nebb fundamental formulas...jan 07, 2016 · = mixed air enthalpy shr = sensible heat ratio h oa =...

A = Area (ft²) IP, (m²) SI M = Mass (lb) IP, (kg) SI

ACH = Air Changes per Hour ma = Mixed Air

Ak = Effective Area m = meter (metre)

AV = Average m³/s = Volumetric Flow: Cubic Meters Per Second

BHP = Brake Horsepower (IP) HP NLA = No Load Amperage

BP = Brake Power (SI) kW NPSHA = Net Positive Suction Head Available

Btu = British Thermal Unit oa = Outside Air

Btu/h = Btuh = BTUH = BTU/Hour % oa = % of Outside Air

℄ = Center Distance (used in belt formula) Ω = Ohm

°C = Degrees Celsius, °C P = Pressure

C = Friction Loss Coefficient (For Duct Fittings) Pa = Atmospheric Pressure

CCF = 100 Cubic Feet Pab = Absolute Pressure (Atmospheric Pressure + Gauge Pressure)

CFM = Volumetric Flow: Cubic Feet Per Minute Pa = Pascals, Pressure SI

Cp = Specific Heat π = 3.14

Cv = Flow Constant (IP) PD = Sheave Pitch Diameter

ρ = Density (lb/ft³) IP, (kg/m³) SI P℄ = Pressure at Pump Centerline

d = Diameter (in.) IP, (mm) SI ppm = parts per million

Δ = Difference or Change (Final - Initial) psi = Pounds Per Square Inch

dimp = Impeller Diameter psia = Pounds Per Square Inch Absolute

E = Volts psig = Pounds Per Square Inch Gauge

Eff = Efficiency Pvp = Absolute Vapor Pressure

EP = Pump Efficiency Q (flow) = Volumetric Fluid Flow Rate: (i.e. CFM, GPM, m³/s, l/s, etc.)

°F = Degrees Fahrenheit, °F Q (heat) = Heat Flow Rate (BTU/Hour) IP, (W or kW) SI

f = Friction Factor °R = °Rankin = Degrees Rankin, °R

FLA = Full Load Amps r = Radius (in) IP, (mm) SI

fpm = Feet per Minute (fpm) % ra = % of Return Air

ft = Foot R = Resistance

g = Acceleration of Gravity ra = Return Air

gal = Gallons rad = Radians

GPM = Gallons Per Minute (GPM) RH = Relative Humidity

h = Enthalpy (BTU/lb dry air) IP, (kJ/kg dry air) SI RPM = Revolutions Per Minute

H = Head (in wc, ft wc, psi) IP, (Pa, kPa) SI Rvalue = Thermal Resistance

Hg = Mercury s = second

hma = Mixed Air Enthalpy SHR = Sensible Heat Ratio

hoa = Outside Air Enthalpy SME = Sash Movement Effect Performance Rating (SME-XX yyy)

HP = Horsepower SP = Static Pressure

hr = Hour Sp Gr = Specific Gravity (for water use 1.00)

hra = Return Air Enthalpy T = Temperature

HT = Height (in) IP, (mm) SI Ta = Absolute Temperature (460˚ + T) or °R

I = Amps Tma = Mixed Air Temperature

J = Joules Toa = Outside Air Temperature

K = Kelvin, K TP = Total Pressure

Kv = Flow constant (SI) Tra = Return Air Temperature

kg = Kilogram TS = Tip Speed (fpm) IP, (m/s) SI

kJ = Kilojoule U = Heat Transfer Coefficient

kPa = Kilopascal µ = viscosity, dynamic

kW = Kilowatt = 1000 Watts V = Velocity

l = Liter (Litre) VP = Velocity Pressure

l/s = Volumetric Flow: Liters Per Second W = Watt

lb = Pounds WD = Width (in) IP, (mm) SI

lm = Lumens wg = wc = water gauge = water column

ln = natural log WHP = Water Horsepower (IP)

LG = Length (in) IP, (mm) SI WP = Water Power (SI)

lx = Lux ω = Humidity Ratio (lb or grains of water/lb of dry air) (g H2O/kg dry air)

NEBB Fundamental Formulas

Approved NEBB - May 11, 2016 Page 1 of 8 Version 1.2

Airflow & Velocity Equations

Q = V × A Q = V x A

TP(in wg) = VP + SP TP(Pa) = VP + SP

V( std air) = 4005 × √VP V(std air) = √(1.66 × VP)

V = 1096 × √(VP

𝜌) V = 1.414 × √(

VP

𝜌)

ACH =Q × 60

(LG x WD x HT ) ACH =

Q × 3600

(LG x WD x HT )

AreaRound =π × (

d2

)2

144=

(π × r2)

144 AreaRound =

π × (d2

)2

1,000,000=

(π × r2)

1,000,000

Area(square/rectangular) =(HT × WD)

144 Area(square/rectangular) =

(HT × WD)

1,000,000

AreaOval =

((HT x WD) + (π × (HT2

)2

))

144 AreaOval =

((HT × WD) + (π × (HT2

)2

))

1,000,000

Air Temperature Equations

℉ = (1.8 × ℃) + 32° ℃ = (℉ − 32) ÷ 1.8

°R = (℉ + 460) K = (℃ + 273)

Tma = (%oa × Toa) + (%ra × Tra) hma = (%oa × hoa) + (%ra × hra)

%oa = ((Tra − Tma)

(Tra − Toa)) × 100 %oa = (

(hra − hma)

(hra − hoa)) × 100

Heat Transfer Calculations

Qtotal = 4.5 × CFM × ∆h Qtotal = 1.2 ×l

s⁄ × ∆h

Qsensible = 60 × Cp × ρ × CFM × ∆Tair Qsensible = Cp × ρ ×l

s⁄ × ∆Tair

Qsensible = 1.08 × CFM × ∆Tair Qsensible = 1.23 ×l

s⁄ × ∆Tair

Qlatent = 0.69 × CFM × ∆𝜔gr of H2Olb dry air⁄

Qlatent = 3.0 ×l

s⁄ × ∆𝜔g H2Okg dry air⁄

Qlatent = 4840 × CFM × ∆𝜔lb of H2Olb dry air⁄

SHR = Qsensible ÷ Qtotal Qtotal = Qlatent + Qsensible

Fan Equations

CFM2CFM1

=RPM2RPM1

l

s⁄ 2l

s⁄ 1

=m3

s⁄ sm3

s⁄ 1

=rad

s⁄ 2rad

s⁄ 1

P2P1

= (CFM2CFM1

)2

P2P1

= (l

s⁄ 2l

s⁄ 1

)

2

= (m3

s⁄ 2m3

s⁄ 1

)

2

BHP2BHP1

= (CFM2CFM1

)3

kW2kW1

= (l

s⁄ 2l

s⁄ 1

)

3

= (m3

s⁄ 2m3

s⁄ 1

)

3

Tip Speed = TP =(π × d × rpm)

12 Tip Speed = TP =

(π × d × rpm)

60



Sheave Equations

RPMfan = (PDmotor

PDfan) × RPMmotor

RPMfanRPMmotor

=PDmotor

PDfan

Fan Belt Length = (℄ × 2) + (1.57 × (PDlarge + PDsmall)) + ((PDlarge − PDsmall)

2

4 × ℄)

Electrical Equations

Power(Watts) = E × I 1 kW = 1000 Watts

I = E ÷ Ω Ω = E ÷ I

1 HP = 746 Watts 1 Watt = 3.413 Btu/hr

Power Equations

BHP1 phase =(E × I × PF × Eff)

746

PF=Power Factor

kW1 phase =(E × I × PF)

1000

PF=Power Factor

BHP3 phase =(E × I × PF × Eff × 1.732)

746

PF=Power Factor = 0.8 & Eff=0.9; if not given

kW3 phase =(E × I × PF × 1.732)

1000

BHP = HP × ((Iactual − (NLA × 0.5)

(FLA − (NLA × 0.5))

FLAactual =(FLAtag × Etag)

Eactual

Fan HP =(CFM × TP × SpGr)

(6356 × Eff)

Resistance

Series Circuit: total resistance: Ω = Rtotal Parallel Circuit: total resistance: Ω = Rtotal

RTotalSeries = R1 + R2 + R3 + ⋯ + Rn 1

RTotalParallel=

1

R1+

1

R2+ ⋯ +

1

Rn

Eprimary × Iprimary = Esecondary × Isecondary Voltage Drop = I × RTotal

Conversions

kilowatts (Kw) Btu / hr 413

horsepower (HP) Btu / hr 2545

joules Btu / hr 0.000948

kilogram calories Btu / hr 3.968

tons of cooling (chiller) Btu / hr 12000

tons of cooling (cooling tower) Btu / hr 15000

gallons U.S. (water) pounds U.S. (lb.) 8.33

millimeters inches U.S. 25.4

centimeters inches U.S. 2.54

bar pounds per square inch (PSI) 14.5

inches of water pounds per square inch (PSI) 0.036

inches of Mercury (Hg) pounds per square inch (PSI) 0.491



Hydronic

Pump Equations

GPM2GPM1

=RPM2RPM1

l

s2 ⁄

ls1 ⁄

=m3

s2 ⁄

m3s1 ⁄

=rad

s2 ⁄

rads1 ⁄

GPM2GPM1

=dimp2

dimp1

m3s2⁄

m3s1⁄

=dimp2

dimp1

H2H1

= (GPM2GPM1

)2

H2H1

= (

m3h2

⁄

m3h1

⁄)

2

= (rad

s2 ⁄

rads1 ⁄

)

2

BHP2BHP1

= (GPM2GPM1

)3

BP2BP1

= (m3

s2 ⁄

m3s1 ⁄

)

3

= (rad

s2 ⁄

rads1 ⁄

)

3

WHP =(GPM × H𝑓𝑡 𝑤𝑔 × SpGr)

3960

SpGr = 1.0, unless given, EP use 0.7 if not given

WPkW = 9.81 ×m3

s⁄ × Hm × SpGr

WPW =(l s⁄ × HPa × SpGr)

1002

BHP =(GPM × H𝑓𝑡 𝑤𝑔 × SpGr)

(3960 × EP)


BP =WP

EP

EPin % =(WHP × 100)

BHP EPin % =

(WP × 100)

BP

Hydronic Calculations

Coil ∆P: GPM2 = GPM1 × √(P2P1

) Coil ∆P: m3

h2⁄ = m

3

h1⁄ × √(

P2P1

)

Cv =GPM

√(SpGr∆Ppsi

)

Kv =

m3h⁄

√(SpGr∆PBar

)

GPM = Cv × √(∆Ppsi

SpGr)


m3h⁄ = Kv × √(

∆PBarSpGr

)


∆Ppsi = SpGr × (GPM

Cv)

2


∆PBar = SpGr × (m3

h⁄

Kv)

2


NPSHA = Pa ± Ps + (V2

2g) − Pvp − Pf

Heat Transfer Calculations

𝑄𝐵𝑡𝑢 = 𝐶𝑝 × ρ × 𝐺𝑃𝑀 × ∆𝑇℉ 𝑄𝑘𝑊 = 𝐶𝑝 × ρ × 𝑙𝑠 × ∆𝑇℃

𝑄𝐵𝑡𝑢 = 500 × 𝐺𝑃𝑀 × ∆𝑇℉ 𝑄𝑘𝑊 = 4190 ×

𝑚3𝑠⁄ × ∆𝑇℃

𝑄𝑊 = 4190 ×𝑙

𝑠⁄ × ∆𝑇℃

Boiler Calculations

Output Btu = Input Btu × %Eff Fire Rate =Input Btu

Fuel Btu galhr

⁄

Boiler Operating Cost = Fire Rategalhr

⁄× hrs Burned × $Cost gal⁄ Btu = lb of water × 500 × ∆Twater



Metric Equivalents

acceleration m/s2 meters per second squared 1m/s2 = 3.281 ft/sec2

airflow volumetric flow rate

m3/s cubic meters per second 1 m3/s = 2118.88 cfm

l/s liters per second 1 l/s = 2.12 cfm

m3/hr cubic meters per hour 1 m3/hr = 0.589 cfm

area m2 square meter 1 m2 = 10.764 ft2

mm2 square millimeters 1 mm2 = 0.0016 in2

atmospheric pressure

kPa kiloPascals 101.325 kPa = 29.92 in Hg = 14.696 psi

Bar Barometers 1 Bar = 100kPa = 29.53 in Hg = 14.504 psi

distance. length, or distance

m meter 1 m = 3.281 ft

m meter 1 m = 39.370 in

mm millimeter 1 mm = 0.039 in

lighting intensity lx Lux 1 lx = 0.093 fc

lm/m2 Lumens/square meter 1lm/m2 = 0.0931 fc

pressure kPa kiloPascals = 1000 Pascals 1 kPa = 0.296 in Hg = 0.145 psi

Pa Pascals 1 Pa = 0.004 in wg

temperature °C degrees Celsius °C = (°F - 32) / 1.8

velocity m/s meters per second 1 m/s = 196.9 fpm

volume m3 cubic meters 1 m3 = 35.31 ft3

1 Btu = Energy required to heat 1 lb of H2O from 39 ˚F to 40 ˚F

1 CCF = 100000 Btu

1 ft = inches ÷ 12

1 ft wc = 0.434 psi

1 ft Hg = 5.89 psi

inches = ft x 12

1 mm Hg = 0.535 in wc

1 in Hg = 1.133 ft

1 kW/hr = 3413 Btu

1 lb(moisture) = 7000 grains

1 psi = 2.307 ft wc

1 psi = 27.681 in wc

1 psi = 2.036 in Hg

1 Ton refrigeration = 12000 Btu/hr

Atmospheric. Press = 29.92 in Hg or 14.69 psi

Density of Air (Std) = 0.075 lb/ft3

Density of Water (Std) = 62.4 lb/ft3 or 7.49 gal/ft3 or 8.33 lb/gal

One foot of mercury (Hg) column = 5.89 lb/in2 (psi)

One inch of mercury (Hg) column = 13.6 inches (in wg) = 1.13 ft wg

Specific Heat (Cp) of dry air = 0.24 Btu/lb x ˚F @ 68°F

Specific Heat (Cp) ice = 0.50 Btu/lb x ˚F @ 68°F

Specific Heat (Cp) vapor = 0.45 Btu/lb x ˚F @ 68°F

Specific Heat (Cp) water = 1.00 Btu/lb x ˚F @ 68°F

Specific Volume of Air (Std) = 13.33 ft3/lb



-10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130

DRY BULB TEMPERATURE - °F

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

210

10 15 20 25 3035

40

45

50

55

55

60

60

65

70

ENTH

ALPY

- BT

U P

ER P

OU

ND

OF

DR

Y AI

R

0

5

10

15

20

25

30

35

40

45

50

ENTH

ALPY

- BT

U PE

R PO

UND

OF

DRY

AIR

SATU

RATI

ON

TEM

PERA

TURE

- °F

-50

05

510

1015

1520

20 25

25 30

3035

35 40

40 45

45 50

50 55

55 60

6065

6570

70

75

75

80

80

85 WET BULB TEMPERATURE - °F

85

90

15%

25%

2 %

4 %

6 %

8 %

1 0 % R E LA T I V E H U

M I D I T Y2 0 %

3 0 %

4 0 %

5 0%

60%

70%

80%

90%

12.0

12.5

13.0

13.5

14.0 SPECIFIC

VOLU

ME ft³/lb O

F DR

Y AIR

14.5

15.0

15.5

HU

MID

ITY

RAT

IO -

GR

AIN

S O

F M

OIS

TUR

E PE

R P

OU

ND

OF

DR

Y AI

R

PSYCHROMETRIC CHARTBAROMETRIC PRESSURE 29.921 inches of Mercury

Linric Company Psychrometric Chart, www.linric.com

.1

.2

.3

.4

.5

.6

.7

.8

.9

1

1.1

1.2

1.3

VAPO

R P

RES

SUR

E - I

NC

HES

OF

MER

CU

RY

-20 0

10

20 25

30

35

40

45

50

55

60

65

70

75

80

85

DEW

PO

INT

- °F

0

1.0 1.0

2.0

84.0- 8.

- -8.04.0-2 0.-1.0- -0.540.-0.3-0.2-0.1

0.10.20.3

0.4

0.50.6

0.8

-2000-1000

0.0

50.0

1000

1500

2000

3000

5000

-

SENSIBLE HEAT QsTOTAL HEAT Qt

ENTHALPYHUMIDITY RATIO

hW



lmaianiRectangle

5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

DRY BULB TEMPERATURE - °C

-30 -20 -10 0 10 20 30 40 50 60 7080

90

100

110

120

130

140

150

150

160

160

170

170

180

180

EN

THA

LPY

- K

J P

ER

KIL

OG

RA

M O

F D

RY

AIR

-30

-20

-10

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

ENTH

ALPY

- KJ

PER

KIL

OG

RAM

OF

DRY

AIR

1.02.03.04.05.06.07.08.09.010.011.012.013.014.015.016.017.018.0

19.020.021.0

22.0

23.0

24.0

25.0

26.0

27.0

28.0

29.0

30.0

31.0

32.0

33.0

34.0

35.0

36.0

37.0

38.0

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45.0

46.0

47.0

VA

PO

R P

RE

SS

UR

E -

MM

OF

ME

RC

UR

Y

-10

-5

0

5

10

15

20

25

30

35

DE

W P

OIN

T TE

MP

ER

ATU

RE

- °C

1.00

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.55

0.50

0.45

0.400.350.300.250.20

SENSIBLE HEAT RATIO = Qs / Qt

SE

NS

IBLE

HE

AT

RA

TIO

= Q

s / Q

t

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34

36

38

40

15%

25%

2%

4%

6%

8% RE

LATIV

E HUM

IDITY

10% RELATIVE

HUMIDITY

20%

30%

40%

50%

60%

70%

80%

90%

-30 -25-20 -15

-15 -10

-10 -5

-5

05

510

10

15

15

20

20

25

25

30

30

35 WET BULB TEMPERATURE - °C

35

0.76

0.78

0.80

0.82

0.84

0.86

0.88 VOLU

ME - C

UBIC

METER

PER KG

DR

Y AIR0.90

0.92

0.94

0.96

0.98 1.00

1.02

HU

MID

ITY

RA

TIO

- G

RA

MS

MO

ISTU

RE

PE

R K

ILO

GR

AM

DR

Y A

IR

0

1.0 1.0

-

2.04.08.0-8.0-4.0-2.0-1.0-0.5

-0.4-0.3-0.2-0.1

0.10.20.3

0.4

0.50.6

0.8

-4.6

-2.3

0.0

1.2

2.3

3.5

4.7

7.0

11.7

-

SENSIBLE HEAT QsTOTAL HEAT Qt

ENTHALPYHUMIDITY RATIO

hW

-35 -30 -25 -20 -15 -10 -

PSYCHROMETRIC CHARTPSYCHROMETRIC CHART - METRICNORMAL TEMPERATURENORMAL TEMPERATURESI UnitsSI Units

SEA LEVELSEA LEVELBAROMETRIC PRESSURE: 101.325 kPaBAROMETRIC PRESSURE: 101.325 kPa



Sea Level 1000 2000 3000 4000 5000 6000 7000 8000 9000 1000029.92 28.86 27.82 26.82 25.84 24.90 23.98 23.09 22.22 21.39 20.58407.50 392.80 378.60 365.00 351.70 333.90 326.40 314.80 302.10 291.10 280.10

‐40° 1.26 1.22 1.17 1.13 1.09 1.05 1.01 0.97 0.93 0.90 0.87‐0° 1.15 1.11 1.07 1.03 0.99 0.95 0.91 0.89 0.85 0.82 0.7940° 1.06 1.02 0.99 0.95 0.92 0.88 0.85 0.82 0.79 0.76 0.7370° 1.00 0.96 0.93 0.89 0.86 0.83 0.80 0.08 0.74 0.71 0.69

100° 0.95 0.92 0.88 0.85 0.81 0.78 0.75 0.73 0.70 0.68 0.65150° 0.87 0.84 0.81 0.78 0.75 0.72 0.69 0.67 0.65 0.62 0.60200° 0.80 0.77 0.74 0.71 0.69 0.66 0.64 0.62 0.06 0.57 0.55250° 0.75 0.72 0.70 0.67 0.64 0.62 0.60 0.58 0.56 0.54 0.51300° 0.70 0.67 0.65 0.62 0.60 0.58 0.56 0.54 0.52 0.50 0.48350° 0.65 0.62 0.60 0.58 0.56 0.54 0.52 0.51 0.49 0.05 0.45400° 0.62 0.60 0.57 0.55 0.53 0.51 0.49 0.48 0.46 0.44 0.42450° 0.55 0.56 0.54 0.52 0.50 0.48 0.46 0.45 0.43 0.42 0.40500° 0.58 0.53 0.51 0.49 0.47 0.45 0.44 0.43 0.41 0.39 0.38550° 0.53 0.51 0.49 0.47 0.45 0.44 0.52 0.41 0.39 0.38 0.36600° 0.50 0.48 0.46 0.45 0.43 0.41 0.40 0.39 0.37 0.35 0.34700° 0.46 0.44 0.43 0.41 0.39 0.38 0.37 0.35 0.34 0.33 0.32800° 0.42 0.40 0.39 0.37 0.36 0.35 0.33 0.32 0.31 0.30 0.29

60° 150° 200° 250° 300° 340°1.046 1.070 1.090 1.110 1.150 1.165

Sea Level 250 500 750 1000 1250 1500 1750 2000 2500 3000101.33 98.30 96.30 93.20 90.20 88.20 85.10 83.10 80.00 76.00 71.90

0° 1.08 1.05 1.02 0.99 0.96 0.93 0.91 0.88 0.86 0.81 0.7620° 1.00 0.97 0.95 0.92 0.89 0.87 0.84 0.82 0.79 0.75 0.7150° 0.91 0.89 0.86 0.84 0.81 0.79 0.77 0.75 0.72 0.68 0.6475° 0.85 0.82 0.80 0.78 0.75 0.73 0.71 0.69 0.67 0.63 0.60

100° 0.79 0.77 0.75 0.72 0.70 0.68 0.66 0.65 0.63 0.59 0.56125° 0.74 0.72 0.70 0.68 0.66 0.64 0.62 0.60 0.59 0.55 0.52150° 0.70 0.68 0.66 0.64 0.62 0.60 0.59 0.57 0.55 0.52 0.49175° 0.66 0.64 0.62 0.62 0.59 0.57 0.55 0.54 0.52 0.49 0.46200° 0.62 0.61 0.59 0.57 0.56 0.54 0.52 0.51 0.49 0.47 0.44225° 0.59 0.56 0.56 0.54 0.53 0.51 0.50 0.48 0.47 0.44 0.42250° 0.56 0.55 0.53 0.52 0.50 0.49 0.47 0.46 0.45 0.42 0.40275° 0.54 0.52 0.51 0.49 0.48 0.47 0.45 0.44 0.43 0.40 0.38300° 0.51 0.50 0.49 0.47 0.46 0.45 0.43 0.42 0.41 0.38 0.36325° 0.49 0.48 0.47 0.45 0.44 0.43 0.41 0.40 0.39 0.37 0.35350° 0.47 0.46 0.45 0.43 0.42 0.41 0.40 0.39 0.38 0.35 0.33375° 0.46 0.44 0.43 0.42 0.41 0.39 0.38 0.37 0.36 0.34 0.32400° 0.44 0.43 0.41 0.40 0.39 0.38 0.37 0.36 0.35 0.33 0.31450° 0.41 0.40 0.38 0.37 0.36 0.35 0.34 0.33 0.32 0.31 0.29500° 0.38 0.37 0.36 0.35 0.34 0.33 0.32 0.31 0.30 0.28 0.27

15.5° 65.5° 93.2° 121° 148.7° 170.9°Water Temperature °C

Air Density Correction Factors (Metric Units) Standard Air Density (Sea Level & 20°C) = 1.204 kg/m3 @ 101.325 kPaAltitude (m)

Barometer (kPa)Air Temperature °C

Water Temperature °FFeet head differential per inch Hg differential

Air Density Correction Factors (US Units) Standard Air Density (Sea Level & 70°F) = 0.075 lb/ft3 @ 29.92 in Hg

Air Temperature °F

Altitude (ft)

(in wg)Barometer (in Hg)



nebb fundamental formulas...jan 07, 2016 · = mixed air enthalpy shr = sensible heat ratio h oa =...

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