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8 STEPS - CONTROL OF HEATING SYSTEMS
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
161
TECHNICAL DATA, FORMULAS AND CHARTS
Diagram for local district heating plants and heating and power plant . . . . . . . . . . . . . . .162
Diagram for heating and domestic hot and cold water . . . . . . . . . . . . . . . . . . . . . . . . . . .163
Heat emission from radiators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .164
Conversion chart for radiators in one-pipe systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165
Reduction of heat emission from radiators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .166
Heat losses from uninsulated pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .167
Pressure drops in steel pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .168
Resistance in heating systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169
Sizes of steel pipes for heating systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169
Flow chart for thermostatic radiator valves in one-pipe system . . . . . . . . . . . . . . . . . . . . .170
Flow chart for thermostatic radiator valves in two pipe system . . . . . . . . . . . . . . . . . . . . .171
Flow chart for ∆p control valves for risers or circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .172
Flow chart for control valves in heating systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .173
Flow chart for control valves in district heating systems . . . . . . . . . . . . . . . . . . . . . . . . . . .174
Flow chart for ∆p control valves in district heating systems . . . . . . . . . . . . . . . . . . . . . . . .175
Heat requirements for domestic hot water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .177
Flow limiters for one-pipe circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .178
Calculation of one-pipe systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .180
Calculation of two-pipe systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .182
SI-units, Greek alphabet, Physical properties for water . . . . . . . . . . . . . . . . . . . . . . . . . . . .184
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
162 8 STEPS - CONTROL OF HEATING SYSTEMS
130 °C
70 °C
130 °C
130 °C
70 °C
70 °C
130 °C
130 °C
70 °C
70 °C
130 °C
130 °C
70 °C
70 °C
Diagram for local district heating plants connected to a heating and power plant.
Heating and
power plant
Local heating plant
Flue gas
cooler
Safety
valve
Exp. tank
Boiler
Safety
valve
Heat exchanger
Accumulator
Heat meter
Flue gas
cooler
Safety
valve
Exp. tank
Boiler
Safety
valve
Heat exchanger
Accumulator
Heat meter
Flue gas
cooler
Safety
valve
Exp. tankBoiler
Safety
valve
Heat exchanger
Accumulator
Heat meter
8 STEPS - CONTROL OF HEATING SYSTEMS
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
163
<6 >6
120-70 °C
90 °C
65 °C
Diagram for heating and domestic hot and cold water.
Expansion tank
∆p - control
Flow meter
Domestic hot water
Domestic cold water
Flowmeter> 6 storeys
Heat meter
Domestic hot water 60
Domestic cold water
Circulation
Control valve< 6 storeys
Storeys
40 30 25 20 16
0
1,0
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
1,1
1,2
0 1,0 2,0 Q
90
60
70
80
50
0,5 1,5 2,5
1
2
4
5
6
3
164 8 STEPS - CONTROL OF HEATING SYSTEMS
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
Heat emission from radiators.
Two-pipe system with thermostatic
valves.
Measured 1 : tflow 75 oC, ∆t 8 oC
Heat requirement : 0,83, Q = 2,47
tflow 80 oC : 2 ∆t 16 oC, Q = 1,23
Every point along the horizontal line
0,83 gives the same heat emission.
The influence of gravity forces on heat emission from a radiator in a two-
pipe system
For a correctly sized radiator 3 ( with manual radiator valve in a two-pipe
system ) the heat emission will increases only by 5% when the flow
increases by 23%, 4 , depending on gravity forces. The temperature drop
across the radiator however will decrease by 5oC and that is significant,
because it reduces the capacity of the whole system all the way down to
the heating and power plant.
Resuls ∆t for one- and two - pipe circuits, and required pump capacity
when thermostatic valves utilize internal and external heat gains.
Two-pipe circuit One-pipe circuit
Point Heat Flow ∆t Circuit resi- Pump ca- Flow ∆t Pump ca-
gain % % oC stance % pacity % % oC pacity %
3 0 100 25 100 100 100 25 100
5 10 66 33 44 29 100 22,5 100
6 20 47 39 22 10 100 20 100
n = 1,3 troom = 20 oC tflow = 90 oC ∆t = 25 oC
∆t oC
Heat
emission
Q
12
10
8
6
5
4
165
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
8 STEPS - CONTROL OF HEATING SYSTEMS
0,8
0,9
1,0
1,1
1,2
1,3
1,4
1,5
1,6
1,7
1,8
1,9
2,0
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
90
85
80
75
70
60 65
2
1
Conversion chart for radiators in one-pipe circuits.
Conversion chart for panel and section radiators in one-pipe circuits.
Enter the current tflow and temperature drop and find the conver-
sion factor, Fc.
Multiply the heat requirement by Fc and select size of the radiator
according to the new value.
Example.
Calculated heat requirement: 1.230 W.
tflow : 82 oC, ∆t: 15 oC, 1
Fc = 1,16 2
Converted heat requirement: 1.230 x 1,16 = 1.427 W.
Formula for calculating Fc:
49,33 x ln
t1 - t2[ ]
t1 - tr n
t2 - tr
( ) n
Panel radiator 1,28
Section radiator 1,29
Convector 1,3 - 1,33
F =
tflow
oC
Fc
∆t oC
166 8 STEPS - CONTROL OF HEATING SYSTEMS
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
a
The control unit has to sense the room temperature to be able to control it.
No enclosure
0%
Shelf with
opening
0%
Shelf close to
the wall
10 -2%
Open fronted
recess with a
shelf
12 -6%
Encased with
grille in front
> -15%
Encased with
small grille in
front. Not
recommended.
> -30%
Acceptable
cabinet.
≈ -8 - 10%
Reduction of heat emission from radiators fixed in some type of enclosure
Radiation from a radiator depending on the treatment of the
surface.
Material Surface treatment Radiation %
Steel, cast iron 100
Oil paint 100
Aluminium or
copper bronzes 75
Zinc white 101
Lead white 99
Enamelled White 101
Matt green 96
Aluminium 8
10 - 100 mm 30 - 100 mm
Alternative
openings a+40
>100mm
167
0
100
200
300
400
0
20 40 60 80 100 120
80/89 65/76
50/6
40
32
25
20
10
15
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
8 STEPS - CONTROL OF HEATING SYSTEMS
Heat losses from uninsulated horizontal pipe.
For vertical pipe reduce by 20%
One-pipe above another reduce by 12%
Three pipes above each other reduce by 20%
Temperature above room temperature oC
Heat emission
W/m pipe DN/0
168 8 STEPS - CONTROL OF HEATING SYSTEMS
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
5 7 10 20 30 mmWG/m
,05 ,07 0,1 0,2 0,3 0,4 0,5
kPa/m
25
15
20
32
40
80
50
100
125
150
,01
,015
,02
,03
,04
,05
,07
,1
,15
,2
,3
,5
,4
,7
1
1,5
2
3
4
5
7
10
40
50
15
20
30
1,0
2,0
10
100
1000
10
100
1,5
2
3
4
5
7
15
20
30
40
50
70
150
200
150
200
300
400
500
700
70
50
40
15 40 50
0,15
65
3,0
m/s 0,2
0,3
0,4
0,5
k = 0,00003 m
Density = 1.000 kg/m3
Pressure drop in steel pipes for heating installations.
m3/h DN mm l/s
l/h
0,1
0,2
0,3
0,5
1,0
2
3
,01 ,02,03 ,05 0,1 ,2 ,3 ,5 1
1
2
6
4
3
2 3 4 5 107
169
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
8 STEPS - CONTROL OF HEATING SYSTEMS
∆p for ζ values at differnt rates.
Symbol Units Coefficient of resistance, ζ
Branch tee 1
Through tee 1
Elbow, smooth 0,2
Bend 1
The values for the coefficient of resis-
tance for tees, elbows and bends.
The pressure drop is calculated from:
∆p = ζ 0,5 ρ ν2 ,
Recommended portion of pipe losses for different systems or part of
systems.
Type of system Unit Friction %
Heating Small buildings 50 - 60
Large buildings 60 - 70
Sub-stations Primary and secondary side 20 - 30
Distribution pipe net work Primary side 80 - 90
ζ valuem/s
∆p kPa
Sizes of steel pipes for heating systems. Working pressure 1,0 MPa (10 bar)
Nominal diameter External diameter Wall thickness Internal diameter
mm inch mm mm mm
8 1/4 13,50 2,25 9
10 3/8 17,00 2,25 12,5
15 1/2 21,25 2,75 15,75
20 3/4 26,75 2,75 21,25
25 1 33,50 3,25 27,00
32 1 1/4 42,25 3,25 35,75
40 1 1/2 48,00 3,50 41,00
50 2 60,00 3,50 53,00
65 2 1/2 75,50 3,75 68,00
80 3 88,50 4,00 80,50
100 4 114,00 4,00 106,00
125 5 140,00 4,50 131,00
150 6 165,00 4,50 156,00
30
50
70
100
200
300
500
700
1000
0,1 ,2 ,3 ,4 ,5 ,7 1,0 2 3 kPa
0,01 ,02 ,03 ,07 ,1 ,2 ,3 mWG
,001 ,002 ,004,006 0,01 ,02 ,03 Bar
,01
,02
,03
,05
,07
,1
,2
,3
,05
4 5 7 10 20
,7 1 2
,04 ,06 0,1 ,2
,5
15
2025
170 8 STEPS - CONTROL OF HEATING SYSTEMS
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
Flow chart for RTD-G 15, 20 and 25
RTD - G 15, 20 and 25
l/h l/sValve size
∆pvalve
171
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
8 STEPS - CONTROL OF HEATING SYSTEMS
3
5
7
10
20
30
50
70
100
,001
,002
,003
,005
,007
,01
,02
,03
1 2 3 4 5 7 10 20 30 kPa
0,1 0,2 ,3 ,4 ,5 ,7 1 2 3 mWG
0,01 ,02 ,04 ,06 0,1 ,2 ,3 Bar
,1
,05
,07
500
300
200
N
1
2
3
4
5
67
3
5
7
10
20
30
50
70
100
,001
,002
,003
,005
,007
,01
,02
,03
1 2 3 4 5 7 10 20 30 kPa
0,1 0,2 ,3 ,4 ,5 ,7 1 2 3 mWG
0,01 ,02 ,04 ,06 0,1 ,2 ,3 Bar
,1
,05
,07
500
300
200
N
1
23
45
6
7
Flow chart for thermostatic valves in two-pipe system
l/h
l/sPre-set value
∆pvalve
Pre-set value 1 2 3 4 5 6 7 N
kv values 0,04 0,08 0,12 0,20 0,27 0,36 0,45 0,60
Pre-set value 1 2 3 4 5 6 7 N
kv values 0,10 0,15 0,17 0,25 0,32 0,41 0,62 0,83
l/h
l/sPre-set value
∆pvalve
RTD - N 15
RTD - N 20 - 25
172 8 STEPS - CONTROL OF HEATING SYSTEMS
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
0,1
0,2
0,3
0,5
0,7
1,0
2
3
5
7
10
0,1
0,2
0,3
0,5
0,7
1,0
2
3
,03
,05
,07
1 2 3 4 5 7 10 20 30 40 60 80 kPa
0,1 0,2 ,3 ,4 ,5 ,7 1 2 3 4 5 7 mWG
0,01 ,02 ,04 ,06 0,1 ,2 ,3 ,4 ,5 ,7 Bar
520
8
,8
1,6
2,5
4,0
6,3
10
1
Flow chart for ∆p control valves for riser or circuit in heating systems.
ASV-P, PV 15-40 and ASV-M 15-40
m3/h l/skvs-value
∆pvalve
Working range:
ASV-P 10 kPa
ASV-PV 5 - 25 kPa.
Minimum available ∆p for good functioning: 8 kPa.
Example
Q: 300 l/h. ∆p riser: 7kPa. ∆p radiator including valve: 5 kPa.
∆p-control kv 1,6. ∆pvp = 3,4 kPa, 1
Necessary ∆p = 7+5+8 = 20 kPa.
173
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
8 STEPS - CONTROL OF HEATING SYSTEMS
0,1
0,2
0,3
0,5
0,7
1,0
2
3
5
7
10
0,1
0,2
0,3
0,5
0,7
1,0
2
3
,03
,05
,07
1 2 3 4 5 7 10 20 30 40 60 100 200 kPa
0,1 0,2 ,3 ,4 ,5 ,7 1 2 3 4 5 7 10 15 20 mWG
0,01 ,02 ,04 ,06 0,1 ,2 ,3 ,4 ,5 ,7 1,0 1,5 2 Bar
10
5
7
150
50
30
20
100
200
20
30
50
,4
,63
1,0
1,6
2,5
4,0
6,3
10
16
25
40
63
100145
Flow chart for control valves in heating systems.
m3/h l/skvs-value
∆pvalve
Formulas.
∆p : bar. Q: m3/h. kv = ; ∆p = ; Q = kv √ ∆p ;
Q
√∆p
Q
kv
( )
2
∆p : kPa. Q: l/h. kv = 0,01 ; ∆p = 0,01 ; Q = 100x kv √ ∆p ;
Q
√∆p
Q
kv
( )
2
∆p : kPa. Q: l/s. kv = 36 ; ∆p = 36 ; Q = √ ∆p ;
Q
√∆p
Q
kv
( )
2 kv
36
Q
Q
Q
174 8 STEPS - CONTROL OF HEATING SYSTEMS
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
0,1
0,2
0,3
0,5
0,7
1,0
2
3
5
7
10
0,1
0,2
0,3
0,5
0,7
1,0
2
3
,03
,05
,07
1 2 3 4 5 7 10 20 30 40 60 100 200 kPa
0,1 0,2 ,3 ,4 ,5 ,7 1 2 3 4 5 7 10 15 20 mWG
0,01 ,02 ,04 ,06 0,1 ,2 ,3 ,4 ,5 ,7 1,0 1,5 2 Bar
10
5
7
150
50
30
20
100
200
20
30
50
,4
,63
1,0
1,6
2,5
4,0
6,3
10
16
25
40
63
100145
Flow chart for valves in district heating systems.
m3/h l/skvs-value
∆pvalve
175
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
8 STEPS - CONTROL OF HEATING SYSTEMS
0,1
0,2
0,3
0,5
0,7
1,0
2
3
5
7
10
0,1
0,2
0,3
0,5
0,7
1,0
2
3
,03
,05
,07
1 2 3 4 5 7 10 20 30 40 60 80 kPa
0,1 0,2 ,3 ,4 ,5 ,7 1 2 3 4 5 7 mWG
0,01 ,02 ,04 ,06 0,1 ,2 ,3 ,4 ,5 ,7 Bar
520
8
,8
1,6
2,5
4,0
6,3
10
1
m3/h l/skvs-value
∆pvalve
AVP 15 - 32
Flow chart for ∆p control valves in district heating systems.
176 8 STEPS - CONTROL OF HEATING SYSTEMS
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
0,1
0,2
0,3
0,5
0,7
1,0
2
3
5
7
10
0,1
0,2
0,3
0,5
0,7
1,0
2
3
,03
,05
,07
1 2 3 4 5 7 10 20 30 40 60 100 200 kPa
0,1 0,2 ,3 ,4 ,5 ,7 1 2 3 4 5 7 10 15 20 mWG
0,01 ,02 ,04 ,06 0,1 ,2 ,3 ,4 ,5 ,7 1,0 1,5 2 Bar
10
5
7
150
50
30
20
100
200
20
30
50
,63
1,0
1,6
2,5
4,0
6,3
10
16
25
50
80
125
20
Flow chart for ∆p control valves in district heating systems.
m3/h l/skvs-value
∆pvalve
IVD-IVFS kvs 0,63 - 25,0 m3/h
AFP kvs 50 - 125 m3/h
∆p-regulator, working range: IVD 5 - 50 and 20 - 250 kPa.
AFP 20 - 120 and 50 - 250 kPa
Maximum ∆p valve IVF kvs: 0,63 and 1,0 = 1.000 kPa
2,5 = 630 kPa
4,0 - 25 = 800 kPa
Maximum ∆p valve AFP: 1.200 kPa
177
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
8 STEPS - CONTROL OF HEATING SYSTEMS
0
0,5
1,0
1,5
2,0
2,5
0
50
100
150
200
250
300
350
400
1 10 50 100 150 200 250
Heat requirement for hot water according to the Swedish Board of District Heating
Domestic hot water, Q L/s. Effect, P kW
Number of apartments.
178 8 STEPS - CONTROL OF HEATING SYSTEMS
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
0,07
0,1
0,15
0,2
0,3
0,4
0,5
0,6
0,7
0,8
1,0
0,9
20 30 40 50 60 70 80
m /h
3
∆p kPav
0,2 0,3 0,4 0,5 0,6 0,7 0,8
∆
p Barv
1
2
3
4
5
8
6,5
0,2
0,3
0,4
0,5
0,7
2,0
1,5
1,0
0,9
0,8
0,6
20 30 40 50 60 70 80
m /h
3
∆p kPav
0,2 0,3 0,4 0,5 0,6 0,7 0,8
∆
p Barv
10
12
14
2
4
6
8
Flow limiter, ASV-Q 15, Flow limiter, ASV-Q 20
Set values
Set values
ASV-Q Capacity l/h Set value
15 100 - 800 1 - 8
20 200 - 1400 2 - 14
25 400 - 1600 4 - 16
32 500 - 2500 5 - 30
179
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
8 STEPS - CONTROL OF HEATING SYSTEMS
2,0
1,7
1,5
1,2
1,0
0,9
0,8
0,7
0,6
0,5
0,4
30 40 50 60 70 80
m /h
3
∆p kPav
0,3 0,4 0,5 0,6 0,7 0,8
∆
p Barv
10
12
14
16
4
6
8
4,0
3,0
2,0
1,5
1,2
1,0
0,9
0,8
0,7
0,6
0,5
0,4
m /h
3
30 40 50 60 70 80
∆p kPav
0,3 0,4 0,5 0,6 0,7 0,8
∆
p Barv
5
15
10
20
25
30
Flow limiter, ASV-Q 25, Flow limiter, ASV-Q 32
Set values
Set values
180 8 STEPS - CONTROL OF HEATING SYSTEMS
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
Calculation of one-pipe system
6
31 m
6 m6 m6 m6 m
1200
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1200
1200
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1200
1200
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1200
1200
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1200
6 m 6 m 6 m
1200
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1200
1200
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1200
1200
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1200
1200
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1200
3x12=36m
1,5 m
0
2345
2345
6
789
1
10
10 m
181
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
8 STEPS - CONTROL OF HEATING SYSTEMS
Calculation of one-pipe system
182 8 STEPS - CONTROL OF HEATING SYSTEMS
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
Calculation of two-pipe system
12001200 1200 120012001200 1200 1200
1200 12001200 12001200 12001200 1200
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
3 m 6 m 6 m 6 m
12345
6
7
8
9
10
11
12
13
14
15
16
17
3m3m
31 m
183
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
8 STEPS - CONTROL OF HEATING SYSTEMS
Calculation of two-pipe system
184 8 STEPS - CONTROL OF HEATING SYSTEMS
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
SI-units.
Effect, P. Pressure, p.
W kcal/h Pa kPa bar mWG
1 0,85985 1 0,001 0,00001 0,0001
1,163 1 1.000 1 0,01 0,1
100.000 100 1 10
10.000 10 0,1 1
Flow, Q (ϕ). Temperature, t (θ).
l/s m3/h Kelvin K Celsius oC
1 3,6 0 -273,15
0,278 1 273,15 ± 0
373,15 100
Greek alphabet.
Α α Β β Γ γ ∆ δ Ε ε Ζ ζ Η η Θ θ Ι τ
alfa beta gamma delta epsilon seta eta theta iota
Κ κ Λ λ Μ µ Ν ν Ξ ξ Ο ο Π π Ρ ρ Σ σ
kappa lamda my ny xi omikron pi ro sigma
Τ τ Υ υ ϑ ϕ Χ χ Ψ ψ Ω ω
tau ypsilon phi chi psi omega
Physical properties for water.
Temperature Pressure Density Isobaric heat
υ oC p kPa ρ kg/m3 capacitivity
cp J/ (kg x K)
0 - 999,84 4218
10 - 999,70 4192
20 - 998,205 4182
30 - 995,65 4178
40 - 992,2 4178
50 - 998,14 4181
60 - 983,21 4184
70 - 977,78 4190
80 - 971,80 4196
90 - 965,33 4205
100 1,3 958,35 4216
110 43,26 951,0 -
120 98,54 943,1 4245
130 170,11 934,8 -
140 261,36 926,1 4287
150 375,97 916,9 -
185
CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS
8 STEPS - CONTROL OF HEATING SYSTEMS

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Chapter8

  • 1. 8 STEPS - CONTROL OF HEATING SYSTEMS CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 161 TECHNICAL DATA, FORMULAS AND CHARTS Diagram for local district heating plants and heating and power plant . . . . . . . . . . . . . . .162 Diagram for heating and domestic hot and cold water . . . . . . . . . . . . . . . . . . . . . . . . . . .163 Heat emission from radiators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .164 Conversion chart for radiators in one-pipe systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165 Reduction of heat emission from radiators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .166 Heat losses from uninsulated pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .167 Pressure drops in steel pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .168 Resistance in heating systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169 Sizes of steel pipes for heating systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169 Flow chart for thermostatic radiator valves in one-pipe system . . . . . . . . . . . . . . . . . . . . .170 Flow chart for thermostatic radiator valves in two pipe system . . . . . . . . . . . . . . . . . . . . .171 Flow chart for ∆p control valves for risers or circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .172 Flow chart for control valves in heating systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .173 Flow chart for control valves in district heating systems . . . . . . . . . . . . . . . . . . . . . . . . . . .174 Flow chart for ∆p control valves in district heating systems . . . . . . . . . . . . . . . . . . . . . . . .175 Heat requirements for domestic hot water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .177 Flow limiters for one-pipe circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .178 Calculation of one-pipe systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .180 Calculation of two-pipe systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .182 SI-units, Greek alphabet, Physical properties for water . . . . . . . . . . . . . . . . . . . . . . . . . . . .184
  • 2. CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 162 8 STEPS - CONTROL OF HEATING SYSTEMS 130 °C 70 °C 130 °C 130 °C 70 °C 70 °C 130 °C 130 °C 70 °C 70 °C 130 °C 130 °C 70 °C 70 °C Diagram for local district heating plants connected to a heating and power plant. Heating and power plant Local heating plant Flue gas cooler Safety valve Exp. tank Boiler Safety valve Heat exchanger Accumulator Heat meter Flue gas cooler Safety valve Exp. tank Boiler Safety valve Heat exchanger Accumulator Heat meter Flue gas cooler Safety valve Exp. tankBoiler Safety valve Heat exchanger Accumulator Heat meter
  • 3. 8 STEPS - CONTROL OF HEATING SYSTEMS CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 163 <6 >6 120-70 °C 90 °C 65 °C Diagram for heating and domestic hot and cold water. Expansion tank ∆p - control Flow meter Domestic hot water Domestic cold water Flowmeter> 6 storeys Heat meter Domestic hot water 60 Domestic cold water Circulation Control valve< 6 storeys Storeys
  • 4. 40 30 25 20 16 0 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 1,1 1,2 0 1,0 2,0 Q 90 60 70 80 50 0,5 1,5 2,5 1 2 4 5 6 3 164 8 STEPS - CONTROL OF HEATING SYSTEMS CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS Heat emission from radiators. Two-pipe system with thermostatic valves. Measured 1 : tflow 75 oC, ∆t 8 oC Heat requirement : 0,83, Q = 2,47 tflow 80 oC : 2 ∆t 16 oC, Q = 1,23 Every point along the horizontal line 0,83 gives the same heat emission. The influence of gravity forces on heat emission from a radiator in a two- pipe system For a correctly sized radiator 3 ( with manual radiator valve in a two-pipe system ) the heat emission will increases only by 5% when the flow increases by 23%, 4 , depending on gravity forces. The temperature drop across the radiator however will decrease by 5oC and that is significant, because it reduces the capacity of the whole system all the way down to the heating and power plant. Resuls ∆t for one- and two - pipe circuits, and required pump capacity when thermostatic valves utilize internal and external heat gains. Two-pipe circuit One-pipe circuit Point Heat Flow ∆t Circuit resi- Pump ca- Flow ∆t Pump ca- gain % % oC stance % pacity % % oC pacity % 3 0 100 25 100 100 100 25 100 5 10 66 33 44 29 100 22,5 100 6 20 47 39 22 10 100 20 100 n = 1,3 troom = 20 oC tflow = 90 oC ∆t = 25 oC ∆t oC Heat emission Q 12 10 8 6 5 4
  • 5. 165 CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 8 STEPS - CONTROL OF HEATING SYSTEMS 0,8 0,9 1,0 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2,0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 90 85 80 75 70 60 65 2 1 Conversion chart for radiators in one-pipe circuits. Conversion chart for panel and section radiators in one-pipe circuits. Enter the current tflow and temperature drop and find the conver- sion factor, Fc. Multiply the heat requirement by Fc and select size of the radiator according to the new value. Example. Calculated heat requirement: 1.230 W. tflow : 82 oC, ∆t: 15 oC, 1 Fc = 1,16 2 Converted heat requirement: 1.230 x 1,16 = 1.427 W. Formula for calculating Fc: 49,33 x ln t1 - t2[ ] t1 - tr n t2 - tr ( ) n Panel radiator 1,28 Section radiator 1,29 Convector 1,3 - 1,33 F = tflow oC Fc ∆t oC
  • 6. 166 8 STEPS - CONTROL OF HEATING SYSTEMS CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS a The control unit has to sense the room temperature to be able to control it. No enclosure 0% Shelf with opening 0% Shelf close to the wall 10 -2% Open fronted recess with a shelf 12 -6% Encased with grille in front > -15% Encased with small grille in front. Not recommended. > -30% Acceptable cabinet. ≈ -8 - 10% Reduction of heat emission from radiators fixed in some type of enclosure Radiation from a radiator depending on the treatment of the surface. Material Surface treatment Radiation % Steel, cast iron 100 Oil paint 100 Aluminium or copper bronzes 75 Zinc white 101 Lead white 99 Enamelled White 101 Matt green 96 Aluminium 8 10 - 100 mm 30 - 100 mm Alternative openings a+40 >100mm
  • 7. 167 0 100 200 300 400 0 20 40 60 80 100 120 80/89 65/76 50/6 40 32 25 20 10 15 CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 8 STEPS - CONTROL OF HEATING SYSTEMS Heat losses from uninsulated horizontal pipe. For vertical pipe reduce by 20% One-pipe above another reduce by 12% Three pipes above each other reduce by 20% Temperature above room temperature oC Heat emission W/m pipe DN/0
  • 8. 168 8 STEPS - CONTROL OF HEATING SYSTEMS CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 5 7 10 20 30 mmWG/m ,05 ,07 0,1 0,2 0,3 0,4 0,5 kPa/m 25 15 20 32 40 80 50 100 125 150 ,01 ,015 ,02 ,03 ,04 ,05 ,07 ,1 ,15 ,2 ,3 ,5 ,4 ,7 1 1,5 2 3 4 5 7 10 40 50 15 20 30 1,0 2,0 10 100 1000 10 100 1,5 2 3 4 5 7 15 20 30 40 50 70 150 200 150 200 300 400 500 700 70 50 40 15 40 50 0,15 65 3,0 m/s 0,2 0,3 0,4 0,5 k = 0,00003 m Density = 1.000 kg/m3 Pressure drop in steel pipes for heating installations. m3/h DN mm l/s l/h
  • 9. 0,1 0,2 0,3 0,5 1,0 2 3 ,01 ,02,03 ,05 0,1 ,2 ,3 ,5 1 1 2 6 4 3 2 3 4 5 107 169 CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 8 STEPS - CONTROL OF HEATING SYSTEMS ∆p for ζ values at differnt rates. Symbol Units Coefficient of resistance, ζ Branch tee 1 Through tee 1 Elbow, smooth 0,2 Bend 1 The values for the coefficient of resis- tance for tees, elbows and bends. The pressure drop is calculated from: ∆p = ζ 0,5 ρ ν2 , Recommended portion of pipe losses for different systems or part of systems. Type of system Unit Friction % Heating Small buildings 50 - 60 Large buildings 60 - 70 Sub-stations Primary and secondary side 20 - 30 Distribution pipe net work Primary side 80 - 90 ζ valuem/s ∆p kPa Sizes of steel pipes for heating systems. Working pressure 1,0 MPa (10 bar) Nominal diameter External diameter Wall thickness Internal diameter mm inch mm mm mm 8 1/4 13,50 2,25 9 10 3/8 17,00 2,25 12,5 15 1/2 21,25 2,75 15,75 20 3/4 26,75 2,75 21,25 25 1 33,50 3,25 27,00 32 1 1/4 42,25 3,25 35,75 40 1 1/2 48,00 3,50 41,00 50 2 60,00 3,50 53,00 65 2 1/2 75,50 3,75 68,00 80 3 88,50 4,00 80,50 100 4 114,00 4,00 106,00 125 5 140,00 4,50 131,00 150 6 165,00 4,50 156,00
  • 10. 30 50 70 100 200 300 500 700 1000 0,1 ,2 ,3 ,4 ,5 ,7 1,0 2 3 kPa 0,01 ,02 ,03 ,07 ,1 ,2 ,3 mWG ,001 ,002 ,004,006 0,01 ,02 ,03 Bar ,01 ,02 ,03 ,05 ,07 ,1 ,2 ,3 ,05 4 5 7 10 20 ,7 1 2 ,04 ,06 0,1 ,2 ,5 15 2025 170 8 STEPS - CONTROL OF HEATING SYSTEMS CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS Flow chart for RTD-G 15, 20 and 25 RTD - G 15, 20 and 25 l/h l/sValve size ∆pvalve
  • 11. 171 CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 8 STEPS - CONTROL OF HEATING SYSTEMS 3 5 7 10 20 30 50 70 100 ,001 ,002 ,003 ,005 ,007 ,01 ,02 ,03 1 2 3 4 5 7 10 20 30 kPa 0,1 0,2 ,3 ,4 ,5 ,7 1 2 3 mWG 0,01 ,02 ,04 ,06 0,1 ,2 ,3 Bar ,1 ,05 ,07 500 300 200 N 1 2 3 4 5 67 3 5 7 10 20 30 50 70 100 ,001 ,002 ,003 ,005 ,007 ,01 ,02 ,03 1 2 3 4 5 7 10 20 30 kPa 0,1 0,2 ,3 ,4 ,5 ,7 1 2 3 mWG 0,01 ,02 ,04 ,06 0,1 ,2 ,3 Bar ,1 ,05 ,07 500 300 200 N 1 23 45 6 7 Flow chart for thermostatic valves in two-pipe system l/h l/sPre-set value ∆pvalve Pre-set value 1 2 3 4 5 6 7 N kv values 0,04 0,08 0,12 0,20 0,27 0,36 0,45 0,60 Pre-set value 1 2 3 4 5 6 7 N kv values 0,10 0,15 0,17 0,25 0,32 0,41 0,62 0,83 l/h l/sPre-set value ∆pvalve RTD - N 15 RTD - N 20 - 25
  • 12. 172 8 STEPS - CONTROL OF HEATING SYSTEMS CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 0,1 0,2 0,3 0,5 0,7 1,0 2 3 5 7 10 0,1 0,2 0,3 0,5 0,7 1,0 2 3 ,03 ,05 ,07 1 2 3 4 5 7 10 20 30 40 60 80 kPa 0,1 0,2 ,3 ,4 ,5 ,7 1 2 3 4 5 7 mWG 0,01 ,02 ,04 ,06 0,1 ,2 ,3 ,4 ,5 ,7 Bar 520 8 ,8 1,6 2,5 4,0 6,3 10 1 Flow chart for ∆p control valves for riser or circuit in heating systems. ASV-P, PV 15-40 and ASV-M 15-40 m3/h l/skvs-value ∆pvalve Working range: ASV-P 10 kPa ASV-PV 5 - 25 kPa. Minimum available ∆p for good functioning: 8 kPa. Example Q: 300 l/h. ∆p riser: 7kPa. ∆p radiator including valve: 5 kPa. ∆p-control kv 1,6. ∆pvp = 3,4 kPa, 1 Necessary ∆p = 7+5+8 = 20 kPa.
  • 13. 173 CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 8 STEPS - CONTROL OF HEATING SYSTEMS 0,1 0,2 0,3 0,5 0,7 1,0 2 3 5 7 10 0,1 0,2 0,3 0,5 0,7 1,0 2 3 ,03 ,05 ,07 1 2 3 4 5 7 10 20 30 40 60 100 200 kPa 0,1 0,2 ,3 ,4 ,5 ,7 1 2 3 4 5 7 10 15 20 mWG 0,01 ,02 ,04 ,06 0,1 ,2 ,3 ,4 ,5 ,7 1,0 1,5 2 Bar 10 5 7 150 50 30 20 100 200 20 30 50 ,4 ,63 1,0 1,6 2,5 4,0 6,3 10 16 25 40 63 100145 Flow chart for control valves in heating systems. m3/h l/skvs-value ∆pvalve Formulas. ∆p : bar. Q: m3/h. kv = ; ∆p = ; Q = kv √ ∆p ; Q √∆p Q kv ( ) 2 ∆p : kPa. Q: l/h. kv = 0,01 ; ∆p = 0,01 ; Q = 100x kv √ ∆p ; Q √∆p Q kv ( ) 2 ∆p : kPa. Q: l/s. kv = 36 ; ∆p = 36 ; Q = √ ∆p ; Q √∆p Q kv ( ) 2 kv 36 Q Q Q
  • 14. 174 8 STEPS - CONTROL OF HEATING SYSTEMS CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 0,1 0,2 0,3 0,5 0,7 1,0 2 3 5 7 10 0,1 0,2 0,3 0,5 0,7 1,0 2 3 ,03 ,05 ,07 1 2 3 4 5 7 10 20 30 40 60 100 200 kPa 0,1 0,2 ,3 ,4 ,5 ,7 1 2 3 4 5 7 10 15 20 mWG 0,01 ,02 ,04 ,06 0,1 ,2 ,3 ,4 ,5 ,7 1,0 1,5 2 Bar 10 5 7 150 50 30 20 100 200 20 30 50 ,4 ,63 1,0 1,6 2,5 4,0 6,3 10 16 25 40 63 100145 Flow chart for valves in district heating systems. m3/h l/skvs-value ∆pvalve
  • 15. 175 CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 8 STEPS - CONTROL OF HEATING SYSTEMS 0,1 0,2 0,3 0,5 0,7 1,0 2 3 5 7 10 0,1 0,2 0,3 0,5 0,7 1,0 2 3 ,03 ,05 ,07 1 2 3 4 5 7 10 20 30 40 60 80 kPa 0,1 0,2 ,3 ,4 ,5 ,7 1 2 3 4 5 7 mWG 0,01 ,02 ,04 ,06 0,1 ,2 ,3 ,4 ,5 ,7 Bar 520 8 ,8 1,6 2,5 4,0 6,3 10 1 m3/h l/skvs-value ∆pvalve AVP 15 - 32 Flow chart for ∆p control valves in district heating systems.
  • 16. 176 8 STEPS - CONTROL OF HEATING SYSTEMS CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 0,1 0,2 0,3 0,5 0,7 1,0 2 3 5 7 10 0,1 0,2 0,3 0,5 0,7 1,0 2 3 ,03 ,05 ,07 1 2 3 4 5 7 10 20 30 40 60 100 200 kPa 0,1 0,2 ,3 ,4 ,5 ,7 1 2 3 4 5 7 10 15 20 mWG 0,01 ,02 ,04 ,06 0,1 ,2 ,3 ,4 ,5 ,7 1,0 1,5 2 Bar 10 5 7 150 50 30 20 100 200 20 30 50 ,63 1,0 1,6 2,5 4,0 6,3 10 16 25 50 80 125 20 Flow chart for ∆p control valves in district heating systems. m3/h l/skvs-value ∆pvalve IVD-IVFS kvs 0,63 - 25,0 m3/h AFP kvs 50 - 125 m3/h ∆p-regulator, working range: IVD 5 - 50 and 20 - 250 kPa. AFP 20 - 120 and 50 - 250 kPa Maximum ∆p valve IVF kvs: 0,63 and 1,0 = 1.000 kPa 2,5 = 630 kPa 4,0 - 25 = 800 kPa Maximum ∆p valve AFP: 1.200 kPa
  • 17. 177 CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 8 STEPS - CONTROL OF HEATING SYSTEMS 0 0,5 1,0 1,5 2,0 2,5 0 50 100 150 200 250 300 350 400 1 10 50 100 150 200 250 Heat requirement for hot water according to the Swedish Board of District Heating Domestic hot water, Q L/s. Effect, P kW Number of apartments.
  • 18. 178 8 STEPS - CONTROL OF HEATING SYSTEMS CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 0,07 0,1 0,15 0,2 0,3 0,4 0,5 0,6 0,7 0,8 1,0 0,9 20 30 40 50 60 70 80 m /h 3 ∆p kPav 0,2 0,3 0,4 0,5 0,6 0,7 0,8 ∆ p Barv 1 2 3 4 5 8 6,5 0,2 0,3 0,4 0,5 0,7 2,0 1,5 1,0 0,9 0,8 0,6 20 30 40 50 60 70 80 m /h 3 ∆p kPav 0,2 0,3 0,4 0,5 0,6 0,7 0,8 ∆ p Barv 10 12 14 2 4 6 8 Flow limiter, ASV-Q 15, Flow limiter, ASV-Q 20 Set values Set values ASV-Q Capacity l/h Set value 15 100 - 800 1 - 8 20 200 - 1400 2 - 14 25 400 - 1600 4 - 16 32 500 - 2500 5 - 30
  • 19. 179 CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 8 STEPS - CONTROL OF HEATING SYSTEMS 2,0 1,7 1,5 1,2 1,0 0,9 0,8 0,7 0,6 0,5 0,4 30 40 50 60 70 80 m /h 3 ∆p kPav 0,3 0,4 0,5 0,6 0,7 0,8 ∆ p Barv 10 12 14 16 4 6 8 4,0 3,0 2,0 1,5 1,2 1,0 0,9 0,8 0,7 0,6 0,5 0,4 m /h 3 30 40 50 60 70 80 ∆p kPav 0,3 0,4 0,5 0,6 0,7 0,8 ∆ p Barv 5 15 10 20 25 30 Flow limiter, ASV-Q 25, Flow limiter, ASV-Q 32 Set values Set values
  • 20. 180 8 STEPS - CONTROL OF HEATING SYSTEMS CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS Calculation of one-pipe system 6 31 m 6 m6 m6 m6 m 1200 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1200 1200 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1200 1200 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1200 1200 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1200 6 m 6 m 6 m 1200 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1200 1200 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1200 1200 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1200 1200 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1200 3x12=36m 1,5 m 0 2345 2345 6 789 1 10 10 m
  • 21. 181 CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 8 STEPS - CONTROL OF HEATING SYSTEMS Calculation of one-pipe system
  • 22. 182 8 STEPS - CONTROL OF HEATING SYSTEMS CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS Calculation of two-pipe system 12001200 1200 120012001200 1200 1200 1200 12001200 12001200 12001200 1200 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 3 m 6 m 6 m 6 m 12345 6 7 8 9 10 11 12 13 14 15 16 17 3m3m 31 m
  • 23. 183 CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 8 STEPS - CONTROL OF HEATING SYSTEMS Calculation of two-pipe system
  • 24. 184 8 STEPS - CONTROL OF HEATING SYSTEMS CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS SI-units. Effect, P. Pressure, p. W kcal/h Pa kPa bar mWG 1 0,85985 1 0,001 0,00001 0,0001 1,163 1 1.000 1 0,01 0,1 100.000 100 1 10 10.000 10 0,1 1 Flow, Q (ϕ). Temperature, t (θ). l/s m3/h Kelvin K Celsius oC 1 3,6 0 -273,15 0,278 1 273,15 ± 0 373,15 100 Greek alphabet. Α α Β β Γ γ ∆ δ Ε ε Ζ ζ Η η Θ θ Ι τ alfa beta gamma delta epsilon seta eta theta iota Κ κ Λ λ Μ µ Ν ν Ξ ξ Ο ο Π π Ρ ρ Σ σ kappa lamda my ny xi omikron pi ro sigma Τ τ Υ υ ϑ ϕ Χ χ Ψ ψ Ω ω tau ypsilon phi chi psi omega Physical properties for water. Temperature Pressure Density Isobaric heat υ oC p kPa ρ kg/m3 capacitivity cp J/ (kg x K) 0 - 999,84 4218 10 - 999,70 4192 20 - 998,205 4182 30 - 995,65 4178 40 - 992,2 4178 50 - 998,14 4181 60 - 983,21 4184 70 - 977,78 4190 80 - 971,80 4196 90 - 965,33 4205 100 1,3 958,35 4216 110 43,26 951,0 - 120 98,54 943,1 4245 130 170,11 934,8 - 140 261,36 926,1 4287 150 375,97 916,9 -
  • 25. 185 CHAPTER 8 • TECHNICAL DATA, FORMULAS AND CHARTS 8 STEPS - CONTROL OF HEATING SYSTEMS