Basics of Hydronics Systems In chilled water systems,
water as a secondary refrigerant, is distributed throughout
the entire hydraulic network in order to achieve the design
heat transfer in every coil of the building. A heat load
is the rate of heat transfer from the case coils required
to maintain an environment comfort standard. The liquid
flow rate required to transport a given heat load is determined
as follows:
Flow rate required: Where:
LFR:
Liquid flow rate (gal/min) HL:
Heat load (BTU/hr) D: Liquid
density (water density = 8.34 lb/gal) SG:
Liquid specific gravity (water specific gravity = 1) SH:
Liquid specific heat (water specific heat = 1 BTU/lb-°F) DeltaT:
Liquid temperature change during heat transfer process (°F)
The required pump head can be calculated
by applying Bernoulli’s equation. Bernoulli’s
relationship applies to any pumping system but the typical
hydronic system, as chilled water loop, is a special case.
As water re-circulates, picking up heat at one heat exchanger
(AHU or fan-coil) and dropping it off at the other (chiller’s
evaporator), points a and b could be defined at the same
point. In closed systems the first three terms of the Bernoulli
equation equals zero. Solely the friction of the system
determines pump head.
Bernoulli’s
relationship: Where: H:Pump
head required to move water from the point a to point
b in the system (ft) P:Pressure
at points a or b (lb/ft2) Ganma :
Liquid density (water density = 62.4 lb/ ft3) Z:Elevation
of the liquid surface at a or b from any constant reference
level (ft) V:Velocity
at a or b (ft/sec) g:Gravitational
constant (32.2 ft/sec2 ) hfriction:Friction
loss in the pipes, heat exchangers, coils and fittings
in ft-lb of work per pound of liquid required to overcome
friction (ft)
The
friction loss in a hydraulic system comes from the
head losses in components such as evaporator heat
exchanger, cooling coils and control valves. Equipment
manufacturers provide these component head losses
measured in feet of head loss or pounds per square
inch difference (psid) at some specific flow rate.
Other sources of friction loss in a hydraulic system
are pipes and fittings that can represent a significant
amount of friction loss in large systems. The total
friction loss of all these components, calculated
at the design flow rate, determines the pump head
required.
The Darcy-Weisbach equation is
a commonly used empirical expression for friction
head loss in piping:
Darcy-Weisbach equation:
Where:
hfriction:
Friction head loss (ft) f: Friction
factor L:
Length of the pipe (ft) D:
Diameter of the pipe (ft) V: Average
flow velocity (ft/sec) g:Gravitational
constant (ft/sec2)
Some important conclusions arise from the Darcy-Weisbach
relationship:
• Long, slim pipes have greater friction
loss than short, wide pipes, all else being equal.
• Friction head loss is a squared function
of fluid velocity so its small change will cause
a greater one in friction head loss.
A wider analysis of the Darcy Weisbach equation
leads to state that system head loss is a squared
function of system flow:
Head-flow relationship:
In theory, friction
losses which occur as liquid flows through a piping system
must be calculated by means of complicated formulae, taking
into account such factors as liquid density and viscosity,
and pipe inside diameter and material. Luckily, these formulae
have been reduced to tables and charts which, though somewhat
tedious and repetitive, are nevertheless not too complex.
Table 1 shows a typical pipe friction table for water at
60° F flowing through schedule 40 steel pipes. If the
pipe schedule or material is other than schedule 40 steel
pipes, a different table or an adjustment to the table must
be used. Friction data for other pipe materials and inside
diameters are often found in engineering data tables, or
are sometimes available from the manufacturers of pipe.
Table 1
Pipe Friction: Water/Schedule 40 Steel Pipe (fragment)
U.S.
Gallons
per minute
2
In. (2.067" I. D.)
2
1/2 In. (2.469" I. D.)
3
In. (3.068" I. D.)
3
1/2 In. (3.548" I. D.)
U.S.
Gallons
per minute
V
V2/2g
hf
V
V2/2g
hf
V
V2/2g
hf
V
V2/2g
hf
30
2.87
0.128
1.82
2.01
0.063
0.75
30
35
3.35
0.174
2.42
2.35
0.085
1.00
35
40
3.82
0.227
3.10
2.68
0.112
1.28
40
50
4.78
0.355
4.67
3.35
0.174
1.94
2.17
0.073
0.66
50
60
5.74
0.511
6.59
4.02
0.251
2.72
2.60
0.105
0.92
1.95
0.059
0.45
60
80
7.65
0.909
11.4
5.36
0.447
4.66
3.47
0.187
1.57
2.60
0.105
0.77
80
100
9.56
1.42
17.4
6.70
0.698
7.11
4.34
0.293
2.39
3.25
0.164
1.17
100
120
11.5
2.05
24.7
8.04
1.00
10.0
5.21
0.421
3.37
3.89
0.236
1.64
120
140
13.4
2.78
33.2
9.38
1.37
13.5
6.08
0.574
4.51
4.54
0.321
2.18
140
160
15.3
3.64
43.0
10.7
1.79
17.4
6.94
0.749
5.81
5.19
0.419
2.80
160
180
17.2
4.60
54.1
12.1
2.26
21.9
7.81
0.948
7.28
5.84
0.530
3.50
180
200
19.1
5.68
66.3
13.4
2.79
26.7
8.68
1.17
8.90
6.49
0.655
4.27
200
220
21.0
6.88
80.0
14.7
3.38
32.2
9.55
1.42
10.7
7.14
0.792
5.12
220
240
22.9
8.18
95.0
16.1
4.02
38.1
10.4
1.69
12.6
7.79
0.943
6.04
240
260
24.9
9.60
111
17.4
4.72
44.5
11.3
1.98
14.7
8.44
1.11
7.04
260
280
26.8
11.1
128
18.8
5.47
51.3
12.2
2.29
16.9
9.09
1.28
8.11
280
300
28.7
12.8
146
20.1
6.28
58.5
13.0
2.63
19.2
9.74
1.47
9.26
300
350
23.5
8.55
79.2
15.2
3.57
26.3
11.3
2.00
12.4
350
400
26.8
11.2
103
17.4
4.68
33.9
13.0
2.62
16.2
400
500
33.5
17.4
160
21.7
7.32
52.5
16.2
4.09
25.0
500
600
26.0
10.5
74.8
19.5
5.89
35.6
600
700
30.4
14.3
101
22.7
8.02
48.0
700
800
34.7
18.7
131
26.0
10.5
62.3
800
1000
32.5
16.4
96.4
1000
Usually velocity (labeled "V" in Table 1) is used
as the criteria for choosing al least a preliminary line
size, with the trade-off between piping system cost, pump
capital cost, and lifetime energy costs being considered.
Common velocity guidelines are 4 to 6 ft/sec for suction
piping and 6 to 10 ft/sec for discharge piping.
With the design capacity and the chosen preliminary pipe
size, the friction tables give the head loss in feet per
100 linear feet of pipe (labeled "hf" in Table
1). The total friction head loss in a given length of
pipe will then be obtained multiplying the value found
in Table 1 by the actual pipe length divided by 100.
Friction head loss in a given length of pipe:
Where: Hf: Total friction head loss
in a given length of pipe (ft) L: Actual length of pipe (ft) hf: Head loss per 100 linear
feet of pipe (ft)
The friction loss in valves and fittings is determined
by the following formula:
Friction loss in valves and fittings:
Where: Hf: Friction head loss in a
given valve or fitting (ft) K: Resistance coefficient for
the particular valve or fitting V2/2g: Value found in Table 1
entering with valve/fitting diameters and flow rate
The value of K for the particular
valve or fitting is determined using one of the charts
in Figures 50(a) and 50(b),
which has a different K chart for each type of valve
or fitting. The K values shown in such charts are
generic only. If particular valves are already chosen,
the valve manufacturer may have more precise coefficients.
Fig.
Nº50(a). Resistance
coefficients (K) for valves and fittings.
Click on image
to enlarge
Fig.
Nº50(b). Resistance
coefficients (K) for valves and fittings..
Click on image
to enlarge
An example: In order to illustrate the procedure
to be followed in pipe sizing a typical chilled water distribution
system and calculating its pressure drop, a three-zone loop
serving the coils of their air handling units (AHU) will
be used. The system is shown in
Figure 51
Chiller Plant Data:
Design thermal load:
120 Ton Chilled water supply temperature:
42 °F Chilled water return temperature:
54 °F Equipment Room Pressure Drop:
The total water flow rate required of 240 GPM
determines the system components selection and the
equipment room pipe and fittings size selection. The
system will use Schedule 40 steel piping and Table1
indicates that 3 ½" size will carry the
design flow. The pressure drops of the system components,
including piping and fittings at the equipment room,
are as follows:
Fig.
Nº51. Chilled
water distribution system serving a three-zone
loop.
Click on image
to enlarge
Component
Cant.
Pressure
drop
Chiller's evaporator
1
2.9'
3 ½" Piping (240 GPM from A to B)
32'
1.9'
Triple duty valve
1
2.3'
90°-Elbow
8
5.1'
Flanged gate valve
1
0.2'
Equipment
Room Pressure Drop to A-B:
12.4'
zone 1:
Component
Cant.
Pressure
drop
Coil
1
3'
2 ½" Piping (80 GPM
from A to D)
200'
9.3'
Screwed tee-branch flow
1
0.7'
90°-Elbow
6
2.3'
3" Piping (180 GPM from
D to B)
12'
0.9'
Screwed tee-branch flow
1
1.4'
2 ½" Balance valve (wide
open)
1
2.7'
Zone
1 Pressure Drop (Less control valve):
20.3'
Zone 2:
Component
Cant.
Pressure
drop
Coil
1
2'
3" Piping (160 GPM from
A to C)
3'
0.2'
Screwed tee-line flow
1
0.7'
2" Piping (60 GPM from
C to B)
130'
8.6'
Screwed tee-line flow
1
0.5'
90°-Elbow
7
3.5'
2" Balance valve (wide
open)
1
1.5'
Zone
2 Pressure Drop (Less control valve):
17'
Zone 3:
Component
Cant.
Pressure
drop
Coil
1
5'
3" Piping (160 GPM from
A to C)
3'
0.2'
Screwed tee-line flow
1
0.7'
2 ½" Piping (100 GPM
from C to D)
220'
15.6'
Screwed tee-branch flow
1
1.1'
90°-Elbow
5
0.6'
3" Piping (180 GPM from
D to B)
12'
0.9'
Screwed tee-line flow
1
0.9'
2 ½" Balance valve (wide
open)
1
4.2'
Zone
3 Pressure Drop (Less control valve):
29.2'
Control Valves Selection:
In order to provide stable flow conditions,
the control valves should be selected for initial
pressure drops on the order of three times the coil
pressure drop if possible. On the other hand, valves
should generally not be sized for over 20' pressure
drop because of velocity problems. The circuit with
the highest pressure drop should have its valve
selected first, with the other valves selected to
help balance their pressure drop to this one.
Zone 3 has the highest pressure drop,
with its coil pressure drop being 5' so a valve
selection for 15' @ 100 GPM should be attempted.
This requires a valve with a Cv of 39. The closest
selection available could be a 2" valve with Cv
= 34, having a pressure drop of 19.3' at 100 GPM.
The total pressure drop of Zone 3 will then be 48.5'
(29.2' + 19.3').
Zone 1 has a pressure drop, exclusive
of its control valve, of 20.3', so a valve can be
selected for the difference between this and 48.5'
to balance it to Zone 3. This difference is 28.2',
well over the allowable 20' maximum pressure drop.
A valve, to provide 20' resistance at 80 GPM would
require a Cv of 27. The closest selection available
could be a 2" valve with Cv = 29, having a pressure
drop of 17' at 80 GPM. The total pressure drop of
Zone 1 will then be 37.3' (20.3' + 17').
Zone 2 requires a valve with a pressure
drop of 31.5' (48.5' - 17') to balance it to Zone
3. Such value is again well above the allowable
20' maximum pressure drop. A valve, to provide 20'
resistance at 60 GPM would require a Cv of 20. The
closest selection available could be a 2" valve
with Cv of 22, having a pressure drop of 16.6' at
60 GPM. The total pressure drop of Zone 2 will then
be 33.6' (17' + 16.6'). The pressure drops, including
control valve, are now as follows:
Zone
Pipe, coil and fittings
Control
valve
Total
1
20.3'
17'
37.3'
2
17'
16.6'
33.6'
3
29.2'
19.3'
48.5'
Zone Balance: In order to balance Zone 1 to
Zone 3, the balancing valve will have to be
set at 3.8 turns to provide 11.2' (48.5' - 37.3')
of additional resistanceat the 80 GPM flow.
The balancing valve of Zone 2 must be set at
3.2 turns to provide 14.9' (48.5' – 33.6')
of additional resistance at the zone rated flow
of 60 GPM. The balancing valve of the Zone 3
remains wide open. The settings of each balancing
valve will be as follows:
Zone
Valve
size
Flow(GPM)
PressureDrop
needed
Setting
(turns)
1
2
½"
80
11.2'
3.8
2
2
½"
60
14.9'
3.2
3
2
½"
100
4.2'
4
Fig.
Nº52. Curve
of the pump selected.
Click
on image to enlarge
Total System Pressure
Drop:
Once all
three zones have been balanced at their
design flows, with pressure drops corresponding
to Zone3's pressure drop of 48.5', it is
now possible to calculate the total system
pressure drop as follows:
Total system
pressure drop = Equipment
room pressure drop + Zone's pressure drop Total
system pressure drop =
12.4' + 48.5' Total
system pressure drop =
60.9'
A pump may now be selected for 240 GPM
@ 60.9' head. A pump with an 8" impeller and 7½ HP
is selected for this application. The Figure 52 shows
the pump curve.
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