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GS Engineering & Construction Corp. Calculation Sheet - Pump Hydraulics

TITLE :

Doc. No.

:

Rev. No.

:

Rev. Date

:

Page

:

0 28 May. 2013 1

of

3

Calculation Sheet - Pump Hydraulics

Classification

REVISION STATUS :

Name

Rev. No

Date

0

28 May. 2013

Prepared by Ammar Alobud

Signature Date Reviewed :

:

28 May. 2013

GS Engineering & Construction Corp.

Standard Form

Descriptions

Remarks

First Issue

Checked by

Approved by

GS Engineering & Construction Corp. TITLE :

Calculation Sheet - Pump Hydraulics

Doc. No.

:

Rev. No.

:

Rev. Date

:

Page

:

0 0 28 May. 2013 2

of

3

1 2

1. Introduction

3 4

이 Calculation Sheet는 Process Engineer가 빈번하게 수행하는 Pump Hydraulics Calculation을 정확하고 일관성 있게 계산 할 수 있도록 하기

5

위하여 준비되었다.

6 7

이 Calculation Sheet는 하나의 Pump에 대하여 가간단한 scheme을 sketch하고 fluid의 properties를 입력한 후 그에 따라 정해진 line의

8

pressure drop을 구하고 pump hydraulic을 수행하여 그 결과를 pressure profile에 정리되도록 구성하였다.

9 10

Fluid type은 Liquid flow, Vapor flow, Mixed flow로 나누어지므로 line differential pressure calculation sheet를 3가지로 나누어 두어서 fluid 종류에

11

따라 달리 구해지는 결과를 정리할수 있도록 하였다. 그 외에 line의 fitting 구성에 따라 변경되는 equivalent length를 계산하기 위한

12

'EQ_L Calcaulation' sheet를 추가하였다. 또한, line pressure drop을 계산하기 위한 Pipe line의 ID를 정리한 sheet가 포함되었으며, sketch의

13

편의를 위해 가각 equipment 및 element의 그림을 Drawing sheet에 추가하였다.

14 15

Control Valve의 pressure drop calculation method는 no control valve, Conventional, LDM 중 선택하여 계산 되도록 하였으며 Manual input을

16

이용한 방법도 포함하여 project specification을 따르거나 혹은 상황에 따라 달리 적용해야 할 경우에 사용할 수 있도록 하였다.

17 18

Report에는 Coversheet, Pump Calculation, Sketch, Pressure Profile이 포함되고, Equivalent Length와 Line Pressure drop calculation은

19

계산시 활용하며, Guideline과 Equivalent Length, Pipe ID는 계산시 참고자료로 사용한다.

20 21

이 Calculation Sheet에 Green Blank는 Calculation을 위하여 사용자가 직접 넣어주어야 하는 가값이며 Yellow Blank는 주어진 정보를 기준으로

22

자동으로 계산되는 가값이다. 가각 Sheet에 대한 소개는 다음 Section에 기술하였다.

23 24

2. Description for Each Worksheet

25 26

Pump Calculation

27

양식은 Hydrosys output excel file을 참고하였으며, Green Blank를 직접 넣어주면 Yellow Blank에서 계산되어 자동으로 fill-up 된다.

28

Pump suction은 Rated flow 에서의 입력가값을 기준으로 Normal과 Minimum flow에서의 가값들을 유도하였으며, Pump discharge는 Normal flow

29

에서의 가값을 기준으로 Rated와 Minimum flow에서의 가값들이 자동으로 계산된다.

30

Control Valve pressure drop은 Control valve calculation method, control valve type, reflux 유무에 따라 달리 계산되게 하였다.

31

이를 선정해 주면 가각 방법에 따라 달리 계산되어, Control valve DP란에 자동으로 입력된다.

32 33

Sketch

34

해당 Pump Circuit을 Hydraulic calculation의 편의를 위해 개략적으로 그린다. User의 편리함과 drawing의 통일성을 위해 print 되지 않는 영역에

35

symbols을 그려놓았고, 이를 복사에서 사용하면 된다. Job no.와 Project name, Client는 Coversheet에서 불러오며 그밖의 Green Blank는

36

User가 직접 채워 넣는다. 그러면, Pump Calculation, Pressure Profile, Equivalent Length Calculation sheet 도 자동으로 변경된다.

37

사용자가 더 많은 data를 sketch를 통해 가간략히 확인하고 싶을 경우, 직접 input하거나 다른 sheet에서 계산된 결과가값을 불러오면 된다.

38 39

Pressure Profile

40

Case별로 sketch가 다르고 equipment, instrument의 개수와 종류가 다양하기 때문에, Pressure Profile의 공란은 user가 직접 입력해야 한다.

41

Section 혹은 equipment, instrument 별로 pressure drop을 입력 하거나 link시키고, 가각 point에서 static head를 계산하여 inlet pressure를 계산한다.

42

양식은 HydroSys output excel file을 참고하였다.

43

External Fire Case에 대한 Relieving Load를 계산하는 경우 고려되어야 하는 Environment Factor, Latent Heat을 Table,

44

그래프를 통해 도출할 수 있다.

45 46

GS Engineering & Construction Corp. TITLE :

Calculation Sheet - Pump Hydraulics

Doc. No.

:

Rev. No.

:

Rev. Date

:

Page

:

0 0 28 May. 2013 3

of

3

1 2

EQ_L Calculation

3

User가 Nominal Diameter와 Enlarger, Reducer의 size를 결정하고, 가각종 fitting의 개수를 green blank에 입력하면 'EQ_L Calculation' sheet는

4

yellow blank에 'Euivalent Length' sheet에서 data를 읽어온후 합산을 한다. Overdesign의 사용 유무와 사용시 %를 입력하면 최종적으로

5

계산된 equivalent length가 표시된다.

6

가각 section 및 segment 별로 나눠서 계산한 뒤 line pressure drop의 100m 당 pressure drop과 함께 'Pressrue Profile'에 정리한다. 이를 곱하여,

7

pressure drop을 계산하면, 'Pressure Profile'이 완성된다.

8 9

Liquid

10

Line Differential Pressure Calculation for Liquid Flow을 위한 sheet이다. Pump circuit의 liquid line의 pressure drop을 darcy equiation을 이용하여

11

계산한다. Flow rate, density, viscosity, roughness와 nominal size와 schedule을 통해 계산된 pipe ID로 100m당 pressure drop과 velocity를

12

구하고, 'Guideline'을 참고하여 pressure drop과 velocity limit을 입력하여 비교한다.

13

여기서 구해진 100m당 pressure drop은 앞에서 계산된 equivalent length와 함께 line의 pressure loss를 구하는데 사용된다.

14

이 sheet는 "GDP-6BDT-404 Line Sizing Calculation sheet"를 참고하였다.

15 16

Two_Phase

17

유체의 Control valve 후단 압력가강하에 따른 상변화나, Heat exchanger 에 의한 온도변화에 따른 상변화등, Pump circuit에서 발생할 수 있는

18

two phase fluid의 line pressure drop 계산을 위해 첨부하였다.

19

Fluid 의 Properties와 condition을 입력하면, Homogeneous model과 Duckler method를 이용하여 pressure drop 및 velocity, vapor volume

20

fraction을 계산하고, Baker Chart와 G-W Chart를 통해 flow regime, Average / Inplace density를 계산한다.

21

이 sheet는 "GDP-6BDT-404 Line Sizing Calculation sheet"를 참고하였다.

22 23

Vapor

24

Line Differential Pressure Calculation for Vapor Flow을 위한 sheet이다. Pump circuit에 포함될 수 있는 vapor line을 isothermal method를 통해

25

계산한다. Flow rate, molecular weight, viscosity, Z, k(Cp/Cv), pressure, know Pressure(upstream or downstream), temperature를 입력하면

26

100m당 pressure drop과 velocity가 계산된다.

27

이 sheet는 "GDP-6BDT-404 Line Sizing Calculation sheet"를 참고하였다.

28 29

Guideline

30

Line Differential Pressure Calculation에서 계산되는 pressure drop과 velocity의 limit를 제시해 주는 guideline이다.

31

Process, 용도, line의 위치에 따라 limit가 다르기 때문에 적절히 적용해야 한다.

32 33

Equivalent Legth

34

Equivalent Legth calculation에 쓰이는 database로 LDM의 chart를 옮겨 놓았다.

35 36

Pipe_ID

37

Line differential pressure calculation에서 line의 nominal diameter와 schedule을 입력하면, 이 sheet에서 ID를 읽어와서 계산에 사용된다.

38 39 40 41 42 43 44 45 46

GS Engineering & Construction Corp. Calculation Sheet - Pump Hydraulics

TITLE :

Doc. No.

:

Rev. No.

:

Rev. Date

:

Page

:

1 of X

Calculation Sheet - Pump Hydraulics

REVISION STATUS :

Name

Project No. Project Name Clients

: : :

Item No. Service

: :

Rev. No

Prepared by Ammar Alobud

Signature Date Reviewed :

GS Engineering & Construction Corp.

111580 RABIGH PHASE II ARAMCO

Date

Descriptions

Checked by

Remarks

Approved by

GS Engineering & Construction Corp. TITLE :

Calculation Sheet - Pump Hydraulics

Doc. No.

:

Rev. No.

:

Rev. Date

:

Page

:

0

2 of X

SHEETS REVISED THIS ISSUE Sheet No.

Sheet No.

Sheet No.

NOTES; (a)

The revised parts shall be written in bold character with shade background, and the revision status is shown on the last column of the calculation sheet. If the revised part is a cancelled text, it shall be identified in shade background only.

GS Engineering & Construction Corp.

Sheet No.

heet - Pump Hydraulics

Approved by

S REVISED THIS ISSUE Sheet No.

JOB NO NOTE - These data are confidential and the property of GSE&C and shall not be disclosed to others or reproduced in any manner or used for any purpose whatsoever except by written permission or as provided in a signed agreement with GSE&C relating to such data.

PROJECT

111580 RABIGH PHASE II

UNIT NAME PUMP CALCULATION WORK SHEET CLIENT

ARAMCO

LOCATION

Rabigh,KSA

DESCRIPTION SR NAPHTHA FEED PUMPS

PUMP

S030-P-0900A/B 18. FLOW RATE

SUCTION END

19. STATIC HEAD

m

-0.3

kg/cm^2

-0.02

CONTROL VALVE

FV-2901

21. TERMINAL PRESS. AT LIQUID LEVEL kg/cm^2[g]

9.80

22. MISCELLANEOUS LOSSES

kg/cm^2

0.00

23. FLOW METER LOSSES

kg/cm^2

0.20

kg/cm^2[g]

9.98

SPECIAL REQUIREMENTS

Y

24. TOTAL DISCH. FIXED PRESS.

12

VARIABLE LOSSES

14

PUMP FLUID CHARACTERISTICS

15

FLUID NAME

16

PUMPING TEMP.

17

VAPOR PRESS.

18

SPECIFIC GRAVITY

19

VISCOSITY

SR NAPHTHA

0.00 0.00

0.690

(C) MISCELLANEOUS

0.00

0.00

0.400

2X. MISCELLANEOUS LOSSES

kg/cm^2

0.00

0.00

27. TOTAL DISCH. VARIABLE

kg/cm^2

###

###

###

kg/cm^2

###

###

###

kg/cm^2

###

###

###

kg/cm^2

###

###

###

###

###

###

###

###

###

kg/cm^2

4.650

0.000

0.00

kg/cm^2

###

###

###

m

###

###

###

kg/cm^2[g]

###

###

###

kW

###

###

###

%

###

###

###

kW

###

###

###

DESIGN FOR CONTINUOUS MIN FLOW OF

NOR

RTD

MIN

m^3/h

565

622

225

%

100

110

40

(NO.25 + NO.2X + NO.26) DIFFERENTIAL 28. TOTAL VARIABLE LOSSES (NO.10 + NO.27)

25

29. TOTAL FIXED PRESS. CALCULATIONS

27

(NO.24 - NO.6)

SUCTION SYSTEM

30. TOTAL LOSSES

28

FIXED PRESSURE

29

1. ELEVATION OF MIN. LIQUID LEVEL

mm

0

30

2. ELEVATION OF PUMP BASE PLATE

mm

300

31

3. MIN. STATIC HEAD (NO.1 - NO.2)

32

4. MIN. STATIC PRESS.

(NO.28 + NO.29)

m

-0.30

kg/cm^2

#VALUE!

31. % VARIABLE LOSS (NO.28 / NO.30 x 100) 32. % TOTAL LOSS FOR CONTROL VALVE (NO.33/NO.30 x 100)

(NO.3 x SpGr / 10.2)

33. CONTROL VALVE DP

34

5. MIN. PRESS. AT LIQUID LEVEL

kg/cm^2[g]

1.00

35

6. TOTAL SUC. FIXED PRESS.

kg/cm^2[g]

#VALUE!

(NO.32 x NO.30 / 100) OR (NO.34 - NO.30) 34. PUMP DIFFERENTIAL PRESS.

(NO.4 + NO. 5)

(NO.30 + NO.33)

37

VARIABLE LOSSES

38

7. SUCTION LINE LOSSES

kg/cm^2

###

###

###

39

8. MISCELLANEOUS LOSSES

kg/cm^2

0.00

0.00

0.00

40

9. SUCTION EQUIPMENT LOSSES

kg/cm^2

0.06

0.07

0.01

41

10. TOTAL SUC. VARIABLE LOSSES

NOR

RTD

MIN

kg/cm^2

###

###

###

35. PUMP DIFFERENTIAL HEAD 36. PUMP DISCH. PRESS (NO.11 + NO.34) POWER

(NO.7 + NO.8 + NO.9)

37. HYDRAULIC POWER

11. PUMP SUC. PRESS.

kg/cm^2[g]

###

###

###

(NO.6 - NO.10)

45

###

0.00

PUMP CAPACITY

26

MIN

### 0.00

24

3x. ESTIMATED EFFICIENCY NPSH

12. PUMP SUC. PRESS. AT RATED

kg/cm^2[a]

#VALUE!

38. ESTIMATED BRAKE HORSE POWER

FLOW (NO.11 + 1 atm)

(NO.37 / EFF.)

13. RECIP. PUMP SUCTION

kg/cm^2

0.00

ESTIMATED SHUTOFF PRESSURE

ACCEL. LOSSES

50

14. VAPOR PRESS.

51

15. AVAILABLE PRESS

39. MAX. SUCTION PRESS kg/cm^2

0.51

(AS PER SPECIFICATION)

kg/cm^2[a]

#VALUE!

40. SHUTOFF DIFFERENTIAL

(NO.12 - NO.13 - NO.14) PLATE (NO.15 x 10.2 / SpGr)

55

17. Estimated NPSH REQUIRED

kg/cm^2[g]

1.04

kg/cm^2

#VALUE!

kg/cm^2[g]

#VALUE!

(AS PER SPECIFICATION)

16. NPSH AVAILABLE AT PUMP BASE

54 56

kg/cm^2

RTD

(B) HEATERS

OPERATING FLOW PERCENTAGE

53

26. EQUIPMENT LOSSES

###

(A) EXCHANGERS

VOLUMETRIC FLOW RATE @ PT

52

kg/cm^2

40

23

49

NOR

25. DISCH. LINE LOSSES

0.507

22

48

225

degC

21

47

MIN

kg/cm^2 cp

20

46

0

(SUM OF NO. 20 THRU 23)

13

44

1

(NO.19 x SpGr / 10.2)

11

43

622

20. STATIC PRESS.

GOVERNING PATH ?

42

RTD

565

B.L.

10

36

NOR m^3/h

DISCHARGE END

09

33

OF

FIXED PRESSURE

07 08

1

REV.

DISCHARGE SYSTEM

05 06

PAGE

GENERAL

03 04

0 DATE

MAIN CIRCUIT

01 02

0

CASE

m

#VALUE!

41. SHUTOFF DISCH. PRESS (NO.39 + NO.40)

m

#VALUE!

(N=10000 for water, 3550 rpm) REVISION DATE BY/CHECKED

GS ENGINEERING & CONSTRUCTION

/

/

/

/

/

/

/

NOTE - These data are confidential and the property of GSE&C and shall not be disclosed to others or reproduced in any manner or used for any purpose whatsoever except by written permission or as pr

JOB NO

PROCESS HYDRAULICS - PRESSURE PROFILE SUMMARY SHEET

111580 UNIT NAME

0 CASE

0

PROJECT

RABIGH PHASE II

MAIN CIRCUIT

0 REV

0

CLIENT

ARAMCO

SEG CIRCUIT

0 DATE

12/30/1899

LOCATION

RABIGH , KSA

DESCRIPTION

SR NAPHTHA FEED PUMP

PAGE

1

OF

1

01 02

Ciruit Components

03

Normal 100.0

Maximum

%

110.1

Minimum

%

39.8

%

04

Inlet Press Press Drop Inlet Press Press Drop Inlet Press Press Drop

05

kg/cm^2[g]

kg/cm^2 kg/cm^2[g]

kg/cm^2 kg/cm^2[g]

kg/cm^2

Nominal

Sch

Inside

Equiv.

Specific

Diameter

No

Diameter

Length

Press

in

m

^2/100m

m/s

10.020

75

#VALUE!

#VALUE!

Pipe in

Velocity

Static

Nozzle

Equip

Flow

Head

Elev

Elev

Rate

mm

mm

mm

kg/hr

Drop

Class

06 07

1203F Splitter Receiver

1.00

0.00

1.00

0.00

1.00

0.00

08

Section 1

1.00

#VALUE!

1.00

#VALUE!

1.00

#VALUE!

09

Static Head

10

SPLIT

11

Section 2

12 14

Section 3

16

Static Head FV315

18

Section 3-1

19

Static Head

20

B.L.

21

Section 4

22

Static Head

23

1813C

24

Section 5

25 26 27

Section 6

28

Static Head

29

1806C

30

Section 6-1

31

Static Head

32

HV045

33

Section 7

34

Static Head

35

0.00

#VALUE!

0.00

#VALUE!

0.00

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

0.00

#VALUE!

0.00

#VALUE!

0.00

0.02

PV100

36 37 38 39 GS ENGINEERING & CONSTRUCTION

0.02

-0.02 4.65

#VALUE!

0.00

#VALUE!

0.00

#VALUE!

0.00

#VALUE!

0.00

#VALUE!

0.00

0.00

0.00

#VALUE!

0.00

#VALUE!

0.00

#VALUE!

0.00

#VALUE!

0.00

#VALUE!

0.00

0.00

0.58

#VALUE!

0.70

#VALUE!

0.11

#VALUE!

0.00

#VALUE!

0.00

#VALUE!

0.00

0.00

0.28

#VALUE!

0.34

#VALUE!

0.05

#VALUE!

0.00

#VALUE!

0.00

#VALUE!

0.00

0.95

0.29

#VALUE!

0.35

#VALUE!

0.06

#VALUE!

0.00

#VALUE!

0.00

#VALUE!

0.00

-0.91

0.00

#VALUE!

0.00

#VALUE!

0.00

#VALUE!

0.00

#VALUE!

0.00

#VALUE!

0.00

#VALUE!

0.00

0.00 #VALUE!

0.00

#VALUE!

0.00 #VALUE!

0.00

391,000 300 300

4

40

4.026

0

0.00

0.0

0 -300 0

4

40

4.026

0

0.00

0.0

0 0 0

4

40

4.026

0

0.00

0.0

0 0 0

4

40

4.026

0

0.00

0.0

0 0 0

4

40

4.026

0

0.00

0.0

0 14000 14000

4

40

4.026

0

0.00

0.0

-0.91

#VALUE!

0.00

#VALUE!

0.95

#VALUE!

-0.91

3800

0.00

#VALUE!

0.95

6.065

0.00

#VALUE!

0.00

40

0.00

#VALUE!

0.00

0 6

-0.02

#VALUE!

391,000 -6850

0.02

-0.02

0.00

40

-0.46

#VALUE!

Static Head 1811F

-0.46

#VALUE! Static Head

1214J/JA

15 17

-0.46

6850 10

0 -13400 600

4

40

4.026

0

0.00

0.0

0 0 600

NOTE - These data are confidential and the property of GSE&C and shall not be disclosed to others or reproduced in any manner or used for any purpose whatsoever except by written permission or as pr

JOB NO

PROCESS HYDRAULICS - HYDRAULIC CIRCUIT DIAGRAM

111580 UNIT NAME

PROJECT

RABIGH PHASE II

MAIN CIRCUIT

REV

CLIENT

ARAMCO

SEG CIRCUIT

DATE

LOCATION

RABIGH , KSA

DESCRIPTION

BL

12" SEC2

SEC1 16" STR0900A

T

Notes:

1 2 3 4 5

GS ENGINEERING & CONSTRUCTION

CASE

S030-P-0900A/B

SR NAPHTHA FEED PUMP

NAPHTHA REFORMER (R410)

PAGE

0

1

OF

1

Rev

Date

Made by

Checked by

Equivalent Summary Sheet Client :

ARAMCO

JOB No.:

Location :

RABIGH , KSA

Unit No. :

Project :

RABIGH PHASE II

Unit Name :

111580

Main Circuit

0

Circuit Description

SR NAPHTHA FEED PUMP

0

Line No. : Stream No : From : To : Nominal Dia. Straight Length 90° elbow 45° elbow Tee Glove Fully Open Valve

Check Valve Three Way Cock Valve Ball Valve Plug Valve Straight

[m] Short Radius Long Radius Short Radius Long Radius Flow Branch Flow Through 90%φ 60%φ 45%φ Swing Ball Lift Straight Flow Flow Branch Full Port Reduced Port Full Port Reduced Port

Straight Cock Valve Butterfly Valve Diaphram Valve Gate Valve Fully Open Angle Valve 180% Return bend 90% Return bend 45% Return bend 90% Meter bend

Section 1

Section 2

TIE-IN POINT

S040-P-0810 A/B

S040-P-0810 A/B

161 2

2 Short Radius Long Radius Short Radius Long Radius Short Radius Long Radius 3 meter 4 meter

Reducers

From To From To

Calculated Equiv. Length (m) Overdesign % is Applied ? (Y/N) Overdesign % if Applied ?

BL

121

75.0

Exit Inward Projecting Entrance Sharp edged Entrance Slightly rounded Entrance 'Well rounded Entrance Enlargers

15

1 NONE NONE1

1 NONE

13 3800.0

0 15.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 NONE NONE1

2

2

2

1 NONE 1 NONE

0 12.2 0 0 0 12.2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 NONE 1 NONE 98

NONE

1 NONE 1 NONE

0

1 NONE 1 NONE

1 NONE 1 NONE

0

1 NONE 1 NONE

3,831

N 5

Rev

Date

Made by

Checked by

Equivalent Summary Sheet Client :

ARAMCO

JOB No.:

Location :

RABIGH , KSA

Unit No. :

Project :

RABIGH PHASE II

Unit Name : 75

Selected Equiv. Length (m)

111580

Main Circuit

0

Circuit Description

SR NAPHTHA FEED PUMP

0 3,800

-

Client :

ARAMCO

Location :

RABIGH , KSA

Project :

RABIGH PHASE II Line No. : Stream No : From : To : Nominal Dia. NONE

Straight Length 90° elbow 45° elbow Tee Glove Fully Open Valve

Check Valve Three Way Cock Valve Ball Valve Plug Valve Straight

1

[m] Short Radius Long Radius Short Radius Long Radius Flow Branch Flow Through 90%φ 60%φ 45%φ Swing Ball Lift Straight Flow Flow Branch Full Port Reduced Port Full Port Reduced Port

Straight Cock Valve Butterfly Valve Diaphram Valve Gate Valve Fully Open Angle Valve 180% Return bend 90% Return bend 45% Return bend 90% Meter bend

Short Radius Long Radius Short Radius Long Radius Short Radius Long Radius 3 meter 4 meter

Exit Inward Projecting Entrance Sharp edged Entrance Slightly rounded Entrance 'Well rounded Entrance Enlargers

Reducers

From To From To

Calculated Equiv. Length (m) Overdesign % is Applied ? (Y/N) Overdesign % if Applied ?

0 NONE NONE NONE 0 NONE NONE NONE N 5

Client :

ARAMCO

Location :

RABIGH , KSA

Project :

RABIGH PHASE II

Selected Equiv. Length (m)

-

Line Differential Pressure Calculation for Liquid Flow Project No. : Project Name :

Revision No. : Revision Date: Flow rate

ID

Service

2

Section 1 From : To : Line No.: Note : Section 2 From : To : Line No.: Note :

TIE-IN POINT S040-P-0810 A/B

S040-P-0810 A/B BL

Viscosity

Nominal size

Pipe ID

Schedule

inch

Rough F.

Press.

Temp.

Press. Drop limit

1 2

391,000 430,100

692.0 692.0

0.400 0.400

16 16

40 40

#VALUE! #VALUE!

0.00015 0.00015

40.0 40.0

(kg/cm2)/ 100m 0.12 0.12

1 2

391,000 430,100

692.0 692.0

0.400 0.400

12 12

40 40

#VALUE! #VALUE!

0.00015 0.00015

40.0 40.0

0.12 0.12

kg/hr 1

Density

Case kg/m3

cP

ft

kg/cm2 g

C

o

Press. Drop

Velocity

Velocity limit

(kg/cm2))/ 100m #VALUE! #VALUE!

#VALUE! #VALUE!

1.83 1.83

#VALUE! #VALUE!

#VALUE! #VALUE!

1.83 1.83

m/sec

Darcy Friction Factor Constant

Pipe ID

P i p Flow rate e

Nre

m/sec

inch

I D M

F

A

B

C

m3/hr

#VALUE! #VALUE!

### ###

### ###

### ###

### #VALUE! ### #VALUE!

565.0 ### 621.5 ###

#VALUE! #VALUE!

### ###

### ###

### ###

### #VALUE! ### #VALUE!

565.0 ### 621.5 ###

# #

# #

# #

# #

# #

# #

# #

# #

Line Differential Pressure Calculation for Vapor Flow Project No. : Project Name :

Revision No. : Revision Date: Flow rate

ID

Service

Case

MW kg/hr

3 From : To : Line No.: Note : 4 From : To : Line No.: Note :

1 2 3 4 1 2 3 4

Visco.

11,561 11,561 1,324 1,324

Nm3/hr 14,396 14,396 1,649 1,649 #DIV/0! #DIV/0! #DIV/0! #DIV/0!

cP 18.00 18.00 18.00 18.00

0.010 0.010 0.010 0.010

Comp. Factor

specific heat ratio

Press.

Z

k(Cp/Cv)

Barg

1.00 1.00 1.00 1.00

1.30 1.30 1.30 1.30

2.65 2.65 2.65 2.65

Press.

Know P

kg/cm2 g 2.7 2.7 2.7 2.7 -

1-Up, 2-Down 1 1 1 1

Temp. o

C

149.0 149.0 149.0 149.0

Nominal size Schedule 12 12 4 4

40 40 40 40

Pipe ID inch #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Rough F. ft 1.5.E-04 1.5.E-04 1.5.E-04 1.5.E-04

Press. Drop Press. (Calc'ed Drop limit *1.2) bar/ barg/ 100m 100m ### ### ### ### ### ### ### ###

0.10

Press. Drop (kg/cm2)/L #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Velocity m/sec

Velo. Limit

Outlet Press.

m/sec

Barg

### 6~12 ### ### ### #DIV/0! #DIV/0! #DIV/0! #DIV/0!

Nre

Ma out

Equi. Length

Density

m

kg/m3

### ### ### ###

### ### ### ###

### ### ### ###

100 100 100 100

1.88 1.88 1.88 1.88

### ### ### ###

### ### ### ###

### ### ### ###

100 100 100 100

#DIV/0! #DIV/0! #DIV/0! #DIV/0!

Line Differential Pressure Calculation for Mixed Flow Project No. : Project Name :

Revision No. : Revision Date: Temp.

ID

Service

5

Flow rate

Density

kg/hr

kg/m

Visc.

MW

Cases

2,055 345 2,055 345 2,055 345 2,055 345

3

902.4 2.59 902.4 2.59 902.4 2.59 902.4 2.59

C Barg 100.0 43.99 347.0 45.59 308.0 43.19 350.0 45.39 o

cP 0.179 0.014 0.179 0.014 0.179 0.014 0.179 0.014

Inlet Press.

161.4 38.47 162.6 59.39 166.3 34.46 164.3 58.07

Nominal Size

Inlet Press.

Schdule

kg/cm g 2

44.9

inch -

inch #VALUE! 0.00015 #VALUE! 0.00015 #VALUE! 0.00015 #VALUE! 0.00015

m/sec #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

L V

From :

2

L V

To :

3

L V

Line :

4

L V

1

L V

-

#VALUE!

From :

2

L V

-

#VALUE!

To :

3

L V

-

#VALUE!

Line :

4

L V

-

#VALUE!

44.0 46.3

Two Phase Velocity

Press Drop

Roughness Vapor Vol. Frac, Homo. Method factor Fv

1

46.5

3.0 40.0 3.0 40.0 3.0 40.0 3.0 40.0

PipeID

Duckler

Flow Regime, Horizontal Line (Baker Average Chart) Density Flow Regime, Vertical Line (G-W Chart)

Inplace Density

Cal'ced Bar

Calc * 1.5 Bar

Regime

x

y

kg/m

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

### ### ### ### ### ### ### ###

### ### ### ### ### ### ### ###

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

### ### ### ### ### ### ### ###

### ### ### ### ### ### ### ###

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

3

Surface Tension

dyne/cm

Pressure Drop(kg/cm2) Homogeneous

Duckler

kg/cm2

kg/cm2

48.4

#VALUE!

#VALUE!

48.4

#VALUE!

#VALUE!

48.4

#VALUE!

#VALUE!

48.4

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

#VALUE!

Note : 6

Note :

Line sizing guideline

LDM

Type of service

Parson Maximum P

Velocity ft/sec

m/s

psi / 100 ft

kg/cm2/100m

Maximum P

Velocity bar / 100 m

ft/s

m/s

bar / 100 m

Liquid lines Pump Suction Boiling liquid Non-boiling liquid Pump discharge 0-250 gpm, 0~ 57 m3/hr 250-700 gpm, 57~159 m3/hr > 700 gpm, > 159 m3/hr Bottom outlet Reboiler trap out Liquid from condenser Liquid to chiller Refrigent line Gravity run lines Liquid feed to towers Steam condensate line Drains Waste water collection systems Reboiler downcomer Sidestream draw-off

2 4

6 8

0.61 1.22

1.83 2.44

0.5 1

0.12 0.23

0.11 0.23

6 8 10 4 1 3 4 2 3 4 0.5 2 3 3

8 10 15 6 4 6 6 4 8 6 1 6 8 7

1.83 2.44 3.05 1.22 0.30 0.91 1.22 0.61 0.91 1.22 0.15 0.61 0.91 0.91

2.44 3.05 4.57 1.83 1.22 1.83 1.83 1.22 2.44 1.83 0.30 1.83 2.44 2.13

6 4 2 0.6 0.15 0.5

1.38 0.92 0.46 0.14 0.03 0.12

1.36 0.90 0.45 0.14 0.03 0.11

0.4 0.4

0.09 0.09

0.09 0.09

Amine, Carbonate, Sour water Sodium carbonate Salt water Erosion limit

4 5.2 10

1.22 1.58 3.05

0.01 0.05 0.2

0.06 0.22 0.5

4

1.22

0.06

0.1

7 2.13 4~6 1.22~1.83 10 3.05 API-RP-14E

Water lines General service 1 inches 2 inches 4 inches 6 inches 8 inches 10 inch 12 inch 16 inch 20 inches and up Pump suction and drain Pump discharge BFW Refinery water lines Cooling water * From condenser Hydrocarbon vapor General recommendation Subatmospheric ~50 psig, 3.5 kg/cm2g, 3.5 barg ~150 psig, 10.5 kg/cm2g, 10.3 barg ~200 psig, 14.0 kg/cm2g, 13.8 barg ~500 psig, 35.2 kg/cm2g, 34.5 barg > 500 psig, 35.2 kg/cm2g, 34.5 barg

2 2

16 3

0.61 0.61

4.88 0.91

3 5 7 8 10 10 10 10 4 5 8 2 12 3

4.5 7 9 10 12 14 15 16 7 10 15 5 16 5

0.91 1.52 2.13 2.44 3.05 3.05 3.05 3.05 1.22 1.52 2.44 0.61 3.66 0.91

1.37 2.13 2.74 3.05 3.66 4.27 4.57 4.88 2.13 3.05 4.57 1.52 4.88 1.52

0.1 0.15 0.3 0.6 1.5 2

Max. 200 [100/ ()0.5] or Max. 50% sonic

2

0.46

0.45

2.5 2

0.58 0.46

0.57 0.45

0.1 0.15 0.3 0.6 1.5 2

0.02 0.03 0.07 0.14 0.35 0.46

0.02 0.03 0.07 0.14 0.35 0.46

0.02 0.03 0.07 0.14 0.34 0.45

0.02 0.03 0.07 0.14 0.34 0.45

Subatmospheric ~ 6.9 bara ~ 69 bara > 69 bara Gas line within BL Compressors piping suction Reciprocating Centrifugal Compressors piping discharge Refrigant suction lines Refrigant discharge lines Tower overhead Vacuum ( < 10 psig, 0.7 kg/cm2g) Atmospheric > 50 psig, 3.5 kg/cm2g, 3.5 barg Gas turbine inlet line Vacuum exhaust lines Two phase flow Reboiler riser (liq./vap.) High velocity flow (Pressure letdown)

Steam line to drivers, heat exchanger and heating coils Steam main : < 500 psig, 35.2 kg/cm2g Steam main : > 500 psig, 35.2 kg/cm2g Steam lead : < 500 psig, 35.2 kg/cm2g Steam lead : > 500 psig, 35.2 kg/cm2g

0.5 0.5

0.12 0.12

0.12 0.12

0.11 0.11

0.11 0.11

76.20 10.67 18.29

1

1

0.23

0.23

0.23

0.23

38.10 18.29

60.96 30.48

0.05 0.2 0.2

0.1 0.5 0.5

0.01 0.05 0.05

0.02 0.12 0.12

0.01 0.05 0.05

0.02 0.11 0.11

45.72

106.7 137.2 22.86 13.72

200

22.86

60.96

100 10 35

250 35 60

30.48 3.05 10.67

125 60

200 100

150

350 450 75 45

35 35

10.67 10.67

76.20 60.96 45.72 30.48

20~40 40~80

6~12 12~25

0.01 0.06 0.13 0.2%

0.06 0.13 0.5

0.1 0.1

0.9 Mach

Steam lines General recommendation ~50 psig, 3.5 kg/cm2g, 3.5 barg ~150 psig, 10.5 kg/cm2g, 10.3 barg ~300 psig, 21.1 kg/cm2g, 20.7 barg > 300 psig, 21.1 kg/cm2g, 20.7 barg Saturated steam Superheated steam Feed lines to pumps & reciprocating engines Power house equipment & process piping Boiler & turbine leads (superheated > 200 psig, 14 kg/cm Exhaust steam line for exhaust steam main Exhaust steam line for leads to header

0.5 0.5

75

250 200 150 100

50(d) d=inch

0.5

0.25 0.5 1 1.5 200 250 12.5 100 115

15 170 330

0.06 0.12 0.23 0.35

0.06 0.11 0.23 0.34

60.96 76.20 3.81 30.48 35.05

4.57 51.82 100.6 0.2

0.3 0.5 1.5

0.05

0.07 0.12 0.35

0.05

0.07 0.11 0.34

0.5 1 1 1

1.5 2 2 3

0.12 0.23 0.23 0.23

0.35 0.46 0.46 0.69

0.11 0.23 0.23 0.23

0.34 0.45 0.45 0.68

15(d)0.5 d=inch

0.02

0.6

EQUIVALENT PIPE LENGTH(m) for STEEL PIPE Nominal Size(inches) Inside Diameter(inches)

1/2 0.622

Schdule No. 90° elbow

Short Radius Long Radius Short Radius Long Radius Flow Branch Flow Through 90%φ 60%φ 45%φ Swing Ball Lift Straight Flow Flow Branch Full Port Reduced Port Full Port Reduced Port

Tee Glove Fully Open Valve

Check Valve

Three Way Cock Valve Ball Valve Plug Valve Straight Straight Cock Valve Butterfly Valve Diaphram Valve Gate Valve Fully Open Angle Valve 180% Return bend

90% Meter bend Exit Inward Projecting Entrance Sharp edged Entrance Slightly rounded Entrance Well rounded Entrance NOTE

1.6 0.5 10.7

4

1.2 0.8 0.7 0.5 2.5 0.8 16.4 8.2 7.2 5.5 6.1

12 1.8 5.7 0.3 0.6 1.5

2.5 0.3 5.3 1 0.8

0.6 0.5 0.3 0.1

2 1/2 2.469

3 3.068

4 4.026

6 6.065

8 7.981

10 10.020

12 11.938

d1

d2

d2

d1

0.8 0.7 0.4 0.2

1.2 0.9 0.6 0.3 0.05

1.6 2.5 0.8 1.3 0.4 0.7

1.9 1.5 1 0.5

1.6 1.1 0.8 0.6 3.2 1.1 21 10.5 9.2 7.1 7.9 27.5 2.4 7.4 0.6 2.5 0.9 2 1.1 2.5 7 0.6 10.5 1.9 3.1 1 1.6 0.5 0.8

1.9 1.3 1 0.7 3.8 1.3 25.1 12.5 11 8.5 9.4 2.8 8.8

1.3 3.1

2.2 3.7 1.1 1.9 0.6 1

2.8 2.2 1.4 0.7 0.1

2.3 1.6 1.2 1 4.7 1.6 31.2 15.6 13.6 10.5 11.7 46 3.5 10.9 0.9 3 1.5 4.5 1.6 4 10 0.8 15.6 2.5 5 1.5 2.5 0.7 1.5

3.1 2 1.6 1.5 6.1 2 40.9 20.5 17.9 13.8 15.3 76 4.6 14.3 1 6 2 7.5 2 4.5 17 1 20.5 3.5 6.5 2 3.5 0.9 2

4.6 3.1 2.5 2 9.2 3.1 61.6 30.8 27 20.8 23.1 107 6.9 21.6 2 14 3 15 3.1 6 35 2 30.8 5.5 9.5 3 5 1.5 2.5

6.1 4.1 3.2 2.5 12.2 4.1 81.1 40.5 35.5 27.4 30.4 137 9.1 28.4 2.5 17 4 27.5 4.1 8 36.5 2 40.5 7 12.5 3.5 6.5 2 3.5

7.6 5.1 4.1 2.5 15.3 5.1 101.8 50.9 44.5 34.4 38.2 168 11.5 35.6 3 20 5 38 5.1 9 46 3 50.9 9 15.5 4.5 8 2.5 4

4.3 3.4 2.2 1 0.2

6 4.7 3 1.4 0.2

10.3 8 5.1 2.5 0.4

14.5 11.3 7.2 3.5 0.6

18.9 14.7 9.4 4.5 0.8

9.1 6.1 4.9 3.5 18.2 6.1 121.3 60.6 53.1 40.9 45.5 199

4 24.5 5.5 45.5 6.1 10.5 68.5 3.5 60.6 10 18.5 5 9.5 2.5 5 6.1 5.5 23.3 18.2 11.7 5.6 0.9

14 13.250

16 15.250

18 17.250

20 19.250

22 21.250

24 23.250

30 10.1 6.7 5.4 3.5 20.2 6.7 134.6 67.3 58.9 45.4 50.5

30 11.6 7.7 6.2 4 23.2 7.7 154.9 77.5 67.8 52.3 58.1

20 13.1 8.8 7 4.5 26.3 8.8 175.3 87.6 76.7 59.2 65.7

20 14.7 9.8 7.8 5 29.3 9.8 195.6 97.8 85.6 66 73.3

20 16.2 10.8 8.6

20 17.7 11.8 9.4 6 35.4 11.8 236.2 118.1 103.3 79.7 88.6

4.5 29 6

5 33.5 7.5

5.5

6

8

9

6.7 11.5 76 4 67.3 12 20.5 6 10.5 3 5.5 6.7 6.1 26.7 20.8 13.4 6.4 1.1

7.7 12

8.8 13

9.8 14

4 77.5 13 23.5 6.5 12 3.5 6 7.7 7 31.2 24.4 15.6 7.5 1.2

4.5 87.6 15 26 7.5 13 4 6.5 8.8 7.9 36.5 28.5 18.3 8.8 1.5

5 97.8 16.5 30.5 8.5 15.5 4.5 8 9.8 8.8 41.4 32.3 20.7 9.9 1.7

32.4 10.8 215.9 108 94.5 72.9 81

26 25.250

28 27.250

30 29.250

32 31.250

34 33.250

36 35.250

42 41.250

48 47.250

54 53.250

60 59.250

66 65.125

72 71.125

84 83.125

96 95.000

7/16"wall

3/8"wall

108 107.000

NONE

120 119.000

1/2 3/4 1 1 1/2 2 2 1/2 3 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 84 96 108 120

1/2"wall

19.2 12.8 10.3

20.8 13.8 11.1

22.3 14.9 11.9

23.8 15.9 12.7

25.3 16.9 13.5

26.9 17.9 14.3

31.4 21 16.8

36 24 19.2

40.6 27.1 21.6

45.1 30.1 24.1

49.6 33.1 26.5

54.2 36.1 28.9

63.3 42.2 33.8

72.4 48.3 38.6

81.5 54.4 43.5

90.7 60.5 48.4

38.5 12.8 256.5 128.3 112.2 86.6 96.2

41.5 13.8 276.9 138.4 121.1 93.4 103.8

44.6 14.9 297.2

47.6 15.9 317.5

50.7 16.9 337.8

53.7 17.9 358.1

62.9 21 419.1

72 24 480.1

81.2 27.1

90.3 30.1

99.3 33.1

108.4 36.1

126.7 42.2

144.8 48.3

163.1 54.4

181.4 60.5

100.3

107.2

114

120.9

141.4

162

12.8

13.8 21.5

29

36.5

40

7.5

9.5

11

12

25 44

29 52

35 60

40 68

45.5 77.5

51 87.5

56 93.5

61 101.5

70.5 116.5

80 129

86 144

86.5 158

17.9 16.1 82.9 64.7 41.5 19.9 3.3

21 18.9 97.9 76.4 49 23.5 3.9

24 21.6 118.8 92.7 59.4 28.5 4.8

27.1 24.3 133.9 104.5 67 32.1 5.4

30.1 27.1 150.5 117.4 75.2 36.1 6

33.1 29.8 165.4 129 82.7 39.7 6.6

36.1 32.5 180.7 140.9 90.3 43.4 7.2

211.1 164.7 105.6 50.7 8.4

241.3 188.2 120.7 57.9 9.7

271.8 212 135.9 65.2 10.9

302.3 235.8 151.1 72.5 12.1

7.5 11 10.8

108

10.8 9.7 46.1 36 23.1 11.1 1.8

11.8 17 6 118.1 20 37 10 18.5 5 9.5 11.8 10.6 50.9 39.7 25.5 12.2 2

128.3

12.8 11.5 56.3 43.9 28.1 13.5 2.3

138.4

13.8 12.5 61.8 48.2 30.9 14.8 2.5

14.9 13.4 66.9 52.2 33.5 16.1 2.7

15.9 14.3 72.2 56.3 36.1 17.3 2.9

16.9 15.2 77.5 60.4 38.7 18.6 3.1

For partially closed glove valves and gate valves, multiplt tabulated values by 3 for one-half open and by 70 for one-quarter open. for two phase flow, multiply these values by a factor of 2.0. For elbow s, short radius means R=1D and long radius means R=10. For bends, short radius means R=5D and long radius means R=10D. If flow conditions are not in the fully turbulent zone use K-factor instead of equivalent length. K=4fT(L/D)

d1 d2

Nominal size(inches)

Enlargers (gradual) Reducers (gradual)

0.8 0.5 0.4

Short Radius Long Radius Short Radius Long Radius Short Radius Long Radius 3 meter 4 meter

45% Return bend

NOTE

1 1/2 2 1.61 2.067

0.8 1.9

90% Return bend

d1

1 1.049

40

45° elbow

d2

3/4 0.824

d1 d2 d2/d1=1/2 d2/d1=3/4 d2/d1=1/2 d2/d1=3/4

3/4 1/2

1/2

3/4

1 1/2 3/4 1

1

1 1/2

1 1/2

2

2

3

3

4

4

6

4

10 6

8

6

12 8

10

6

8

10

12

8

10

12

14

10

12

14

16

12

14

16

18

18

20

0.2

0.4

1 0.2

0.5

0.4

0.7

2 0.4

1.2

3 0.9

1.5

0.9

2.4

1.2

3.7

2.2

4.6

4.3

1.9

5.8

4.3

2.0

6.7

6.7

4.6

1.9

8.3

3.0

4.6

2.2

9.1

7.0

4.6

1.2

9.1

6.4

4.0

1.5

7.6

3.7

0.2

0.3

0.2

0.3

0.3

0.4

0.4

0.8

0.7

1.0

1.0

1.6

1.3

2.2

2.2

2.5

2.9

1.9

3.7

3.7

2.0

4.3

4.3

4.0

1.9

5.2

5.2

4.6

2.2

5.8

5.8

4.6

1.3

7.1

7.1

4.0

1.5

7.6

0.3 0.9 2.0 0.3 0.3 0.3 0.3 0.3 0.6 0.3 0.3 0.3 Length in terms of smaller diameter. For two phase flow, mutiply these values by factor of 2.0.

4

3.0 0.9 1.0 0.6

6

5.0 0.9 2.0 0.6

8

5.5 0.9 2.0 0.6

6.0 1.0 3.5 0.9

9.0 1.0 3.5 0.9

14

12.0 2.0 4.5 2.0

16

16.5 3.0 6.0 2.0

18

20.0 3.0 8.0 2.0

20

26.0 4.0 10.0 3.0

24

3.7 32.0 4.5 12.5 3.0

Enlargers ### 3/4 NONE 3/4 1

0 0

1 1/2

0.2 0.7

2 3 4 6 8 10 12 14 16 18 20 24

1

0.4 0.7

1 1/2

0.4 1.2

2

2 1/2

0.9 1.5

3

0.9 2.4

4

6

1.2 3.7 4.6

2.2 4.3 5.8 6.7

8

2 4.6 3 9.1

10

2 4.6 3 9.1

12

1.9 4.6 7 9.1

14

2.2 4.6 6.4

16

1.2 4

18

1.5 7.6

20

22

24

26

28

30

32

34

36

42

48

54

60

66

72

84

96

108

120

24

26

28

30

32

34

36

42

48

54

60

66

68

72

84

96

108

120

3.7

Reducers ##

3/4

1

0.2

0.3 0.2

1 1/2

2

2 1/2

3

4

6

8

10

12

14

16

18

20

NONE 1/2 3/4 1 1 1/2 2 3 4 6 8 10 12 14 16 18 20

0.3 0.3

0.4 0.4

0.8 0.7

1 1

1.6 1.3

2.2 2.2

2.5 2.9 1.9

3.7 3.7 2

4.3 4.3 4 1.9

5.2 5.2 4.6

5.8 5.8 4.6 1.3

7.1 7.1 4 1.5

7.6 4.5

PIPE ID OF STEEL PIPE STD

10

20

30

40

60

80

100

120

140

160

0.410 0.674 0.884

0.622 0.824

0.546 0.742

0.466 0.612

0.446 0.612

NONE 1/4 1/2 3/4

0.364 0.622 0.824

1

1.049

1.097

1.097

1.049

0.957

0.815

0.815

1 1/2

1.610

1.682

1.682

1.610

1.500

1.388

1.388

2

2.067

2.157

2.157

2.067

1.939

1.687

1.687

2 1/2

2.469

2.469

2.323

3

3.068

3.260

3.260

3.068

2.900

2.624

2.624

4

4.026

4.260

4.260

4.026

3.826

3.624

3.438

6

6.065

6.357

6.357

6.065

5.761

5.501

8

7.981

8.125

8.071

7.981

7.813

7.625

7.437

7.187

7.001

10

10.020

10.250

10.136

10.020

9.750

9.562

9.312

9.062

8.750

8.500

12

12.000

12.250

12.090

11.938

11.626

11.374

11.062

10.750

10.500

10.126

14

13.250

13.500

13.376

13.250

13.124

12.812

12.500

12.124

11.812

11.500

11.188

16

15.250

15.500

15.376

15.250

15.000

14.688

14.312

13.938

13.562

13.124

12.812

18

17.250

17.500

17.376

17.124

16.876

16.500

16.124

15.688

15.250

14.876

14.438

20

19.250

19.500

19.250

19.000

18.812

18.376

17.938

17.438

17.000

16.500

16.062

22

21.250

21.500

21.250

21.000

20.250

19.750

19.250

18.750

18.250

17.750

24

23.250

23.500

23.250

22.624

22.062

21.562

20.938

20.376

19.876

19.312

26

25.250

25.376

25.000

28

27.250

27.376

27.000

26.750

30

29.250

29.376

29.000

28.750

32

31.250

31.376

31.000

30.750

30.624

34

33.250

33.312

33.000

32.750

32.624

36

35.250

35.376

35.000

34.750

34.500

41.000

40.750

40.500

42

22.876

2.125

5.187 6.813

48

48.000

48.000

48.000

48.000

54

54.000

54.000

54.000

54.000

54.000

54.000

54.000

54.000

54.000

54.000

60

60.000

60.000

60.000

60.000

60.000

60.000

60.000

60.000

60.000

60.000

66

66.000

66.000

66.000

66.000

66.000

66.000

66.000

66.000

66.000

66.000

72

72.000

72.000

72.000

72.000

72.000

72.000

72.000

72.000

72.000

72.000

84

84.000

84.000

84.000

84.000

84.000

84.000

84.000

84.000

84.000

84.000

96

96.000

96.000

96.000

96.000

96.000

96.000

96.000

96.000

96.000

96.000

108

108.000

108.000

108.000

108.000

108.000

108.000

108.000

108.000

108.000

108.000

120

120.000

120.000

120.000

120.000

120.000

120.000

120.000

120.000

120.000

120.000

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