• H = Annual heating load in Btu

• PHL = peak heating load (heat loss) in Btu/hr

• HDD = heating degree days

• ▲T = temperature difference, °F

**CALCULATION OF COOLING DEGREE DAYS**Cooling Degree Days (CDD) for a particular climate is obtained by subtracting each day's mean outdoor dry bulb temperature from the balance point temperature; this result is the number of CDDs for that day. For example, if the maximum and minimum outdoor dry bulb temperatures of a place were 90°F and 60°F respectively, and the balance point temperature were 65°F, then CDD of the place for that particular day would have been [(90+60)/2]-65 = 10. If the mean outdoor dry bulb temperature is equal to or lower than the balance point temperature, then the CDD would be equal to 0.

An

**nual cooling load**A preliminary estimate of annual heating load, using degree day method, can be obtained by the following formula:

C = PCL x 24 x CDD / ▲T

Where

• C = Annual cooling load in Btu

• PCL = peak cooling load (heat gain) in Btu/hr

• CDD = cooling degree days

• ▲T = temperature difference, °F

### AIR BALANCE EQUATIONS

SA = RA + OA = RA + EA + RFA

Where

• SA = Supply Air

• RA = Return Air

• OA = Outside Air

• EA = Exhaust Air

• RFA = Relief Air

If minimum OA (ventilation air) is greater than EA, then the space will be positive pressurized and

OA = EA + RFA

If EA is greater than minimum OA (ventilation air), then the space will be under negative pressure and

OA = EA; RFA = 0

For Economizer Cycle

OA = SA = EA + RFA; RA = 0

Where

• SA = Supply Air

• RA = Return Air

• OA = Outside Air

• EA = Exhaust Air

• RFA = Relief Air

If minimum OA (ventilation air) is greater than EA, then the space will be positive pressurized and

OA = EA + RFA

If EA is greater than minimum OA (ventilation air), then the space will be under negative pressure and

OA = EA; RFA = 0

For Economizer Cycle

OA = SA = EA + RFA; RA = 0

### SUPPLY AIR FLOW RATE

Supply air flow rate to a space is based only on the total space sensible heat load, thus

Q = 1.08 x [Hs / (TR – TS)]

Where

• Q = air flow in cubic feet per minute (CFM)

• 1.08 = conversion constant = 0.244 X (60/13.5); 0.244 = specific heat of moist air, Btu/lb of dry air and 13.5 = specific volume of moist air, cu-ft. per lb of dry air (@70° F, 50% RH) and 60 is conversion from hour to minute.

• HS = total room sensible heat gain, BTU per hr.

• TR = Room dry bulb temperature, °F usually 75ºF

• TS = Supply air or leaving air temperature from the cooling coil in ºF

The selection of temperature differential (TR – TS) is stated for simplicity above but actually it is little tricky as the real operating temperature differential is determined by the laws of “Psychrometrics” governing the performance of air system. As a rule of thumb following table provides an indicative relationship between the sensible heat ratio and leaving air temperature. Once the TD is known, the

supply airflow rate (CFM) can be calculated.

Q = 1.08 x [Hs / (TR – TS)]

Where

• Q = air flow in cubic feet per minute (CFM)

• 1.08 = conversion constant = 0.244 X (60/13.5); 0.244 = specific heat of moist air, Btu/lb of dry air and 13.5 = specific volume of moist air, cu-ft. per lb of dry air (@70° F, 50% RH) and 60 is conversion from hour to minute.

• HS = total room sensible heat gain, BTU per hr.

• TR = Room dry bulb temperature, °F usually 75ºF

• TS = Supply air or leaving air temperature from the cooling coil in ºF

The selection of temperature differential (TR – TS) is stated for simplicity above but actually it is little tricky as the real operating temperature differential is determined by the laws of “Psychrometrics” governing the performance of air system. As a rule of thumb following table provides an indicative relationship between the sensible heat ratio and leaving air temperature. Once the TD is known, the

supply airflow rate (CFM) can be calculated.

### SENSIBLE HEAT FACTOR or RATIO (SHR)

SHR = Hs / Ht = Hs / (Hs + HL )

Where

• SHR = Sensible heat ratio

• HS = Sensible heat gain

• HL = Latent heat gain

• Ht = Total heat gain

1. SHR from 0.95 - 1.00 for Precision air conditioning (computers and data centres)

2. SHR from 0.65 - 0.75 for Comfort cooling (people)

3. SHR from 0.50 - 0.60 for Dehumidification (pools and outside air)

Lower SHR value indicates that the dehumidification requirement will be high and the supply air leaving the cooling coil shall be at lower temperature to meet the dehumidification needs. The supply airflow rate will be less. (See below for further justification)

Where

• SHR = Sensible heat ratio

• HS = Sensible heat gain

• HL = Latent heat gain

• Ht = Total heat gain

**Notes:**1. SHR from 0.95 - 1.00 for Precision air conditioning (computers and data centres)

2. SHR from 0.65 - 0.75 for Comfort cooling (people)

3. SHR from 0.50 - 0.60 for Dehumidification (pools and outside air)

Lower SHR value indicates that the dehumidification requirement will be high and the supply air leaving the cooling coil shall be at lower temperature to meet the dehumidification needs. The supply airflow rate will be less. (See below for further justification)

### COOLING & HEATING EQUATIONS

**Roofs, External Walls & Conduction through Glass**The equation used for sensible loads from the opaque elements such as walls, roof, partitions and the conduction through glass is:

H = U * A * (CLTD)

Where

• H describes Sensible heat flow (Btu/Hr)

• U = Thermal Transmittance for roof or wall or glass. See 1997 ASHRAE Fundamentals, Chapter 24 or 2001 ASHRAE Fundamentals, chapter 25. (Unit- Btu/Hr Sq-ft °F)

• A = area of roof, wall or glass calculated from building plans (sq-ft)

• CLTD = Cooling Load Temperature Difference (in °F) for roof, wall or glass. For winter months CLTD is ( Ti - T0 ) which is temperature difference between inside and outside. For Summer cooling load, this temperature differential is affected by thermal mass, daily temperature range, orientation, tilt, month, day, hour,latitude, solar absorbance, wall facing direction and other variables and therefore adjusted CLTD values are used. Refer 1997 ASHRAE Fundamentals, Chapter 28, tables 30, 31, 32, 33 and 34.

**Solar Load through Glass, Skylights and Plastic Sheets**Heat transfer through glazing is both conductive and transmission. It is calculated in two steps:

**Step # 1**

The equation used for sensible loads from the conduction through glass is:

H = U * A * (CLTD)

Where

• H = Sensible heat gain (Btu/Hr)

• U = Thermal Transmittance for roof or wall or glass. See 1997 ASHRAE Fundamentals, Chapter 24 or 2001 ASHRAE Fundamentals, chapter 25. (Unit- Btu/Hr Sq-ft °F)

• A = area of roof, wall or glass calculated from building plans (sq-ft)

• CLTD = Cooling Load Temperature Difference (in °F) for glass. Refer 1997 ASHRAE

Fundamentals, Chapter 28, tables 30, 31, 32, 33 and 34.

**Step # 2**

The equation used for radiant sensible loads from the transparent/translucent elements such as window glass, skylights and plastic sheets is:

H = A*(SHGC)*(SC)*(CLF)

Where

• H = Sensible heat gain (Btu/Hr)

• A = area of roof, wall or glass calculated from building plans (sq-ft)

• SHGC = Solar Heat Gain Coefficient. See 1997 ASHRAE Fundamentals, Chapter 28, table 35

• CLF = Solar Cooling Load Factor. See 1997 ASHRAE Fundamentals, Chapter 28, table 36.

**Partitions, Ceilings & Floors**The equation used for sensible loads from the partitions, ceilings and floors:

H = U * A * (Ta - Tr)

Where

• H = Sensible heat gain (Btu/Hr)

• U = Thermal Transmittance for roof or wall or glass. See 1997 ASHRAE Fundamentals, Chapter 24 or 2001 ASHRAE Fundamentals, and Chapter 25. (Unit- Btu/Hr Sq-ft °F)

• A = area of partition, ceiling or floor calculated from building plans (sq-ft)

• Ta = Temperature of adjacent space in °F (Note: If adjacent space is not conditioned and temperature is not available, use outdoor air temperature less 5 ° F)

• Tr = Inside room design temperature of conditioned space in °F (assumed constant usually 75°F)

**Ventilation & Infiltration Air**Ventilation air is the amount of outdoor air required to maintain Indoor Air Quality for the occupants (refer ASHRAE Standard 62 for minimum ventilation requirements) and makeup for air leaving the space due to equipment exhaust, exfiltration and pressurization.

Hsensible = 1.08 * CFM * (T0 – Tc)

Hlatent = 0.68 x CFM x ▲WGR

Hlatent = 4840 x CFM x▲W Lb

Htotal = 4.5 * CFM * (ho – hc)

Htotal = H sensible + H latent

Where

• H sensible = Sensible heat gain (Btu/hr)

• Hlatent = Latent heat gain (Btu/hr)

• Htotal = Total heat gain (Btu/hr)

• CFM = Ventilation airflow rate in cubic feet per minute

• To = Outside dry bulb temperature, °F

• Tc = Dry bulb temperature of air leaving the cooling coil, °F

• ▲WGR = Humidity Ratio Difference (Gr H2O/Lb of dry air) = (WO – WC)

• ▲WLB = Humidity Ratio Difference (Lb H2O /Lb of dry air) and = (WO – WC)

• WO = Outside humidity ratio, Lb H2O per Lb (dry air)

• WC = Humidity ratio of air leaving the cooling coil, Lb H2O per Lb (dry air)

• hO = Outside/Inside air enthalpy, Btu per lb (dry air)

• hC = Enthalpy of air leaving the cooling c oil Btu per lb (dry air) Refer to 1997 ASHRAE Fundamentals , Chapter 25, for determining infiltration

**People**The heat load from people is both sensible load and the latent load. Sensible heat is transferred through conduction, c onvection and radiation while latent heat from persons is transferred through water vapor released in breathing and/or perspiration. The total heat transferred depends on the activity, clothing, air temperature and the number of persons in the building.

H se ns ib le = N * (H S ) * (CLF)

H la t en t = N * (H L)

Where

• H se ns ib le = Total Sensible heat gain (Btu/hr)

• H la t en t = Total latent heat gain (Btu/hr)

• N = number of people in space.

• HS, HL = Sensible and Latent heat gain from occupancy is given in 1997 ASHRAE

Fundamentals Chapter 28, Table 3 (Btu/hr per person depending on nature of activity)

• CLF = Cooling Load Factor, by hour of occupancy. See 1997 ASHRAE Fundamentals,

Chapter 28, table 37.

Note: CLF = 1.0, if operation is 24 hours or of cooling is off at night or during weekends.

The sensible heat influence on the air temperature and latent heat influence the moisture content of indoor space.

**Lights**The lights result in sensible heat gain.

H = 3.41 * W * F UT * F BF * (CLF)

Where

• H = Sensible heat gain (Btu/hr)

• W = Installed lamp watts input from electrical lighting plan or lighting load data

• F BF = Lighting use factor, as appropriate

• F BF = Blast factor allowance, as appropriate

• CLF = Cooling Load Factor, by hour of occupancy. See 1997 ASHRAE Fundamentals,

Chapter 28, Table 38.

Note: CLF = 1.0, if operation is 24 hours or if cooling is off at night or during weekends .

**Power Loads & Motors**Three different equations are used under different scenarios:

a. Heat gain of power driven equipment and motor when both are located inside the space to be conditioned

H = 2545 * (P / Eff) * F UM * F L M

Where

• H = Sensible heat gain (Btu/hr)

• P = Horsepower rating from electrical power plans or manufacturer’s data (HP)

• Eff = Equipment motor efficiency, as decimal fraction

• F UM = Motor us e factor (normally = 1.0)

• F UM = Motor load factor (normally = 1.0)

• Note: F UM = 1.0, if operation is 24 hours

b. Heat gain of when driven equipment is loc ated inside the space to be conditioned space and the motor is outside the space or air stream

H = 2545 * P * F UM * F L M

Where

• H = Sensible heat gain (Btu/hr)

• P = Horsepower rating from electrical power plans or manufacturer’s data (in HP)

• Eff = Equipment motor efficiency, as decimal fraction

• F U M = Motor us e factor

• F L M = Motor load factor

• Note: F UM = 1.0, if operation is 24 hours

c. Heat gain of when driven equipment is located outside the space to be conditioned space and the motor is inside the space or air stream

H = 2545 * P * [(1.0-Eff)/Eff] * F UM * F L M

Where

• H = Sensible heat gain (Btu/hr)

• P = Horsepower rating from electrical power plans or manufacturer’s data (HP)

• Eff = Equipment motor efficiency, as decimal fraction

• F U M = Motor us e factor

• F L M = Motor load factor

• Note: F UM = 1.0, if operation is 24 hours

**Appliances**H = 3.41 * W * F u * F r * (CLF)

Where

• H = Sensible heat gain (Btu/hr)

• W = Installed rating of appliances in watts. See 1997 ASHRAE Fundamentals, Chapter 28; Table 5 thru 9 or use manufacturer’s data. For computers, monitors, printers and miscellaneous office equipment, see 2001 ASHRAE Fundamentals, Chapter 29, Tables 8,9 & 10.

• F u = Usage factor. See 1997 ASHRAE Fundamentals, Chapter 28, Table 6 and 7

• F r = Radiation factor. See 1997 ASHRAE Fundamentals, Chapter 28, Table 6 and 7

• CLF = Cooling Load Factor, by hour of occupancy. See 1997 ASHRAE Fundamentals,

Chapter 28, Table 37 and 39. Note: CLF = 1.0, if operation is 24 hours or of cooling is off at night or during weekends.

**Conductive Heat Transfer**Conductive heat flow occurs in the direction of decreasing temperature and takes place when a temperature gradient exists in a solid (or stationary fluid) medium. The equation used to express heat transfer by conduction is k nown as Fourier’s Law and is expressed as:

H = k x A x ▲T / t

Where

• H = Hat transferred per unit time (Btu/hr)

• A = Heat transfer area (ft2)

• k = Thermal conductivity of the material (Btu/ (hr0F ft2/ft))

• ▲T = Temperature difference across the material (°F)

• t = material thickness (ft)

**R-Values/U-Values**R = 1/ C = 1/K x t

U = 1/ ∑R

Where

• R = R-Value (Hr Sq-ft °F/Btu)

• U = U-Value (Btu/Hr Sq-ft °F)

• C = Conductance (Btu/hr Sq-ft °F)

• K = Conductivity (Btu in/ hr Sq-ft °F)

• ∑R = Sum of the thermal resistances for each component used in the construction of the wall or roof section.

• t = thickness (ft)

Notes: The lower the U-factor, the greater the material's resistance to heat flow and the better is the insulating value. U-value is the inverse of R-value (hr sq-ft °F /Btu).

**Heat Loss by Conduction & Convection through Roof & Walls**Heat loss by conduction and convection heat transfer through any surface is given by:

H sensible = A * U * (Ti – To)

Where

• H = heat transfer through walls, roof, glass, etc. (Btu/hr)

• A = surface areas (sq-ft)

• U = air-to-air heat transfer coefficient (Unit- Btu/Hr Sq-ft °F)

• Ti = indoor air temperature (°F)

• To = outdoor air temperature (°F)

**Heat Loss through Floors on Slab**The slab heat loss is calculated by using the following equation:

H = F* P * (T i -T o)

Where:

• H = Sensible heat loss (Btu/hr)

• F = Heat Los s Coefficient for the particular construction and is a function of the degree days of heating. (Unit- Btu/Hr Sq-ft °F)

• P = Perimeter of slab (ft)

• T i = Inside temperature (°F)

• T o = Outside temperature (°F)

Heat loss from slab-on- grade foundations is a function of the slab perimeter rather than the floor area. The losses are from the edges of the slab and insulation on these edges will significantly reduce the heat losses.

**Heat loss through Infiltration and Ventilation**The heat loss due to infiltration and controlled natural ventilation is divided into sensible and latent losses. The energy associated with having to raise the temperature of infiltrating or ventilating air up to indoor air temperature is the sensible heat loss, which is estimated by:

H sensible = V * рair * Cp * (Ti – To)

Where:

• H sensible = Sensible heat loss

• V = volumetric air flow rate

• рair is the density of the air

• Cp = specific heat capacity of air at constant pressure

• Ti = indoor air temperature

• To = outdoor air temperature

The energy quantity associated with net loss of moisture from the space is latent heat loss which is given by:

Hlatent = V * рair * hfg * (Wi – Wo)

Where

• Hlatent = Latent heat loss

• V = volumetric air flow rate

• рair is the density of the air

• Wi = humidity ratio of indoor air

• Wo = humidity ratio of outdoor air

• hfg = latent heat of evaporation at indoor air temperature

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