The figure 1 above presents a crudely simplified centralised water heating system. The system comprises of two heating lines, the first line having one radiatorand the second has four radiators in series.The pressure after the pump (point (1)) 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, KCV1? (c) How much is the pressure, in bar, at the end of the line at section 4? CV1The first heating lineCV2R1.1The second heating lineR2.4R2.3R2.2R2.1Also, for simplicity we can assume the pipes to be hydraulically smooth andestimate the friction factors with the Blasius correlationf =Table 1: Minor loss coefficients and pressure losses0.3164Re¹/4EquipmentT-junction after the pump, flow going directlyT-junction after the pump, flow going to the branchControl valve CV290° bendPressure loss in a single radiatorCombining t-junction, flow going directlyCombining t-junction, flow coming from the branchSectionPump →→ t-junctiont-junction radiator R1.1radiator R1.1 →→ t-junctiont-junction →→ radiator R2.1radiator R2.1 → radiator R2.2radiator R2.2 → radiator R2.3radiator R2.3 → radiator R2.4radiator R2.4 → t-junctiont-junction →→ endTable 2: Pipe lengths and diametersMinor loss coefficient,124442412Length [m] Inner pipe diameter [mm]66242212121818180.92181822120.74 kPa0.92(1)

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Elements Of Electromagnetics

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ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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The figure 1 above presents a crudely simplified centralised water heating system. The system comprises of two heating lines, the first line having one radiatorand the second has four radiators in series.
The pressure after the pump (point (1)) 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, KCV1?
(c) How much is the pressure, in bar, at the end of the line at section 4?

CV1
The first heating line
CV2
R1.1
The second heating line
R2.4
R2.3
R2.2
R2.1
Also, for simplicity we can assume the pipes to be hydraulically smooth and
estimate the friction factors with the Blasius correlation
f =
Table 1: Minor loss coefficients and pressure losses
0.3164
Re¹/4
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
Minor loss coefficient,
12
4
4
4
24
12
Length [m] Inner pipe diameter [mm]
6
6
24
22
12
12
18
18
18
0.9
2
18
18
22
12
0.7
4 kPa
0.9
2
(1)

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