The figure 1 above presents a crudely simplified centralised water heating sys- em. The system comprises of two heating lines, the first line having one radiator nd the second has four radiators in series. The pressure after the pump (2) is 2 bar, and the flow velocity is 1.2 m/s. or simplicity we can assume the water to be in constant temperature of 60°C. oss coefficients and pressure losses are listed in Table 1, and pipe lengths and iameters are given in Table 2. for the system balancing, the target is to divide the mass flow so, so that 20% f the mass flow goes to the first line (i.e. through radiator R1.1) and 80% of he flow goes to the second line (R2.1 - R2.4): (a) How large pressure loss is needed in the control valve CV1 to get the desired flow rates in the two lines? (b) How large is then the minor loss coefficient of the said valve, Kevi?! (c) How much is the pressure, in bar, at the end of the line at section 4?
The figure 1 above presents a crudely simplified centralised water heating sys- em. The system comprises of two heating lines, the first line having one radiator nd the second has four radiators in series. The pressure after the pump (2) is 2 bar, and the flow velocity is 1.2 m/s. or simplicity we can assume the water to be in constant temperature of 60°C. oss coefficients and pressure losses are listed in Table 1, and pipe lengths and iameters are given in Table 2. for the system balancing, the target is to divide the mass flow so, so that 20% f the mass flow goes to the first line (i.e. through radiator R1.1) and 80% of he flow goes to the second line (R2.1 - R2.4): (a) How large pressure loss is needed in the control valve CV1 to get the desired flow rates in the two lines? (b) How large is then the minor loss coefficient of the said valve, Kevi?! (c) How much is the pressure, in bar, at the end of the line at section 4?
Transcribed Image Text:Also, for simplicity we can assume the pipes to be hydraulically smooth and
estimate the friction factors with the Blasius correlation
f =
0.3164
Re¹/4
Table 1: Minor loss coefficients and pressure losses
Equipment
T-junction after the pump, flow going directly
T-junction after the pump, flow going to the branch
Control valve CV2
90° bend
Pressure loss in a single radiator
Combining t-junction, flow going directly
Combining t-junction, flow coming from the branch
Section
Pump → t-junction
t-junction
radiator R1.1
radiator R1.1 → t-junction
t-junction radiator R2.1
radiator R2.1
radiator R2.2
radiator R2.2→ radiator R2.3
radiator R2.3 →→ radiator R2.4
radiator R2.4 → t-junction
t-junction end
Table 2: Pipe lengths and diameters
6
6
24
12
4
4
Minor loss coefficient, K
4
24
12
Length [m] Inner pipe diameter [mm]
22
12
12
18
18
18
0.9
2
18
18
22
12
0.7
4 kPa
0.9
2
(1)
Transcribed Image Text:CV1
2
The first heating line
3
CV2
R1.1
The second heating line
R2.4
R2.3
R2.2
R2.1
Figure 1: Crudely simplified centralised water heating system.
The figure 1 above presents a crudely simplified centralised water heating sys-
tem. The system comprises of two heating lines, the first line having one radiator
and the second has four radiators in series.
The pressure after the pump (2) is 2 bar, and the flow velocity is 1.2 m/s.
For simplicity we can assume the water to be in constant temperature of 60°C.
Loss coefficients and pressure losses are listed in Table 1, and pipe lengths and
diameters are given in Table 2.
For the system balancing, the target is to divide the mass flow so, so that 20%
of the mass flow goes to the first line (i.e. through radiator R1.1) and 80% of
the flow goes to the second line (R2.1 - R2.4):
(a) How large pressure loss is needed in the control valve CV1 to get the
desired flow rates in the two lines?
(b) How large is then the minor loss coefficient of the said valve, Kevi?!
(c) How much is the pressure, in bar, at the end of the line at section 4?
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![Also, for simplicity we can assume the pipes to be hydraulically smooth and
estimate the friction factors with the Blasius correlation
f =
0.3164
Re¹/4
Table 1: Minor loss coefficients and pressure losses
Equipment
T-junction after the pump, flow going directly
T-junction after the pump, flow going to the branch
Control valve CV2
90° bend
Pressure loss in a single radiator
Combining t-junction, flow going directly
Combining t-junction, flow coming from the branch
Section
Pump → t-junction
t-junction
radiator R1.1
radiator R1.1 → t-junction
t-junction radiator R2.1
radiator R2.1
radiator R2.2
radiator R2.2→ radiator R2.3
radiator R2.3 →→ radiator R2.4
radiator R2.4 → t-junction
t-junction end
Table 2: Pipe lengths and diameters
6
6
24
12
4
4
Minor loss coefficient, K
4
24
12
Length [m] Inner pipe diameter [mm]
22
12
12
18
18
18
0.9
2
18
18
22
12
0.7
4 kPa
0.9
2
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