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GS Engineering & Construction Corp. Calculation Sheet - Pump Hydraulics
TITLE :
Doc. No.
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Rev. No.
:
Rev. Date
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0 28 May. 2013 1
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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