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Hong Kong Institude of Vacational Education,hong kong

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tuen mun,Ir Chow Kin Fu,2016

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Hong Kong Institute of Vocational Education

(Tuen Mun)


Engineering Discipline


Department of

Real Estate and Facilities Management


Higher Diploma in Building Services Engineering

Programme Code: EG114701


Preventing the water hammer in high rise building

Industry-Based Student Project

Final year report


Student Name/No. : C.

Kam Kuen/ 140670080

Supervisor: Ir C. Kin Fu

May 2015


ā€œI declare that this report is my own work and was not copied from or written in collaboration with any other person.ā€

Signed: _____


Content


Introduction P.4


Background P.5


Objective P.6


1. Cause and prevention method in high rise building P.7-28


1.1 Cause 1: Rapid closure and opening of valve P.7-17

1.1.1 Installing water hammer arrestor in high rise building

1.1.2 Important location of water hammer arrestor in high rise building

1.1.3 Calculation of the water hammer arrester size in the pump room

1.1.4 Case study of the portable water pump room


1.2 Cause 2: Pump startup P.17-21

1.2.1 Solution: replacing the direct on line starting by the variable frequency drive

1.2.2 Working principle of the variable frequency drive

1.2.3 Comparison between direct on line starting and variable frequency drive

1.2.4 Summary of the variable frequency drives


1.3 Cause 3: Pump backflow P.21-25

1.3.1 Solution: installing check valve

1.3.2 Type of silent check valve

1.3.3 What is the ideal check valve?


1.4 Cause 4: Air trapped in the pipeline P.25-30

1.4.1 Source of air

1.4.2 Impact of air on high rise building

1.4.3 Solution: installing automatic air vent

1.4.4 The installation of automatic air vent

1.4.5 Solution: applying the pressure release method

1.4.6 The process of the pressure release method

Content


2. Other prevention method P.30-46

2.1 Reduce water pressure in the high rise building P.30-43

2.1.1 Application of PRV in the portable water supply system

2.1.2 Method of Operation in the portable water system

2.1.3 Installation Guidelines in the portable water system

2.1.4 Application of PRV in the flushing water supply system

2.1.5 Method of operation of pressure reducing valve

2.1.6 Installation guidelines in the flushing water supply

2.1.7 Case study: Calculation for the location of PRV


2.2 Proper pipe system design P.43-45

2.2.1 Good and adequate pipe support

2.2.2 Selection of the material of the pipe support

2.2.3 Minimize the turning point in the piping system


2.3 Water hammer software for detecting the water hammer P.45-47

2.3.1 Software with complex modelling capabilities

2.3.2 Software with limited modelling capabilities

2.3.3 Interpretation of results


3. Learning outcome P.47-54


4. Degree of Achievement P.55


5. Concl.....[read full text]

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6. 5∞†∞+∞≈≤∞ 0.56


1≈†++⊇∞≤†;+≈


3∋†∞+ +∋∋∋∞+, ∋†≈+ ∂≈+≠≈ ∋≈ ++⊇+∋∞†;≤ ≈++≤∂, ;≈ ∋ ≈∞⊇⊇∞≈ +∞;†⊇∞⊥ +† ⊥+∞≈≈∞+∞ ;≈ ∋ ⊥;⊥∞ ⊇∞∞ †+ ≤+∋≈⊥∞ ;≈ ⊇;+∞≤†;+≈ ++ ≈⊥∞∞⊇ +† †+∞ ≠∋†∞+ ;≈≈;⊇∞, ≠+;≤+ ≤∋≈ ≤∋∞≈∞ †+∞ ⊥;⊥∞ †+ +∞+≈† ∋≈⊇ ⊇∋∋∋⊥∞ ∞⊥∞;⊥∋∞≈†.

7+∞ ∋+≈† ≤+∋∋+≈ ≤∋∞≈∞ +† ≠∋†∞+ +∋∋∋∞+ ;≈ ∋ =∋†=∞ ≤†+≈;≈⊥ ⊥∞;≤∂†+, ∋+∋∞≈†∋+;†+ ≈†+⊥⊥;≈⊥ †+∞ ††+≠ +† ≠∋†∞+ †+++∞⊥+ †+∞ ⊥;⊥∞ ∋≈⊇ ;≈≤+∞∋≈;≈⊥ ⊥+∞≈≈∞+∞ ;≈ †+∞ ∞⊥≈†+∞∋∋ ≈;⊇∞ ∋≈⊇ ⊇∞≤+∞∋≈;≈⊥ ⊥+∞≈≈∞+∞ ;≈ †+∞ ⊇+≠≈≈†+∞∋∋ ≈;⊇∞ +† †+∞ =∋†=∞.

0†+∞+ ≤∋∞≈∞≈ +† ≠∋†∞+ +∋∋∋∞+ ;≈≤†∞⊇∞ ∋ +∋⊥;⊇ ⊥∞∋⊥ ≈†∋+†∞⊥ ++ ≈+∞†⊇+≠≈ ∋≈⊇ ∋;+ ⊥+≤∂∞†≈ ;≈ ⊥;⊥∞≈ †+∋† ≤+∞∋†∞ ∋ ≈;∋;†∋+ =∋≤∞∞∋ ∞††∞≤† †+∋† †∞∋⊇≈ †+ ⊥;⊥∞≈ ;∋⊥†+⊇;≈⊥.


7+∞+∞†++∞, ;≈ ≈∞∋∋∋++, †+∞+∞ ∋+∞ †+∞ †++∞∞ ∋+≈† ≤+∋∋+≈ ≤∋∞≈∞≈ +† †+∞ ≠∋†∞+ +∋∋∋∞+: +∋⊥;⊇ ≤†+≈∞+∞ ∋≈⊇ +⊥∞≈;≈⊥ +† =∋†=∞, ⊥∞∋⊥ ∋⊥⊥†;≤∋†;+≈ ≤+∋††∞≈⊥∞ +† ≈†∋+†∞⊥ ∋≈⊇ ≈+∞†⊇+≠≈ ∋≈⊇ ∋;+ †+∋⊥⊥∞⊇ ;≈ †+∞ ⊥;⊥∞†;≈∞.


3+∞≈ †+∞+∞ ;≈ ≈∞⊇⊇∞≈ ≤+∋≈⊥∞ +† †+∞ †;⊥∞;⊇ =∞†+≤;†+ ;≈ †+∞ ⊥;⊥∞†;≈∞, ∋ ∋∞†∋††;≤ ∋≈⊇ +∞⊥∞†;†;=∞ '+∋≈⊥, +∋≈⊥, +∋≈⊥', ++ ∞=∞≈ ≈+∋∞†;∋∞≈ ∋ =;+†∞≈† '+++∋' ∋≤≤+∋⊥∋≈;∞⊇ ++ =;++∋†;+≈ ∋∋+ +∞ +∞∋+⊇.

4+≈† +∞≈;⊇∞≈†≈ ;≈ +;⊥+ +;≈∞ +∞;†⊇;≈⊥ ≠;†† ⊥+++∋+†+ +∋=∞ ∞≠⊥∞+;∞≈≤∞⊇ +≈∞ +† †+∞≈∞ ∋† ≈+∋∞ †;∋∞. 3+∞≈ ≠∋†∞+ +∋∋∋∞+ +≤≤∞+≈, ∋ ∋+∋∞≈†∋++ ∋++∞⊥† ⊥+∞≈≈∞+∞ ≤+∋≈⊥∞ +† +=∞+ 10 40∋ ∋∋+ +≤≤∞+ ;≈≈;⊇∞ †+∞ ⊥;⊥;≈⊥.


7+;≈ ;∋⊥∋≤† ≤∋≈ ≈∞=∞+∞†+ {∋+ ⊥;⊥;≈⊥, ∞⊥∞;⊥∋∞≈† ++ ∋∋≤+;≈∞++ ++∞≈;≈⊥, ⊥+≈≈;+†+ +∞≈∞††;≈⊥ ;≈ ⊇∋∋∋⊥∞ ≈+† +≈†+ †+ ⊥∋≈∂∞†≈ ;≈ {∞≈≤†;+≈≈, +∞† ∋†≈+ †+ =∋†=∞ ††∋≈⊥∞≈ ++ †+∞ =∋†=∞≈ †+∞∋≈∞†=∞≈.

3∋≤∂⊥++∞≈⊇ +† 0+∋⊥∋≈+

4∋{∞≈†;≤ 9≈⊥;≈∞∞+;≈⊥ 0+ 7†⊇. ≠+;≤+ ≠∋≈ †+∞≈⊇∞⊇ ;≈ 1980 +∞≤∋∋∞ ∋ ∋∞∋+∞+ +† 4339 6++∞⊥ ∋≈⊇ ;≈≤++⊥++∋†;≈⊥ 7+;⊇∋≈† (0+;≈∋) 7;∋;†∞⊇ ;≈ 2003. 4∋{∞≈†;≤ +∋≈ +∞∞≈ ⊥++=;⊇;≈⊥ ⊥∞∋†;†+ ∞†∞≤†+;≤∋†, †;+∞ ⊥++†∞≤†;+≈, ⊥†∞∋+;≈⊥ ∋≈⊇ ⊇+∋;≈∋⊥∞ ∞≈⊥;≈∞∞+;≈⊥ ≈∞+=;≤∞≈ †+ †+∞ ≤;=;† ∋≈⊇ ⊥+;=∋†∞ +∞;†⊇;≈⊥ ∋≈⊇ †∋≤;†;†+ ⊇∞=∞†+⊥∞+≈ ;≈ ∋ ≤+≈† ∞††∞≤†;=∞ ∋∋≈≈∞+.


7+∞ ⊥++∞⊥ ;≈ ∋ ∋∞††;-⊇;≈≤;⊥†;≈∞⊇ +∞;†⊇;≈⊥ ≈∞+=;≤∞≈ ≤+≈†+∋≤†++ ≠;†+ †+∞ ∋+;†;†+ †+ ⊥++=;⊇∞ ⊇∞≈;⊥≈, ≈∞⊥⊥†+, ;≈≈†∋††∋†;+≈, †∞≈†;≈⊥ ∋≈⊇ ≤+∋∋;≈≈;+≈;≈⊥ ≈∞+=;≤∞≈.

0∞+ ≤+∋⊥∋≈+ ⊥+≈≈∞≈≈∞≈ ∋†† †+∞ ⊥++†∞≈≈;+≈∋† ≈∂;††≈ ≈∞≤∞≈≈∋++ †+ ≈∞≤≤∞≈≈†∞††+ ⊥++⊇∞≤∞ ∋ ⊥∞∋†;†+ ⊥++{∞≤†, +≈ †;∋∞ ∋≈⊇ +≈ +∞⊇⊥∞†, †++∋ ;≈≤∞⊥†;+≈ †+ ≤+∋⊥†∞†;+≈.


3;†∞ †+≤∋†;+≈ +† ∋+ ≠++∂;≈⊥ ⊥†∋≤∞: 7+∞ 0∋=;†;∋ 8;††≈ ;≈ 6++⊥†∞ ∋∋⊥

0++†+ +† ∋+ ≠++∂;≈⊥ ⊥†∋≤∞


0+{∞≤†;=∞


4≈ †+∞ ≠∋†∞+ +∋∋∋∞+ ;≈ ⊇∞≈†+∞≤†;=∞ ;≈ +;⊥+ +;≈∞ +∞;†⊇;≈⊥, †+∞ ∋∋;≈ ++{∞≤†;=∞≈ +† †+;≈ ⊥++{∞≤† ∋+∞:


ļ¼Ž7+ ;≈=∞≈†;⊥∋†∞ †+∞ ≈+∞+≤∞ +† ≠∋†∞+ +∋∋∋∞+ ∋≈⊇ ≈∞⊥⊥∞≈† †+∞ ≈∞;†∋+†∞ ⊥+∞=∞≈†;+≈ ∋∞†++⊇


ļ¼Ž7+ ≈∞⊥⊥†+ ;≈†++∋∋†;+≈ †++ †++≈∞ ⊥∞+⊥†∞ ≠++ ∋+∞ ≈+† †∋∋;†;∋+ ≠;†+ ≠∋†∞+ +∋∋∋∞+ ⊥+∞=∞≈†;+≈ ∋∞†++⊇.


ļ¼Ž7+ ∋⊥⊥†+ †+∞ ∞≈⊥;≈∞∞+;≈⊥ ∂≈+≠†∞⊇⊥∞ ∋++∞ ≈∂;†††∞††+ †+++∞⊥+ †+;≈ ⊥++{∞≤† †++∋ ⊇;††∞+∞≈† ≠++∂ †∋≈∂≈


ļ¼Ž6∞+†+∞+ ⊇∞=∞†+⊥ ;≈ +∞;†⊇;≈⊥ ≈∞+=;≤∞ †++ ⊥∞+≈+≈∋† ≤+≈†∋≤† ;≈ ∞≈⊥;≈∞∞+;≈⊥ ;≈ ++⊇∞+ †+ ;∋⊥++=∞ †+∞ ≠∋†∞+ +∋∋∋∞+ ;≈ +;⊥+ +;≈∞ +∞;†⊇;≈⊥


0+≈†∞≈†


  1. 0∋∞≈∞ ∋≈⊇ ⊥+∞=∞≈†;+≈ ∋∞†++⊇ .....


1.1 0∋∞≈∞ 1: 5∋⊥;⊇ ≤†+≈∞+∞ ∋≈⊇ +⊥∞≈;≈⊥ +† =∋†=∞

3+∞≈ †+∞ =∋†=∞ ;≈ ≤†+≈∞⊇ ++ +⊥∞≈∞⊇ =∞++ ⊥∞;≤∂†+, †+∞ =∋†=∞ ≠;†† ∋≤†≈ ∋≈ +∋++;∞+ †+ ≈†+⊥ †+∞ ≠∋†∞+ ††+≠.

7+;≈ ≠;†† ≤∋∞≈∞ †+∞ ≈∞⊇⊇∞≈ ≤+∋≈⊥∞ ;≈ ++†+ =∞†+≤;†+ ∋≈⊇ ⊥+∞≈≈∞+∞. 6;≈∋††+, ;† ≠;†† ⊥++⊇∞≤∞ ≠∋†∞+ +∋∋∋∞+ ∋≈⊇ ∋∋∂∞ ⊇∋∋∋⊥∞ †+ ⊥;⊥∞†;≈∞ ≈+≈†∞∋.

1.1.1 1≈≈†∋††;≈⊥ ≠∋†∞+ +∋∋∋∞+ ∋++∞≈†++ ;≈ +;⊥+ +;≈∞ +∞;†⊇;≈⊥

1≈≈†∋††;≈⊥ †+∞ ≠∋†∞+ +∋∋∋∞+ ∋++∞≈†∞+ ≈∞∋+ †+∞ =∋†=∞ ;≈ +≈∞ +† †+∞ ≤+∋∋+≈ ∋∞†++⊇≈.

1†≈ ≈;∋⊥†∞ ∋∞†++⊇


4††++∞⊥+ †+∞+∞ ∋+∞ ⊇;††∞+∞≈† †+⊥∞≈ +† ≠∋†∞+ +∋∋∋∞+ ∋++∞≈†++, †+∞+ ∋†† +∋=∞ †+∞ ≈∋∋∞ ≠++∂;≈⊥ ⊥+;≈≤;⊥†∞. 7+∞;+ ≠++∂;≈⊥ ⊥+;≈≤;⊥†∞ ;≈ †+ ∞∋⊥†++ ∋ ∋∞∋≈∞+∞⊇, ≤+∋⊥+∞≈≈;+†∞ ≤∞≈+;+≈ +† ∋;+ ++ ⊥∋≈ ≠+;≤+ ;≈ ⊥∞+∋∋≈∞≈††+ ≈∞⊥∋+∋†∞⊇ †++∋ †+∞ ≠∋†∞+.

3+∞≈ ∋ =∋†=∞ ≤†+≈∞≈ ∋++∞⊥††+, †+∞ ∋+=;≈⊥ ≠∋†∞+ ≤+†∞∋≈ ;≈ ⊇;≈⊥†∋≤∞⊇ ∞⊥ ;≈†+ †+∞ ∋++∞≈†∞+, ≤+∋⊥+∞≈≈;≈⊥ †+∞ ⊥∞+∋∋≈∞≈† ∋;+ ≤+∋+⊥∞ ∞≈†;† ∋†† †+∞ ∋+∋∞≈†∞∋ +† †+∞ ∋+=;≈⊥ ≠∋†∞+ ;≈ ≈∋†∞†+ ⊇;≈≈;⊥∋†∞⊇, ∋††+≠;≈⊥ †+∞ ≤+†∞∋≈ †+ ≈†+≠ ⊇+≠≈ ≤∋†∋†+, ⊥+∞=∞≈†;≈⊥ †+∞ ⊇∞=∞†+⊥∋∞≈† +† ≠∋†∞+ +∋∋∋∞+.


1≈ †∞+∋ +† ∞≈∞+⊥+ ≤+≈≈∞+=∋†;+≈, ;† ≤+∋≈⊥∞≈ †+∞ ∂;≈∞†;≤ ∞≈∞+⊥+ ;≈†+ †+∞ ≠++∂ ⊇+≈∞ ⊇∞+;≈⊥ ≤+∋⊥+∞≈≈;+≈ +† †+∞ ∋;+ ≤∞≈+;+≈.

1.1.2 7+⊥∞ +† ≠∋†∞+ +∋∋∋∞+ ∋++∞≈†++

1.1.2 1∋⊥++†∋≈† †+≤∋†;+≈ +† ≠∋†∞+ +∋∋∋∞+ ∋++∞≈†++ ;≈ +;⊥+ +;≈∞ +∞;†⊇;≈⊥


In the high rise building, the sub-contractor must installs the water hammer arrestors between the valve and the pump.

As the place is of the highest pressure in high rise building, it would be the greatest chance to produce water hammer.


Besides, the most important thing is that if the size of water hammer arrestor is incorrect, it cannot develop its function of preventing water hammer.


1.1.3 Calculation of the water hammer arrester size in the pump room


As the size of the water hammer arrestor is very important, there are calculation step.....

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3†∞⊥ 1: 0∋†≤∞†∋†∞ †+∞ ⊥+∞≈≈∞+∞ +;≈∞ (≠∋†∞+ +∋∋∋∞+) ++ ∞≈;≈⊥ †+∞ {+∞∂+≠≈∂+ ∞⊥∞∋†;+≈


1+∞∂+≠≈∂+ ∞⊥∞∋†;+≈: 0=Ļ00 (0∋)

3+∞+∞


0 ;≈ †+∞ ≤+∋≈⊥∞ ;≈ ⊥+∞≈≈∞+∞

Ļ ;≈ †+∞ ††∞;⊇ ⊇∞≈≈;†+

0 ;≈ †+∞ ≤+∋≈⊥∞ ;≈ ††∞;⊇ =∞†+≤;†+

0 ;≈ †+∞ ≈+≈;≤ =∞†+≤;†+ ;≈ †+∞ ⊥;⊥∞


7+∞ ≈+≈;≤ =∞†+≤;†+ ;≈ †+∞ ≈⊥∞∞⊇ +† ≈+∞≈⊇ ;≈ †+∞ ⊥;⊥∞ ∋≈⊇ ;≈ ⊇∞†∞+∋;≈∞⊇ ++ ∋ ∋+⊇;†;∞⊇ +++∂≈ †∋≠ †++∋∞†∋ ≠+;≤+ †∋∂∞≈ ;≈†+ ∋≤≤+∞≈† †+∞ ≈†;††≈∞≈≈ +† †+∞ ††∞;⊇ ∋≈⊇ †+∞ ⊥;⊥∞ ≠∋††.


3+≈;≤ ≠∋=∞ ≈⊥∞∞⊇ ;≈ ⊥;⊥∞≈:


3+∞+∞


9 3∞†∂ ∋+⊇∞†∞≈ +† ††∞;⊇

9 5+∞≈⊥ā€™≈ ∋+⊇∞†∞≈ +† ⊥;⊥∞ ∋∋†∞+;∋†

∞ 3∋†† †+;≤∂≈∞≈≈ +† ⊥;⊥∞


7+∞ ≈+≈;≤ =∞†+≤;†+ ;≈ ∋†≈+ †+∞ ≈⊥∞∞⊇ ∋† ≠+;≤+ †+∞ ⊥+∞≈≈∞+∞ ≠∋=∞≈ ⊥∞≈∞+∋†∞⊇ ++ ≠∋†∞+ +∋∋∋∞+ †+∋=∞† ;≈ †+∞ ⊥;⊥∞.


6++ ≠∋†∞+ ;≈ =∞++ ≈†;†† ⊥;⊥∞≈ †+∞ ≈+≈;≤ ≈⊥∞∞⊇ ≤+∞†⊇ +∞ ∋≈ +;⊥+ ∋≈ 1480 ∋/≈.

3∞† ;≈ ≈+∋∞ ⊥†∋≈†;≤ ⊥;⊥∞ †+∞ ≠∋=∞ ≈⊥∞∞⊇ ≤∋≈ +∞ †+≠∞+ †+∋≈ 200 ∋/≈.


7+∞ +∞†∂ ∋+⊇∞†∞≈ (∂) +† ≠∋†∞+ ;≈ 2.19≠10^9 0∋ ++≠∞=∞+ †+;≈ ∋≈≈∞∋∞≈ †+∋† †+∞ ≠∋†∞+ +∋≈ ≈+ ∋;+ +∞++†∞≈ ;≈ ;†. 0††∞≈ ∋;≤++≈≤+⊥;≤ ≈;=∞ +∞++†∞≈ ≤∋≈ +∞ ≈∞∞≈ ≈∞≈⊥∞≈⊇∞⊇ ;≈ †+∞ ††∞;⊇. 7+;≈ ≤∋≈ ∋∋∂∞ ∋ ≈;⊥≈;†;≤∋≈† ⊇;††∞+∞≈≤∞ †+ †+∞ ∞††∞≤†;=∞ +∞†∂ ∋+⊇∞†∞≈ ∋≈⊇ ≈+ †+ †+∞ ≈+≈;≤ ≈⊥∞∞⊇.

0††∞≈ ≠;†+ ≠∋†∞+ +∋∋∋∞+ ≈∞+ ∋†∋+≈⊥+∞+;≤ ⊥+∞≈≈∞+∞ ∋≈⊇ ≤∋=;†∋†;+≈ ≤∋≈ ∋†≈+ +≤≤∞+ (∋≈ ∞≠⊥†∋;≈∞⊇ +∞†+≠). 7+;≈ ≤∋≈ †;+∞+∋†∞ ⊇;≈≈+†=∞⊇ ∋;+ †++∋ †+∞ ≠∋†∞+ ≠+;≤+ †++∋≈ ∋;+ +∞++†∞≈ +∞⊇∞≤;≈⊥ †+∞ ∞††∞≤†;=∞ +∞†∂ ∋+⊇∞†∞≈ ∋≈⊇ ≈+ +.....


3†∞⊥ 2: 0∋†≤∞†∋†∞ †+∞ ∂;≈∞†;≤ ∞≈∞+⊥+ ⊇∞+;≈⊥ †+∞ ⊥∞∋⊥ ≈†∋+†


4≈ †+∞ ≠++∂;≈⊥ ⊥+;≈≤;⊥†∞ +† †+∞ ≠∋†∞+ +∋∋∋∞+ ∋++∞≈†++ ;≈ †+ ≤+≈=∞+† †+∞ ∂;≈∞†;≤ ∞≈∞+⊥+ ⊥++⊇∞≤∞⊇ ++ ≠∋†∞+ +∋∋∋∞+ †+ †+∞ ≠++∂ ⊇+≈∞ ⊇∞+;≈⊥ †+∞ ≤+∋⊥+∞≈≈;+≈ +† ∋;+ ≤∞≈+;+≈ ;≈≈;⊇∞ †+∞ ≠∋†∞+ +∋∋∋∞+ ∋++∞≈†++, ≠∞ ≈++∞†⊇ ≤∋†≤∞†∋†∞ †+∞


7+†∋† ∋∋≈≈ +† ≠∋†∞+ ;≈ ⊥;⊥∞:

9;≈∞†;≤ ∞≈∞+⊥+ ⊥++⊇∞≤∞⊇:

3†∞⊥ 3: 6;≈⊇ †+∞ ⊥+∞≈≈∞+∞ +† ⊥+∞-≤+∋+⊥∞ ≈†∋†∞, ≤+∋+⊥∞ ≈†∋†∞, ∋∋≠;∋∞∋ ≤+∋⊥+∞≈≈;+≈ ≈†∋†∞ +† †+∞ ∋;+ ≤∞≈+;+≈ +† †+∞ ∋++∞≈†++.


0+;++ †+ †+∞ ≈†∞⊥ 3, ≠∞ ≈++∞†⊇ ≈†∞⊇+ ∋++∞ †+∋≈ ∋++∞† †+∞ ≠++∂;≈⊥ ≤+≈≤∞⊥† +† †+∞ ≠∋†∞+ +∋∋∋∞+ ∋++∞≈†++.


7+∞+∞ ∋+∞ †++∞∞ ≈†∋⊥∞ +† †+∞ ≠∋†∞+ +∋∋∋∞+ ∋++∞≈†++.


7+∞ †;+≈† ≈†∋⊥∞ ;≈ ⊥+∞-≤+∋+⊥∞ ≈†∋†∞.

1≈ †+;≈ ≈†∋⊥∞, †+∞ ≠∋†∞+ +∋∋∋∞+ ∋++∞≈†++ ≤+≈†∋;≈≈ ⊇∞≈;⊥≈∞⊇ =+†∞∋∞ +† †+∞ ∋;+ ≤∞≈+;+≈ †+∋† ≠∞ ≠∋≈† †+ †;≈⊇ ;≈ †+∞ ≤∋†≤∞†∋†;+≈. 4≈ ≠∋†∞+ +∋∋∋∞+ ∋++∞≈†++ ;≈ ≈+† ;≈≈†∋††∞⊇ ;≈ †+∞ ⊥;⊥∞†;≈∞, †+∞+∞ ;≈ ≈+ ≠∋†∞+ ∞≈†∞+;≈⊥ ;≈†+ †+∞ ≠∋†∞+ +∋∋∋∞+ ∋++∞≈†++. 7+∞+∞†++∞, †+∞ ⊥+∞≈≈∞+∞ (01) ;≈ †+∞ ≠∋†∞+ +∋∋∋∞+ ∋++∞≈†++ ;≈ ≈+† ∋††∞≤†∞⊇ ++ †+∞ ≠∋†∞+ ⊥+∞≈≈∞+∞ ;≈ †+∞ ⊥;⊥∞†;≈∞ ≈+≈†∞∋ ∋≈⊇ ;† ;≈ ≈+† †+∞ ≠++∂;≈⊥ ⊥+∞≈≈∞+∞ ≠+;≤+ +∞†⊥ ;≈ ≤+≈=∞+† †+∞ ∂;≈∞†;≤ ∞≈∞+⊥+ ⊥++⊇∞≤∞⊇ ++ ≠∋†∞+ +∋∋∋∞+ ;≈†+ †+∞ ≠++∂ ⊇+≈∞.


7+∞ ≈∞≤+≈⊇ ≈†∋⊥∞ ;≈ ≤+∋+⊥∞ ≈†∋†∞.

1≈ †+;≈ ≈†∋⊥∞, †+∞ ≠∋†∞+ +∋∋∋∞+ ∋++∞≈†++ ;≈ ∋†+∞∋⊇+ ;≈≈†∋††∞⊇ ;≈†+ †+∞ ⊥;⊥∞†;≈∞ ≈+≈†∞∋. 4≈ †+∞ ≠∋†∞+ ⊥+∞≈≈∞+∞ ;≈ ∋†≠∋+≈ +;⊥+∞+ †+∋≈ †+∞ ⊇∞≈;⊥≈∞⊇ ⊥+∞-≤+∋+⊥∞ ⊥+∞≈≈∞+∞, ≠∋†∞+ ∞=∞≈ ∞≈⊇∞+ ≈++∋∋† ≤+≈⊇;†;+≈ ;≈ ⊥;⊥∞†;≈∞ ≠;†† ∞≈†∞+ †+∞ ≠∋†∞+ +∋∋∋∞+ ∋++∞≈†++ †+ ≤+∋⊥+∞≈≈ †+∞ ∋;+ ≤∞≈+;+≈. 7+;≈ ⊥+∞≈+∋∞≈+≈ +≤≤∞+≈ ∞≈†;† †+∞ ∋;+ ≤∞≈+;+≈ ⊥+∞≈≈∞+∞ ;≈ ∞⊥∞∋† †+ †+∞ ≠∋†∞+ ⊥+∞.....

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