Viessmann VITOCELL 100-W - Sample Calculation; Calculation of the Cylinder Size Based on Water Volume; Calculation of the Cylinder Size Based on Heat Volume

5.4 Sample calculation
A sports centre is equipped with 16 showers which are limited to
15 l/min.
According to design requirements, 8 showers are operated simulta-
neously for up to 30 min continuously. The drawing temperature
should be 40 °C. A max. of 100 kW boiler output is available for
DHW heating.
c = Spec. thermal capacity
1 kWh
860 l · K
n = Number of DHW cylinders
n
Z
= Number of draw-off points
Φ
D
= Heat volume in kWh available by continuous output
L = Continuous output in kW
Φ
ttl
= Total heat demand in kWh (for production and demand)
Φ
cyl
= Usable heat volume of the total cylinder volume in kWh
Φ
cyl.
ind.
= Usable heat volume of a single DHW cylinder in kWh
t = Time in h
T
a
= Cylinder storage temperature in °C
T
e
= Cold water inlet temperature in °C
ΔT = Temperature differential between draw-off temperature
and cold water inlet temperature in K
´
= Draw-off rate per draw-off point in l/h
V
D
= DHW heated by continuous output in l
V
ttl
= Total draw-off volume in l
V
cyl
= Usable cylinder capacity in l
Calculation of the cylinder size based on water volume
Over a period of 30 min, a total water volume V
ttl
at a temperature of
40 °C is required.
V
ttl.
= n
Z
· ´ · t
= 8 showers · 15 l/min · 30 min
= 3600 l
Of the 3600 l, the 100 kW connected load can deliver a water vol-
ume V
D
over a period of 30 min.
L · t
V
D
=
c · ΔT
100 kW · 0.5 h · 860 l · K
V
D
=
1 kWh · (40 – 10) K
=1433 l
This means that the DHW cylinder must make the following water
volume available at a temperature of 40 °C:
3600 l – 1433 l = 2167 l
At a storage temperature of 60 °C, the required cylinder volume V
cyl
results.
V
cyl.
=
(60 – 10) K
2167 l · (40 – 10) K
=1300 l
The calculated number n of Vitocell 100-L with a volume of 750 l
each results from the following:
n =
750 l
1300 l
= 1.73
Selected cylinder loading system:
2 Vitocell 100-L, each with 750 l capacity, and 1 Vitotrans 222 heat
exchanger set with a heating output of 120 kW (in accordance with
max. available boiler output according to the sample calculation, i.e.
100 kW).
Calculation of the cylinder size based on heat volume
Over a period of 30 min (as per calculation), a total water volume of
3600 l at a temperature of 40 °C is required. This corresponds to a
heat volume of Φ
ttl
.
Φ
ttl.
= V
ttl.
· ΔT · c
1 kWh
= 3600 l · 30 K ·
860 l · K
= 126 kWh
The connected load can, over the drawing period of 30 min, provide
a heat volume of Φ
D
.
Φ
D
= L · t
= 100 kW · 0.5 h = 50 kWh
This means that the DHW cylinder must store a heat volume of Φ
cyl
.
Φ
cyl.
= Φ
ttl.
– Φ
D
= 126 kWh – 50 kWh = 76 kWh
Each individual Vitocell 100-L DHW cylinder with 750 l cylinder
capacity stores the following heat volume Φ
cyl. ind.
:
860 l · K
Φ
cyl. ind.
= 750 l · (60 – 10) K ·
1 kWh
= 43.6 kWh
This results in the calculated number of cylinders n.
43.6 kWh
n =
Φ
cyl. ind.
Φ
cyl.
76 kWh
= = 1.74
Selected cylinder loading system:
2 Vitocell 100-L, each with 750 l cylinder capacity, and 1
Vitotrans 222 heat exchanger set with a heating output of 120 kW (in
accordance with max. available boiler output according to the sam-
ple calculation, i.e. 100 kW).
Cylinder loading systems — Vitocell 100-L with Vitotrans 222
(cont.)
32
VIESMANN
DHW heating
5
5414646