EXAMPLES

Design Phase LCC calculations can be either for a single device or a whole system. Comparison of different systems is a typical consideration for the de­sign phase. In the tender phase, the supplier can use LCC calculations to show the improved economy of a single device. Figure 16.5 shows that the present value of investment and energy cost are the most significant. Typically, invest­ment in a heat recovery system reduces the total cost. Maintenance costs in this case are not significant. The proportion of disposal costs is also small, but could be a more significant factor in the future.

Different filter areas and types are compared in Fig. 16.6. Due to the short annual operating time in this case, the optimum area was rather small. In the sensitivity analysis the variation of the interest rate did not significantly influ­ence the ranking of the alternatives. An increase in operating time results in larger filter areas becoming more cost-effective.

EXAMPLES

L. ife cycle costs (present value). EUR

TABLE 16.1 Example of a Spreadsheet for Calculating Energy and Maintenance Costs in the Procurement Process: a Liquid Cooling Unit

Cooling power dissipa­tion per year, kW

Operating

Time at

Partial

Cooling

Power,

H/y

Cooling

Energy,

MWh/y

COP,*

Quoted

Estimate

Of

Supplier

Electric

Power,

Quoted

Estimate

Of

Supplier,

KW

Electric

Energy,

Quoted

Estimate

Of

Supplier,

MWh/y

Energy

Costs,

Quoted

Estimate

Of

Supplier,

EUR/y

Estimated maint­enance costs, quoted estimate of supplier, EUR/y

I. 000

500

500

6.2

160

80

4 000

2 000

3.50

700

.5,9

340

120

6 000

3 000

250

750

5.2

580

145

7 250

4 000

200

800

4.7

850

170

8 500

5 000

50

250

3.9

1 280

64

3 200

Total

1 350

3 000

579

28 950

5 200

COP, Coefficient of Performance, is equal to cooling power per needed electric power.

Procurement Phase In LCC calculations the energy consumption is of prime importance. Table 16.1 gives an example of the energy calculations for consumption guarantee in the procurement process. In this case, the designer has estimated the power dissipation for a liquid cooling unit and the supplier defines the performance of his equipment by means of COP and energy consumption. The maintenance costs and guaranteed costs are given.

The tender with the lowest total costs (sum of investment, energy and maintenance costs) is the best and the supplier guarantees energy, and mainte­nance costs for, say, a three-year period. If the target costs are exceeded, the supplier pays a penalty; if the operating costs are lowered, the supplier and the customer share the bonus.

This page intentionally left blank


EXAMPLES

TABLE A. I SI Basic Units

Term Name Symbol

Length

Meter

M

Mass

Kilogram

Kg

Time

Second

S

Electric current

Ampere

A

Temperature

Kelvin

К

Luminous intensity

Candela

Cd

Amount of substance

Mole

Mol

EXAMPLES

Magnitude

Term

Symbol

K)-u

Pi CO

P

10-9

Nano

N

10-6

Micro

(j, m

KVi

Milli

M

11)2

Cenri

C

10-‘

Deci

D

I

10

Deca

Da

II)2

Hecto

H

101

Kilo

K

10"

Mega

M

10"

G’ga

G

1012

Tera

T

10!S

Peta

P

10!B

Exa

E

SUPPLEMENTARY AND DERIVED SI UNITS

TABLE A.3 Heat

Quantity

Name

Symbol

Dimension

Heat, work, or energy

Joule

J

N m

Heat flow rate, power

Wart

W

I s~’

Temperature

Kelvin

K

K

(thermodynamic unit)

Temperature

Celsius

E

°C

(customary unit)

Heat flow rare

4-

W nr2

Thermal transmittance

Transmittance

V

Wrrr2K-‘

Coefficient

Thermal conductivity

A

W in“1 K-‘

TABLE A.4 Force and Pressure

Quantity Name

Symbol

Dimension

Force newton

N

Kg m s‘2

Pressure, stress pascal

Pa

N m‘2

Quantity

подпись: quantityName Symbol Dimension

1 O’“4 rrr S"1

10-1 N s nr2

подпись: 1 o'“4 rrr s"1
10-1 n s nr2
Kinematic viscosity stokes St

Dynamic viscosity poise P

TABLE A.6 Mass and Density Quantity Name Symbol Dimension

Mass kilogram M kg

Density—————- p kg m ’

Note: I metric ton = 10-’ k

UNIT CONVERSION FACTORS ■■I TABLE A.7 Electrical

Quantity

Name

Symbol

Dimension

Potential

Volt

V

W A-1

Resistance

Ohm

A

V A‘1

Magnetomotive force ampere

A

A

Charge

Coulomb

C

A s

Capacitance

Farad

F

A s V‘1

Inductance

Henry

H

V s A-‘

Frequency

Hertz

Hz

S*1

TABLE A.8

Light

Quantity

Name Symbol

Dimensions

Luminous flux

. lumen lm

Cd sr

Illuminance

Lux lx

Lm m-2

TABLE A.9 Length (L)

Km

M mm

Mile

Foot

Inch ftm

Km 1

103 10S

6.214 X 10"1

3.281 X 103

— ————

M 10"5

1 103

6.214

X 10^4

3.281

3.937×10 10s

Mm 10-1,

10~3 1

——

3.281 x 10~3

3.937x 10-2 103

Mile 1.609

1.609 X 105 ————

1

5.28 X 103

— ————

Foot 3.048 x 10-4 .3.048 x 10"1 3.048 x 102 ——————-

1

1.2X10 —————-

Inch———-

2.54 xlO"2 2.54 x 10 ———————

1 2.54 X 104

Jim ——

Io-fi U)"3

1

M1

Ft2

In2

M2 1

1.076 x 10

1.55 x 1<P

Ft2 9.29×10-

1

1.44 x 1C)2

APPENDIX

подпись: appendix

TABLE A. 11 Volume (V = L3)

M3

L

Ft3

Gallon

M3

1

To’

3.531 x 10

2.200 x 102

L

10-*

1

3.53 1 x 10“2

2.200 x 10-’

It *

2,832 x 10~2

2.832 x 10

1

6.229

Gallon

4.546 x 10~3

4.546

1.605 x 10-‘

1

Note: The U. S. gallon is 3.78.5 x 10 ‘ m3. TABLE A. 12 Mass (m)

H

G

Lb

Grains

Kg

I

10

2.205

K

UH

1

——

1.543 x 10

Lb

4.536 x 10-‘

4..536 x 102

1

7.0 x 103

TABLE A. 13 Mass per Unit Length (m L~’)

Kg nrr1

Lb ft-1

Kg nr’

1

6.720 x 10-‘

Lb fr]

1.488

1

TABLE A. 14

Mass per Unit Area (m L~2)

Kg nrr2

Lb ft-2

Kg nr2

1

2.048 x 10-‘

Lb fr2

4.882

1

TABLE A. IS

Force (N =

Kg m s-2)

N (kg m sp

-J) kN

Ibf

N 1

Io-3

2.248 x 10-‘

KN 103

1

2.248 x 102

Lb f 4.448

4.448x 10-* 1

Note: 1 kg f

= 9.807 N =

2.205 Lb F.

■■ TABLE A. 16 Power (W = J r1)

W (J s_l) Horsepower

W 1 1.341 x 10-’

Horsepower 7.4.57xl02 1

TABLE A. 17 Quantity of Heat (W)

M]

KWh

Btu

Mj

1

2.778 x 10-‘

9.478 x

102

KWh

3,6

1

3.412 x

U>5

Btu

1.055 x IO—1

——

1

Note: 1 Kcal = 4.187KJ = 3.968 Btu and 1000 Kcal = 1 Thermic.

TABLE A. 18 Specific Heat (c)

Kj kg-1 Btu lb-‘ “F-1

Kj kg-‘

1 2.388 x 10-’

Btu lb“1 °F

4.187 1

TABLE A. 19 Heat Flow Rate ($)

W

Btu h-1

Refrigeration (Ton)

W

1

3.412

2.843 x 10^

Btu h_l

2.9.31 X 101

1

8.333 x 10-’

Refrigeration

(Ton)

3.517×10’

1.200 X 104

1

Note: 1 Kcal Lr1 = 1.163 W = 3.96 Btu h~’.

TABLE A.20 Heat Emission or Gain

W m-J Btu Ft~2 H-‘

W nr2 1 3.170 x 10-1

Btufr2H-1 3.155 1

■■ TABLE A.2I

Heat Transfer Coefficient, U

W m-2 K-‘ Btu ft-2 h-‘ °F-‘

W m-’ K-1 Btu fr2 h-‘ °F-‘

1 1.761 X 10-‘ 5.678 1

■■ TABLE A.22

Heat Flow per Unit Volume

W m 3 Btu ft-3 h-‘

W (n ‘

Btu ft-‘ hr1

1 9.662 x IQ-2 1.035 x 10 1

■■ TABLE A.23

Heat Flow per Unit Length

W

M 1 kW m“1 Btu ft“1 h"1

Wm-1 1 UH 1.040 kWm-1 10’ 1 1.040 x10′ Btu fr1 h"1 9.615 x 10-‘ 9.615 x 10-4 1

■■ TABLE A.24

Thermal Conductivity (a)

W m-‘ K-‘ Btu in ft-2 h-‘ “F-1

W m-1 K-‘

Btu in ft"2 H~’ 0F"

I 6.933 1 1.442x 10-‘ 1

■■1 TABLE A.25

Mass Calorific Value, Latent Heat

Kj kg-1 Btu lb-‘

Kj kg ‘ Btu lb*1

1 4.29.9×10-‘ 2.326 1

■■ TABLE A.26

Volume Calorific Value

MJ m"3 Btu ft-3

TABLE A.27 Pressure (p)

KN trr2 (kPa)

MN m-2 (MPa)

B (bar)

Lbf in*2

Atm

Ft Head

KN nr2

1

1 ()-;i

10~2

1.450 x 10~l

9.869 x 10

3.346 x KH

(kPa)

MN M ’

10’’

1

10

1.450 x 102

9.869

3.346 x I 1

(MPa)

B (bar)

10

Io-1

J

1.450 x 10

9.869 x 10-‘

3.346 x 10

Lbf in—’

6.895

6.895 x 10—1

6.895 x 1(H

1

6.805 x 10~2

2.307

Atm

1.013 x 102

1.013 xlO"1

1.013

1.470 x 10

1

3.390 x 10

Ft head

2.989

2.989 x IO“3

2.989 x lO“2

4.3.35 x 10-‘

2.950 x IO-2

1

Note: 1 kg f/cm2 = 98.07 kN/m2 (kPa) = 14.22 Ibf/m’.

TABLE A.28 Pressure (p)

N m-2 (Pa) mb

In Hg

In H20

N m-2 (Pa) mb in Hg in H20

1 Io-2 102 1 3.386 xlO3 .3.386 x 10 2.491 xlO2 2.491

2.953 X IO"4

2.953 X IO 2 1

7.356 x 10-2

4.15 X IO"3

4.15 X 10*1 1.360 x 10

1

TABLE A.29 Density (p)

Kg rrr3 (g L’1) kg L_l

Lb ft’3

Lb gal-1

Kg nr’

Kg L_1 Lb fr’ lb gal-1

1 10-3 103 1 1.602 x 10 1.602 xlO-2 9.978 x 10 9.978 xlO-2

6.243 X 10-2

6.243 X 10 1

6.229

1.2 X IO-2

1.2 X 10 1.605 x 10-‘ 1

TABLE A.30 Specific Volume

M3 kg (L g -•) L kg-1

Ft3 Lb“1

Gal lb"1

M3 kg _1 L kg-1 Ft 5 lb-1 Gal lb-i

1 IO3

Io-3 1

6.243 x IO“2 6.243 x 10 1.002 xlO“2 1.002 x 10

1.602 X 10

1.602 X IO-2 1

1.605 x 10-‘

9.978 X 10

9.978 X 10“2 6.229

1

G m‘3

Grain ft-3

Oz gal

G nr-’ grain fr3 Oz gal-1

1

2.229

6.236 x 10’

4.370 x 10-‘ 1

2.725 x 10’

1.604 x 10-4 3.670 x 10-4 1

TABLE A.32 Concentration, Mass per Unit Mass

Kgkg-‘

G^r1

Grain lb-1

Kg kg“1 G kgr1

Grain lb"’

1

Io-:}

1.429 x 10"4

10

1

1.429 x 10-‘

7000 x 10’ 7.0 1

TABLE A.33 Mass Fluid Flow (qm)

Ib h —

подпись: ib h-

Kg s-

подпись: kg s-Kgh-

Kgs-1 1 3.6×10’ 7.937 x 10’

Kg h‘1 2.778 x 10‘4 1 2.205

Ibh-1 1.260×10′-‘ 4.536 x 10-1 1

TABLE A.34 Volumetric Flow of Fluids (qv)

M3 s_l

M3 H“1

Ft3 min-1

L s-1

Lh-‘

Gal min-1

Gal H*1

M * s-1

1

3.6 x 10’

2.119 x 10’

10

3.6 x 10,;

1.320 x 104

7.919 x IO5

M* h ~1

2.778 x 10-4

1

5.886 x IQ-1

2.778 x 10-‘

10

3.666

2.20 x 102

Ft3 min-1

4.719 x IO‘4

1.699

I

4.719 x

Io-‘

1.699 x 10’

6.229

3.737 x 10j

L s-1

10‘ ’

3.6

2.119

1

3.6 x 10-’

1.320 x 10

7.919 x 10-

L h-1

2.778 x 10-7

10-’

5.886 x 10-4

2.778 x

1Q-4

1

3.666 x IO”

2.220 x J O‘1

GaJ min‘1

7.577 x :i0-J

2.728 x 10-‘

1.605 x IO‘4

7.577 x

Io-2

2.728 x 102

1

6.0 x 10

Gal h-‘

1.263 x 10-6

4.546 x 10-’

2.676 x 10—’

1.263 x

Io-’

4.546

1.667 x 10“2

1

Fts-

подпись: fts-TABLE A.35 Velocity (v)

Ft min"

Ms“1 1 3.21 1.968 xlO2

Ft s-‘ 3.048 x 10“’ 1 6.0×10

Ftinin-‘ 5.080 x 10—’ 1.667 X 10-2 1

TABLE A.36 Pressure Drop per Unit Length

Pa rrr1

Mm H20 m_l

In HjO ftr1

In HjO 100 Ftr1

Ibf in-21 OOfr1

Pa nr’

Mm H20 nr 1 In H20 fr1 In H20 100 fr1 Ibf iir2100 fr1

1

9.807

8.172 X 102

8.172

2.262 x 102

1.020 x 10-‘ 1

8.333 X 10

8.333 X 10‘1 2.307 x 10

1.224 x 10-‘ 1.200 x 10-2 1

Io-2

2.768 x 10-‘

1,224 x 10‘1 1.200 102 1

2.768 x 10

4.421 x 10 4.335 x 10"2

3.613

3.613 X 10-2 1

TABLE A.37 Absolute (Dynamic) Viscosity (/l)

P (poise) =

10"1 N s Rrr1

CP

(centipoise)

Ibf s Ftr2

Ibf h ftr2

P (poise)

1

102

2.089 x 10-’

5,802 x IO“7

CP

Io-2

1

2.089 x 10-5

5.802 x IO"9

Ibf s fr2

4.788 x 102

4.788 x 104

1

2.778 x 10-4

Ibf h fr2

1.724 x 10

1.724 x 10*

3.600 x 103

1

TABLE A.38

Kinematic Viscosity (v)

St (stokes) = 10-4 m2 s-1

CSt (centistokes)

Ft2 s-1

Ft2h-‘

St

1

102

1.076 x 10-J

3.875

CSt

Io-2

1

1.076 x 10-5

3.875 x 10—

Ft2 S"1

9.290 x 102

9.290 x 104

1

3.600 x 105

Ft2 h"1

2.581 x IO*1

2.581 x 10

2.778 x 10-4

1

GREEK ALPHABET, AND ABBREVIATIONS

TABLE A.39

Symbols

Term

Units

Symbol

A

Absolute radiant heat flow

Wnr2

% bs

Absolute static pressure

Pa

Psa

Absolute total pressure (stagnation pressure)

Pa

Pta

Acceleration

M s‘2

A

Acceleration due to gravity

M s-2

S

Air, gas, vapor, or

1 fluid flow rate

Mass flow volume flow

Kg s-<

M1 s

4m

Term

Units

Symbol

Air leakage factor

M1 S Ni

P

Air leakage rate

Tit S"’1

‘■1, i

Air temperature

°C

Air velocity

M s’

V a

Air velocity at time T

M s‘1

T’.

Allowable exposure time

H

AET

Angle (plane)

Radian (rad) or degree (°)

O’

Angle (solid)

Steradian (Sr)

Ft

Angular acceleration

Rad s-2

Angular velocity

Rad s-’

Ft)

Approach velocity

M S ’

Area

M2

(O

Area, actual (filter face)

M2

(Of

Area, duct cross section

M2

ADc<

Area (filter medium)

M2

AIm

Area (filter surface)

M2

Atmospheric pressure

Pa

Pa

B

Basal metabolic rate

W Ra­

BM

Blade (fan) tangential velocity

In s_l

U

Body heat storage

W in-2

S

Body height

M

H;>

Body mass

Kg

MH

Body surface area

M2

>n

Body surface area covered with

%

Anv

Clothing

Boundary layer insulation

Clo

Ia

Breadth

M

B

Bulge or sag of a duct or enclo­

M

S

Sure

C

Capacity (dust-holding)

Kg kg“1

Qh

Carbon dioxide production

L C02 h-«

CLv. ca.

Cartesian coordinates

——

X, y, z

Celsius temperature

°C

0

Chilling temperature

°c

0*

Coefficient of cuhical

K“1

/3

Expansion

SYMBOLS, GREEK ALPHABET, AND ABBREVIATIONS TABLE A.39 (continued)

Term

Units

Symbol

Counting rate

S-‘

N

Clothing insulation

M2 °C W-1

Clo

Clothing mass variation

Kg

A MAn

Clothing surface temperature

°C

T»clo

Coefficient of thermal conductivity

W m 1 °C

A

Component of air velocity along the X axis

M s~’

V*

Component of air velocity along the >’ Axis

M s‘1

L

Component of air velocity along the Z axis

M s^1

V,

Compressibility factor of a gas

——

Z

Conductive heat exchange

Witt2

V Com)

Convective heat exchange

Wnr2

V ronv

Convective heat exchange (±) From globe thermometer to

Wnr2

Air

Convective heat transfer coefficient

Witt2 Kt1

H.

Core temperature

°C

Ec

Cross section area

M2

D

Darcy friction factor

——

A

Deflection

M

8

Density

Kg m-3

P

Dew point temperature

°C

Orf

Diameter ratio of a flow

——

P

Measuring device Diameter

Outer

——

D

Inner

——

D

Differential pressure

Pa

p

Distance to V m s-1 isovelocity

M

Line

Draft rating

%

DR

Drop of air jet from its leaving

M

Hv

Center line

Dry heat loss

Wnr2

V Dry

Dryness fraction, steam

%

X

Duration, limited exposure

H

Term

Units

Symbol

Dynamic pressure

Pa

Pj

Dynamic viscosity

N s m-2

E

Effective area of a device

M2

Effective clothing insulation

M2 ° C W“1

Effective length

M

/

Effective mechanical power

Wm-2

W

Effective radiant heat flow

Wm-2

V r eff

Effective radiating area of a

Body

M2

Ar

Efficiency

——

V

Efficiency average

——

Vav

Emissivity of a surface or sensor

——

Es

Emissivity of black globe

——

Energy

J

E

Energy loss per unit mass

J kg"’

Ay

Enthalpy per Unir Mass

J kg"’

H

Entropy per unit mass

J kg“’ K-i

S

Equivalent diameter of a rectangular duct

M

De

Evaporative heat transfer coefficient

W nr2 Pa -‘

He

Exposed area

M2

F

Face loading (filter)

Kg m2

——

Fan air power

W

P,

Fan or pump efficiency

——

Vr

Fan equivalent orifice

M2

Ofe

Fan or pump head

M, Pa

H

Fan or pump impeller power

W

P<,

Fan or pump work per unit mass

J kg"1

Y

Fan pressure

Pa

Pf

Fan or pump shaft power

W

Ps

Flow coefficient of leakage

M3 (s Pa")’1

C.

Flow coefficient of subsonic flow in an orifice

——

A

Flow mass

M 5 s*1

Qm

Flow volumetric

M 3 s_1

TABLE A.39 (continued)

Term

Units

Symbol

Fluid density upstream of a

Kg nr3

Pu

Measuring device

Force

N

Ґ

Frequency

S’1

F

G

Globe temperature

°C

%

Gross body mass loss

Kg

Am

H

Heat capacity

JK->

C

Fleat flux

W

<b

Heat flux density

Wnr2

<p

Height

M

H

Height above datum

M

Z

Height of V m s’ isovelocity line

M

By

Humidity ratio

Kg water kg"1 dry air

Wa

Humidity ratio at saturation

Kg water kg-1 dry air

Humidity ratio expired air

Kg water kg-* dry air

W0S

Humidity ratio inhaled air

Kg water kg 1 dry air

Hydraulic diameter

Rn

Dh

1

Impeller tip diameter of a fan

M

D

Impeller tip radius of a fan

M

R

Increase in body core

°C

A0M

Temperature

Internal diameter of a pipe

M

D

Or duct

Insulation of clothing

M2 K W“1

Frf

Internal energy per unit mass

J kg“!

U

Isentropic exponent

——

K

J

Jet angle

0

Jet drop

M

HD

Jet rise

M

Hr

Jet spread

0

P

Jet temperature

°C

Jet throw

M

L,

Term

Units

Symbol

K

Kinematic viscosity

M2 s 1

F

Kinetic energy (mass)

J kg”1

EK

L

Latent heat (mass)

J kg’1

I

Length

M

L

Lewis relationship

°C kPa‘1

LR

Limit value for body heat gam

W h m 2

Qlirn

Or ioss

Local skin temperature

°C

O*

M

Mach number

——

Ma

Mass

Kg

M

Mass of dry air

Kg

MDa

Mass flow rate (gas or fluid)

Kg s-‘

Mass of water vapor

Kg

Maximum body heat storage

W h nr-

Qmvix

Maximum evaporative heat transfer from skin

WnT2

E

Max

Mean penetration (filter)

——

P,„

Mean pressure drop

Pa

H’n,

Mean skin temperature

°C

Mean velocity of flow in a conduit

M s"1

Metabolic rate

Wnr2

M (met!

Molar mass

Kg moH

MM

Momentum

Kg m s‘1

P

Motor input power

W

Pf.

Motor output fan efficiency

——

Vm

Motor power output

W

Pm

N

Natural wet bulb temperature

°C

®wb

Nominal volume air flow

L

/I n’JIIl

O

Operative temperature

°C

Flop

Overall fan efficiency

——

%

TABLE A.39 (continued)

Term

Units

Symbol

Overall hear transfer coefficient Overlap length (ductwork)

W nr2 K-1 Rn

U

K

P

Partial pressure

Pa

Pv

Particle production rate

S-1

Qi>

Particle size

|j. m

Dp

Percentage dissatisfied

%

PD

Periodic rime

S

T

Permeability index for clothing

——

Jcl„

Layer

Plane angle

Rad or 0

A, Я, 7

Plane radiant temperature

K

T,.

Polytropic coefficient

——

N

Position of control setting

% or °

S

Power

W

P

Predicted mean vote

——

PMV

Predicted percentage dissatisfied

%

PPD

Pressure difference between

Pa

AP,.

Points

psetc.

Pressure loss coefficient

——

Pressure total

Pa

Pt

Primary’ air flow rate

M3 s_l or 1 s“1 or kg s*1

*?vp nip

Q

Quantity of hear

J

E

R

Radiation heat transfer coefficient

W nr 2 K-4

Br

Radiation temperature asymmetry

°c:

Radiative heat exchange

Wnr2

Radiative heat exchange between globe thermometer and surroundings

W m-2

VG

Radiative heat transfer coefficient Radius

W irr2K

Br

Inner

M

R

Outer

M

R

Term

Units

Symbol

Radius of curvature

M

Rm

Ratio of specific heat

——

Y

Capacities

Relative fluid velocity to an

M sr‘1

Tv

Impeller

Relative humidity

<P

Reverberation time

S

I

Rotational speed

R1

N

S

Saturation pressure of a vapor

KPa

Pv, i

Saturated water vapor pressure at skin temperature

KPa

Pa,

Saturated water vapor pressure at wet bulb temperature

KPa

Pas. w

Secondary air flow rate

Mass flow

Kg S-‘

<7«.

Volume flow

In1 s“1 Or 1 S"1

Shatt fan power efficiency

Va

Solid angle

Sr

(I

Sound power level

DB

Lu,

Sound pressure level

DB

Lp

Specific heat capacity

J kg-’ K"’

C

Specific heat capacity at constant pressure

Jkg-lK-i

CP

Specific heat capacity at constant volume

J kg"1 K-’

Spread of a jet

M

K

Stagnation pressure

Pa

Pu

Static gauge pressure

Pa

PS

Stefan-Boltzmann constant

Wnr2 K-4

(J

STPD reduction factor

——

Ґ

Surface area

Rn2

A,

Surface heat transfer coefficient

W rrr2 K-1

H

Surface temperature

°C

Es

Surface tension

N m-2

A

T

Tangential component relating to a

Ms1

Cu

Fan, or pump impeller, or fluid

Temperature difference

K or °C*

AT or A 0*

Thermal diffusivity

M 2 S-1

A

TABLE A.39 (continued)

Term

Units

Symbol

Thermodynamic (absolute)

K*

T*

Temperature

Thickness

M

T or D

Thickness of dynamic boundary

M

8

Layer

Thickness of thermal boundary

Laver

M

8T

Throw of a jet

M

L>

Time

S

T

Time constant, exponential

S

R

Change

Tip Reynolds number of a fan

——

Impeller

Tip speed of a fan impeller

M s-1

U

Torque

N m

T

Total gas or air flow rate

Mass flow

Kg s"1

?mr

Volume flow

M1 s-1; L s"1

?vr

Total gauge pressure

Pa

Pt

Total heat transfer coefficient

W rrr2 0C-‘

H

Turbulence intensity

%

T

1 u

U

Universal gas constant

I Kg“1 K-i

R

V

Velocity

M s“1

V

Velocity components in the X. y,

M s“1

U, V, w

Z directions

Velocity of sound

M s‘1

C

Volume

M3

V

Volume flow rare

In’ s_1 or L s_l

<1V

W

Water vapor latent heat of

Win"2

‘Pi.

Vaporization

Water vapor partial pressure

KPa

P„

Water vapor pressure at skin

KPa

Pa

Temperature

Wave length

M

A

Weight

N

G

Weighted sound pressure level

DB A

L PA

DBB

DB C

LrC

Term

Units

Symbol

Wet bulb globe temperature

°C

Wetted duct perimeter

M

A’

Width

M

B

Wind chill index

W nr2

WCI

Work

.1

W

Y

Young’s modulus

Nm"2

E

*In normal work, "C is used in preference to the absolute temperature K. However, it is essential that K be used when working with the gas laws, radiation, and the coefficient of cubical expansion. The symbol for normal temperature is 0 followed by a suffix, while T always denotes absolute temperature.

APPENDIX

подпись: appendixTABLE A.40 The Greek Alphabet

Narne

Symbols

Alpha

A

A

Beta

B

/3

Gamma

R

Y

Delta

A

A

Epsiion

E

F

Zeta

7.

L

Eta

H

V

Thкta

0

E

Iota

I

L

Kappa

K

K

Lambda

A

A

Mu

M

P

Nu

N

Xi

X

X

Omicron

O

O

Pi

N

7T

Rho

P

P

Sigma

2

<T

Tau

T

T

Upsilon

Y

V

Phi

O

<f>

Chi

X

X

Psi

Џ

•P

Omйga

N

U)

TABLE A.41 Symbols for Operations

Symbol

Definition

K

Is identical to

*

Does not equal

= or «

Is approximately equal to

Is directly proportional to

Tends to

Is less than

>

Is greater than

S

Is less than or equal to

A

Is greater than or equal to

Ax

Finite increase in X

Sx

Variation in X

Dx

Total differential in X

Grad

Gradient

Div

Divergence

Curl

Curl

V2

Laplacian

1

Factorial

( )

Parentheses

Exp or Ex

Exponential of X

In a;

Logarithm to base E of X

Log,,) X

Logarithm to base 10 of X

[ J

Brackets

[1J

One-dimensional

[3]

Three-dimensional

V

Summation

TABLE A.42 Abbreviations

Meaning

Abbreviation

About

Ca.

Absolute

Abs

Alternating current

A. c.

Apparatus dew point

Adp

Atomic weight

At. wr.

Boiling point

B. p.

Boundary layer

B. l.

Centerline

C. l.

Compare

Cf.

Meaning

Abbreviation

Direct current

D. c.

Dry bulb temperature

D. b.t.

Electromotive force

Cmf

Equation

Fq.

For example

E. g.

High pressure

H. P.

Hydrogen ion concentration

PH

Fiquid (specified)

I, (followed by the appropriate chemical symbol)

Liquid oxygen

LOX

Liquefied petroleum gas

LPG

Melting point

M. p.

Molecular weight

Mol. wt.

Namely

Viz.

Note well

N. b.

Outside diameter

OD

Parts per million

Ppm

Per cent

%

Relative humidity

RH

Research and development

R & D

Specific

Sp.

That is

I. e.

Latin terms

In the place cited (reference to an earlier quote)

He. cit.

In the work cited (a further reference to a book

Op. cit.

Previously mentioned, but this time in a different

Passage)

In the same place (a reference to a topic covered in a

Ibid.

Preceding reference)

And another or and others

Et al.

(e. g., Burgess et al. rather than Burgess, Ellenbecker, and Treitman)

PHYSICAL CONSTANTS

Mean molecular weight of dry air Ma = 28.969 kg kmol~J Mean molecular weight of water Mv = 18.02 kg kmol-1 Density of dry air at 101.325 kPa and 0 °C = 1.293 kg m-3 Density of water at 4 °C = 1000 kg m~3 Density of water at 20 °C = 998.23 kg m-3

Barometric pressure at standard temperature and pressure = 101.325 kPa Standard temperature and pressure (STP) = 0 °C at 101.325 kPa (also known as normal temperature and pressure)

Universal gas constant Rgas = MR = 8.3143 J mol 1 K 1 Volume of 1 mol of the permanent gases (at 101.325 kPa and 0 °C) =22.4136 m3 Characteristic gas constant for dry air Ra = 287 J kg-1 K~J Characteristic gas constant for steam Rv = 462 J kg-1 K_1 Mean specific heat of air at constant pressure cpa = 1005 J kg-1 K-1 Mean specific heat of air at constant volume Cva = 718 j kg-1 K-1 Mean specific heat of steam of air at constant pressure cpv = 4210 J kg’1 K_l Mean specific heat of steam at constant volume cvv = 1810 J kg-1 K-1 Adiabatic index for air at room temperature and pressure =1.4 Latent heat of steam at 0 °C = 2500 kj kg-1 K-1 Standard gravity = 9.806 65 m s~2

Velocity of sound in air at normal temperature and pressure c = 331.46 m s"1 Stefan’s Constant A = 5.67 x 10~8 W nr2 K 4

DIMENSIONLESS NUMBERS

The following dimensionless numbers may be expressed in various forms due to the use of other relevant parameters.

Archimedes Number

Ar = = Buoyancy force

Fj pV2 Inertia force

The ratio A p/p can be replaced by AT/T. Ar relates the influence of ve­locity and temperature of a jet when discharged into an environment of a dif­ferent temperature. In some instances the Froude number, Galileo number, or Grashof number may replace the Archimedes number.

Colburn j-Factor

Re Pr0 33

подпись: re pr0 33Colburn j-factor = —^un,, = St ■ Pr0’66 Used in heat-transfer applications.

Colburn j-factor = g^-A-Sc0,66 ’ Re Se

(

‘0.33

2 . 3

P gX,

подпись: ( 
'0.33
2 . 3
p gx ,
Used in mass-transfer applications. Condensation Number

Co = B

Eu = = Pressure force

Py1 Inertia force

Froude number

GL Gravity force See Archimedes number.

Graetz number

F7 _ ЧтС XI

Same as Peclet number except ^ considered (entrance region).

Grashof number

П___ j8gp2/3A0 _ (Buoyancy forces)(Inertia force)

— ■■ ■……………. ■ 7

T)~ (Viscous forces)“

Used for free convection. Knudsen number

Kn = ^ = Molecular mean free path

0. 5D Characteristic length

Used for particulate movement in a gas.

Lewis number

Le = — = —

Pr D

Where

K = = Thermal diffusivity Cp Mass diffusivity

Used for calculations involving the vaporization of a fluid.

Mach number

Ma = EtlLi = Y. nr JL. = Inertia force

Kl2 K [K Compressibility force

P 4p

Nusselt number

Nu = -&L = —

АЛ0 A

Ratio of temperature gradients, used for heat transfer taking place with fluid flow.

Peclet number

P _ VlCpP _ R p Heat convection A Heat conduction

Pe = Hi = Mass transfer D Mass diffusivity

Used in mass transfer applications involving aerosols.

Prandtl number

Pr = Ј22 = E = Molecular diffusivity of momentum A K Molecular diffusivity of heat

Used for heat transfer with fluid flow.

Reynolds number

Re = = — = Lnert’a f°rce

R v Viscous force

Relates the nature of the fluid flow in and around bodies. Richardson Number

( 80 Dz

Buoyancy

Momentum gradient

Dv

/ aj

Dz

+ G

~g Ri = —

Dv

T1

Schmidt number

EXAMPLES EXAMPLES
EXAMPLES

Sc = — = Momentum diffusivity D Mass diffusivity

Used for mass transfer = Pr number for mass transfer = Colburn number. Sherwood number

Sh = j3 _ §1 — (Mass transfer coefficient ) ( Length )

D D Diffusion coefficient

I

This is the Nusselt number for mass transfer.

Stanton number

St = Nu _ 4> _ H _ Wall heat-transfer rate

Re • Pr VpcAO V pc Heat transfer by convection

Used for convective heat transfer applications.

Stokes number

Stk = V^f Stopping distance 18 T]L Characteristic length

Where Cf = Cunningham’s factor. Used for particulate settling calcula­tions.

Posted in INDUSTRIAL VENTILATION DESIGN GUIDEBOOK