Czech Technical University in Prague Department of Microenvironmental and Building Services Engineering http://tzb.fsv.cvut.cz BEE1 Heating

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Assignment 4

Calculation of a heating system pressure loss

Working steps:

A. Introduction steps

B. Hydraulic scheme

C. Piping design

A) Introduction steps

A1) Definition of temperature difference

System supply t1

System return t2

Emitter supply tw1

Emitter return tw2

Mean emitter temperature tw

Maximal emitter surface temperature tTp max

Temperature difference - emitter = tw1

- tw2

Temperature difference system = t1

- t2

2

21 www

ttt

, [C]

Recommended system temperatures differences:

Low temperature heating system (feat. Heat pump, condensing boilers, etc): 45/35 C, 50/40 C, 55/45 C.

Expansion

vessel

Heat emmiter

Boiler

l

H

T 1 , 1

T 2 , 2 Supply

Return

t2

t1

tw1

tw2

tTp,max

tw

Czech Technical University in Prague Department of Microenvironmental and Building Services Engineering http://tzb.fsv.cvut.cz BEE1 Heating

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Standard water heating system: 60/50 C, 65/55 C, 70/60 C, 70/50 C, 80/60 C.

A2) Circulation mode

Two basic options are available natural circulation or forced circulation.

Our task is forced circulation, when heating system is equipped with a pump.

B) Hydraulic scheme

B1) Definition of main branch for design, piping system segments

Main branch: a loop between heat source and the most distanced heating emitter. Distance is measured as length of piping.

Piping system segment: a part of piping with constant mass flow rate

- Always constant flow rate within the segment, so no other branches start between the beginning and the end of it.

- No matter if it is straight pipe or with elbows.

- Usually between two distanced branches.

- See following figure

Fig. 1 Main branch, piping segments

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C) Piping design

Please follow chart Design of water heating system available on the web site.

C1) Gathering necessary parameters

a) Thermal output transferred by water flowing through the segment to following branches of a heating system.

Starting with the segment including a boiler, here is the highest thermal output equal to boiler output. Every other segment has lower transferred thermal output as side branches leave the main loop.

E.g.: At fig. 1, segment 6 at supply pipe (same for segment 6 at return pipe) transfer thermal output 2504 W = 2x 665 + 2x 587. Than segments 7 and 7 transfer thermal output 1330 W = 2x 665 and finally segment 8 and 8 is 665 W each.

b) Mass flow rate based on thermal output transferred in the segment

In any point of a heating system is possible to calculate transferred heat according to liquid (water) mass flow rate and supply and return temperature difference.

Heat transferred by the system through a segment

21 ttcMQ ii [W]

M mass flow rate in a segment, [kg/s]

c heat capacity of water, c = 4186 [J/(kg.K)]

From this equation is the mass flow rate Mi calculated for thermal output Qi transferred in the segment i as follows:

21 ttcQ

M ii

c) Total length of the segment

Define length l [m] of each segment from plan and section.

C2) Design of piping dimension

d) Preliminary pipe dimension, water velocity and specific pressure loss

Choose proper material for tubes copper, PPR, PE-X available in Tab. 1 to 3.

Apply one of following method (we recommend the first one)

Method of economical specific pressure loss 60 - 200 Pa/m

Method of optimal velocity 0,05 - 1,0 m/s (!!! Noise)

Proper tube dimension we find based on mass flow rate in segment and specific pressure loss or optimal velocity.

Czech Technical University in Prague Department of Microenvironmental and Building Services Engineering http://tzb.fsv.cvut.cz BEE1 Heating

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In following segments with decreasing mass flow rate would also gradually decrease specific pressure loss.

Example:

Transfer thermal output Qi = 2325 W, supply water temperature tw1 = 60 C, return water temperature tw2 = 50 C.

Mass flow rate is

hkgskgM /8.199/0555.050604186

2325

Presuming specific pressure loss 60 - 200 Pa/m,

and considering copper tubes (Tab. 1) we receive following situation:

Note: Interpolate values between included mass flow rates.

Dimension 15x1 is not acceptable for high pressure loss 213.6 Pa/m

Dimension 22x1 has too low pressure loss 26.5 Pa/m, also velocity 0.18 m/s is low, so we would evaluate the pipe oversized

Dimension 18x1 is perfect solution 106.5 Pa/m, 0.321 m/s

e) Local resistances (elbows, fittings, etc.)

Summarize all local resistances in the segment and find proper local pressure loss

coefficients .

Search each segment for all elbows, joints, T pieces, valves, emitters, boilers, etc., which causes local pressure loss.

In the chart DESIGN OF WATER HEATING SYSTEM are some values for local resistances.

D) Calculation of pressure loss

D1) Calculation of friction pressure loss of segment i

Specific pressure loss R, [Pa/m]

Total length of the segment l, [m]

p,i = R . l [Pa]

For detail calculation of friction pressure loss in a pipe see D'Arcy-Weisbach equation

based on friction coefficient .

Czech Technical University in Prague Department of Microenvironmental and Building Services Engineering http://tzb.fsv.cvut.cz BEE1 Heating

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(http://www.engineeringtoolbox.com/darcy-weisbach-equation-d_646.html)

D2) Calculation of local pressure loss Z of segment i

Local pressure loss coefficient , [-]

Water velocity in pipe v, [m/s]

Water density , [m/s]

2

2vZi

[Pa]

D3) Calculation of total pressure loss of segment i

The total pressure loss of segment is given by sum of friction pressure loss and local pressure loss.

pi = R . l + Z [Pa]

D4) Calculation of the total pressure loss of entire loop

The total pressure loss of entire loop is a sum of total pressure losses of all segments.

ipp [Pa]

Design of a pump Forced heating systems need a pump as mean of water circulation. Proper choice of a pump is based on pressure loss calculation of all the heating system, or at least the main branch.

Two fundamental inputs are the total pressure loss p and maximum mass flow rate M.

In case of high heating system in a building higher than 4 floors is necessary to consider natural pressure given by height and difference in water densities between supply and return temperature.

The design follows diagrams provided by pumps producers such as example at fig. 2.

Czech Technical University in Prague Department of Microenvironmental and Building Services Engineering http://tzb.fsv.cvut.cz BEE1 Heating

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Fig 2. Scheme of a pump diagram

Total head

[Pa]

Characteristic curve of a pump

Characteristic curve of heating system

Point of operation

Mass flow rate [l/s]

The total pressure loss

Maximum mass flow rate

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Tab. 1 Friction losses for copper tubes (tw = 70 C, absolute hydraulic roughness 0.05 mm)

Czech Technical University in Prague Department of Microenvironmental and Building Services Engineering http://tzb.fsv.cvut.cz BEE1 Heating

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Tab. 2 Friction losses for PPR tubes, PN 16 (tw = 70 C, absolute hydraulic roughness 0.01 mm)

Czech Technical University in Prague Department of Microenvironmental and Building Services Engineering http://tzb.fsv.cvut.cz BEE1 Heating

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Tab. 3 Friction losses for PE-X tubes (tw = 70 C, absolute hydraulic roughness 0.01 mm)

Czech Technical University in Prague Department of Microenvironmental and Building Services Engineering http://tzb.fsv.cvut.cz BEE1 Heating

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