sr naphtha feed pump
DESCRIPTION
NAPHTHA_FEEDTRANSCRIPT
GS Engineering & Construction Corp. Doc. No. :
Rev. No. : 0
TITLE :Rev. Date : 28 May. 2013
Page : 1 of 3
Calculation Sheet - Pump Hydraulics
Classification : Standard Form
REVISION STATUS : Rev. No Date Descriptions Remarks
0 28 May. 2013 First Issue
Prepared by Checked by Approved by
Name Ammar Alobud
Signature
Date 28 May. 2013
Reviewed :
GS Engineering & Construction Corp.
Calculation Sheet- Pump Hydraulics
GS Engineering & Construction Corp. Doc. No. : 0
Rev. No. : 0
TITLE :Rev. Date : 28 May. 2013
Page : 2 of 3
1
2 1. Introduction
3
4
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6
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8
9
10
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12
13
14
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17
18
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21
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24 2. Description for Each Worksheet
25
26 Pump Calculation
27
28
29
30
31
32
33 Sketch
34
35
36
37
38
39 Pressure Profile
40
41
42
43
44
45
46
Calculation Sheet- Pump Hydraulics
이 Calculation Sheet는 Process Engineer가 빈번하게 수행하는 Pump Hydraulics Calculation을 정확하고 일관성 있게 계산 할 수 있도록 하기위하여 준비되었다.
이 Calculation Sheet는 하나의 Pump에 대하여 간단한 scheme을 sketch하고 fluid의 properties를 입력한 후 그에 따라 정해진 line의 pressure drop을 구하고 pump hydraulic을 수행하여 그 결과를 pressure profile에 정리되도록 구성하였다.
Fluid type은 Liquid flow, Vapor flow, Mixed flow로 나누어지므로 line differential pressure calculation sheet를 3가지로 나누어 두어서 fluid 종류에따라 달리 구해지는 결과를 정리할수 있도록 하였다. 그 외에 line의 fitting 구성에 따라 변경되는 equivalent length를 계산하기 위한'EQ_L Calcaulation' sheet를 추가하였다. 또한, line pressure drop을 계산하기 위한 Pipe line의 ID를 정리한 sheet가 포함되었으며, sketch의편의를 위해 각 equipment 및 element의 그림을 Drawing sheet에 추가하였다.
Control Valve의 pressure drop calculation method는 no control valve, Conventional, LDM 중 선택하여 계산 되도록 하였으며 Manual input을이용한 방법도 포함하여 project specification을 따르거나 혹은 상황에 따라 달리 적용해야 할 경우에 사용할 수 있도록 하였다.
Report에는 Coversheet, Pump Calculation, Sketch, Pressure Profile이 포함되고, Equivalent Length와 Line Pressure drop calculation은계산시 활용하며, Guideline과 Equivalent Length, Pipe ID는 계산시 참고자료로 사용한다.
이 Calculation Sheet에 Green Blank는 Calculation을 위하여 사용자가 직접 넣어주어야 하는 값이며 Yellow Blank는 주어진 정보를 기준으로 자동으로 계산되는 값이다. 각 Sheet에 대한 소개는 다음 Section에 기술하였다.
양식은 Hydrosys output excel file을 참고하였으며, Green Blank를 직접 넣어주면 Yellow Blank에서 계산되어 자동으로 fill-up 된다.
Pump suction은 Rated flow 에서의 입력값을 기준으로 Normal과 Minimum flow에서의 값들을 유도하였으며, Pump discharge는 Normal flow에서의 값을 기준으로 Rated와 Minimum flow에서의 값들이 자동으로 계산된다.
Control Valve pressure drop은 Control valve calculation method, control valve type, reflux 유무에 따라 달리 계산되게 하였다.
이를 선정해 주면 각 방법에 따라 달리 계산되어, Control valve DP란에 자동으로 입력된다.
해당 Pump Circuit을 Hydraulic calculation의 편의를 위해 개략적으로 그린다. User의 편리함과 drawing의 통일성을 위해 print 되지 않는 영역에symbols을 그려놓았고, 이를 복사에서 사용하면 된다. Job no.와 Project name, Client는 Coversheet에서 불러오며 그밖의 Green Blank는User가 직접 채워 넣는다. 그러면, Pump Calculation, Pressure Profile, Equivalent Length Calculation sheet도 자동으로 변경된다.
사용자가 더 많은 data를 sketch를 통해 간략히 확인하고 싶을 경우, 직접 input하거나 다른 sheet에서 계산된 결과값을 불러오면 된다.
Case별로 sketch가 다르고 equipment, instrument의 개수와 종류가 다양하기 때문에, Pressure Profile의 공란은 user가 직접 입력해야 한다.
Section 혹은 equipment, instrument 별로 pressure drop을 입력 하거나 link시키고, 각 point에서 static head를 계산하여 inlet pressure를 계산한다.
양식은 HydroSys output excel file을 참고하였다.
External Fire Case에 대한 Relieving Load를 계산하는 경우 고려되어야 하는 Environment Factor, Latent Heat을 Table,
그래프를 통해 도출할 수 있다.
GS Engineering & Construction Corp. Doc. No. : 0
Rev. No. : 0
TITLE :Rev. Date : 28 May. 2013
Page : 3 of 3
1
2 EQ_L Calculation
3
4
5
6
7
8
9 Liquid
10
11
12
13
14
15
16 Two_Phase
17
18
19
20
21
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23 Vapor
24
25
26
27
28
29 Guideline
30
31
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33 Equivalent Legth
34
35
36 Pipe_ID
37
38
39
40
41
42
43
44
45
46
Calculation Sheet- Pump Hydraulics
User가 Nominal Diameter와 Enlarger, Reducer의 size를 결정하고, 각종 fitting의 개수를 green blank에 입력하면 'EQ_L Calculation' sheet는yellow blank에 'Euivalent Length' sheet에서 data를 읽어온후 합산을 한다. Overdesign의 사용 유무와 사용시 %를 입력하면 최종적으로계산된 equivalent length가 표시된다.
각 section 및 segment 별로 나눠서 계산한 뒤 line pressure drop의 100m 당 pressure drop과 함께 'Pressrue Profile'에 정리한다. 이를 곱하여,
pressure drop을 계산하면, 'Pressure Profile'이 완성된다.
Line Differential Pressure Calculation for Liquid Flow을 위한 sheet이다. Pump circuit의 liquid line의 pressure drop을 darcy equiation을 이용하여계산한다. Flow rate, density, viscosity, roughness와 nominal size와 schedule을 통해 계산된 pipe ID로 100m당 pressure drop과 velocity를구하고, 'Guideline'을 참고하여 pressure drop과 velocity limit을 입력하여 비교한다.
여기서 구해진 100m당 pressure drop은 앞에서 계산된 equivalent length와 함께 line의 pressure loss를 구하는데 사용된다.
이 sheet는 "GDP-6BDT-404 Line Sizing Calculation sheet"를 참고하였다.
유체의 Control valve 후단 압력강하에 따른 상변화나, Heat exchanger 에 의한 온도변화에 따른 상변화등, Pump circuit에서 발생할 수 있는two phase fluid의 line pressure drop 계산을 위해 첨부하였다.
Fluid 의 Properties와 condition을 입력하면, Homogeneous model과 Duckler method를 이용하여 pressure drop 및 velocity, vapor volume
fraction을 계산하고, Baker Chart와 G-W Chart를 통해 flow regime, Average / Inplace density를 계산한다.
이 sheet는 "GDP-6BDT-404 Line Sizing Calculation sheet"를 참고하였다.
Line Differential Pressure Calculation for Vapor Flow을 위한 sheet이다. Pump circuit에 포함될 수 있는 vapor line을 isothermal method를 통해계산한다. Flow rate, molecular weight, viscosity, Z, k(Cp/Cv), pressure, know Pressure(upstream or downstream), temperature를 입력하면100m당 pressure drop과 velocity가 계산된다.
이 sheet는 "GDP-6BDT-404 Line Sizing Calculation sheet"를 참고하였다.
Line Differential Pressure Calculation에서 계산되는 pressure drop과 velocity의 limit를 제시해 주는 guideline이다.
Process, 용도, line의 위치에 따라 limit가 다르기 때문에 적절히 적용해야 한다.
Equivalent Legth calculation에 쓰이는 database로 LDM의 chart를 옮겨 놓았다.
Line differential pressure calculation에서 line의 nominal diameter와 schedule을 입력하면, 이 sheet에서 ID를 읽어와서 계산에 사용된다.
GS Engineering & Construction Corp. Doc. No. :
Rev. No. :
TITLE :Rev. Date :
Page : 1 of X
Calculation Sheet - Pump Hydraulics
Project No. : 111580
Project Name : RABIGH PHASE II
Clients : ARAMCO
Item No. :
Service :
REVISION STATUS : Rev. No Date Descriptions Remarks
Prepared by Checked by Approved by
Name Ammar Alobud
Signature
Date
Reviewed :
GS Engineering & Construction Corp.
Calculation Sheet- Pump Hydraulics
GS Engineering & Construction Corp. Doc. No. : 0
Rev. No. :
TITLE :Rev. Date :
Page : 2 of X
SHEETS REVISED THIS ISSUE
Sheet No. 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.
Calculation Sheet- Pump Hydraulics
Calculation Sheet - Pump Hydraulics
Approved by
SHEETS REVISED THIS ISSUE
Sheet No.
NO
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JOB NO 111580
PROJECT RABIGH PHASE II
UNIT NAME 0
PUMP CALCULATION WORK SHEET CASE 0 DATE
CLIENT ARAMCO MAIN CIRCUIT PAGE REV.
LOCATION Rabigh,KSA DESCRIPTION SR NAPHTHA FEED PUMPS 1 OF 1 0
01 GENERAL DISCHARGE SYSTEM
02 PUMP S030-P-0900A/B NOR RTD MIN
03 18. FLOW RATE m^3/h 565 622 225
04 SUCTION END FIXED PRESSURE
05 19. STATIC HEAD m -0.3
06 DISCHARGE END B.L. 20. STATIC PRESS. kg/cm^2 -0.02
07 (NO.19 x SpGr / 10.2)
08 CONTROL VALVE FV-2901 21. TERMINAL PRESS. AT LIQUID LEVEL kg/cm^2[g] 9.80
09 22. MISCELLANEOUS LOSSES kg/cm^2 0.00
10 GOVERNING PATH ? Y 23. FLOW METER LOSSES kg/cm^2 0.20
11 SPECIAL REQUIREMENTS 24. TOTAL DISCH. FIXED PRESS. kg/cm^2[g] 9.98
12 (SUM OF NO. 20 THRU 23)
13 VARIABLE LOSSES NOR RTD MIN
14 PUMP FLUID CHARACTERISTICS 25. DISCH. LINE LOSSES kg/cm^2 ### ### ###
15 FLUID NAME SR NAPHTHA 26. EQUIPMENT LOSSES kg/cm^2
16 PUMPING TEMP. degC 40 (A) EXCHANGERS 0.00 0.00
17 VAPOR PRESS. kg/cm^2 0.507 (B) HEATERS 0.00 0.00
18 SPECIFIC GRAVITY 0.690 (C) MISCELLANEOUS 0.00 0.00
19 VISCOSITY cp 0.400 2X. MISCELLANEOUS LOSSES kg/cm^2 0.00 0.00
20 PUMP CAPACITY 27. TOTAL DISCH. VARIABLE kg/cm^2 ### ### ###
21 NOR RTD MIN (NO.25 + NO.2X + NO.26)
22 VOLUMETRIC FLOW RATE @ PT m^3/h 565 622 225 DIFFERENTIAL
23 OPERATING FLOW PERCENTAGE % 100 110 40 28. TOTAL VARIABLE LOSSES kg/cm^2 ### ### ###
24 DESIGN FOR CONTINUOUS MIN FLOW OF (NO.10 + NO.27)
25 29. TOTAL FIXED PRESS. kg/cm^2 ### ### ###
26 CALCULATIONS (NO.24 - NO.6)
27 SUCTION SYSTEM 30. TOTAL LOSSES kg/cm^2 ### ### ###
28 FIXED PRESSURE (NO.28 + NO.29)
29 1. ELEVATION OF MIN. LIQUID LEVEL mm 0 31. % VARIABLE LOSS ### ### ###
30 2. ELEVATION OF PUMP BASE PLATE mm 300 (NO.28 / NO.30 x 100)
31 3. MIN. STATIC HEAD (NO.1 - NO.2) m -0.30 32. % TOTAL LOSS FOR CONTROL VALV ### ### ###
32 4. MIN. STATIC PRESS. kg/cm^2 #VALUE! (NO.33/NO.30 x 100)
33 (NO.3 x SpGr / 10.2) 33. CONTROL VALVE DP kg/cm^2 4.650 0.000 0.00
34 5. MIN. PRESS. AT LIQUID LEVEL kg/cm^2[g] 1.00 (NO.32 x NO.30 / 100) OR (NO.34 - NO.30)
35 6. TOTAL SUC. FIXED PRESS. kg/cm^2[g] #VALUE! 34. PUMP DIFFERENTIAL PRESS. kg/cm^2 ### ### ###
36 (NO.4 + NO. 5) (NO.30 + NO.33)
37 VARIABLE LOSSES NOR RTD MIN 35. PUMP DIFFERENTIAL HEAD m ### ### ###
38 7. SUCTION LINE LOSSES kg/cm^2 ### ### ###
39 8. MISCELLANEOUS LOSSES kg/cm^2 0.00 0.00 0.00 36. PUMP DISCH. PRESS kg/cm^2[g] ### ### ###
40 9. SUCTION EQUIPMENT LOSSES kg/cm^2 0.06 0.07 0.01 (NO.11 + NO.34)
41 10. TOTAL SUC. VARIABLE LOSSES kg/cm^2 ### ### ### POWER
42 (NO.7 + NO.8 + NO.9) 37. HYDRAULIC POWER kW ### ### ###
43 11. PUMP SUC. PRESS. kg/cm^2[g] ### ### ###
44 (NO.6 - NO.10) 3x. ESTIMATED EFFICIENCY % ### ### ###
45 NPSH
46 12. PUMP SUC. PRESS. AT RATED kg/cm^2[a] #VALUE! 38. ESTIMATED BRAKE HORSE POWER kW ### ### ###
47 FLOW (NO.11 + 1 atm) (NO.37 / EFF.)
48 13. RECIP. PUMP SUCTION kg/cm^2 0.00 ESTIMATED SHUTOFF PRESSURE
49 ACCEL. LOSSES 39. MAX. SUCTION PRESS kg/cm^2[g] 1.04
50 14. VAPOR PRESS. kg/cm^2 0.51 (AS PER SPECIFICATION)
51 15. AVAILABLE PRESS kg/cm^2[a] #VALUE! 40. SHUTOFF DIFFERENTIAL kg/cm^2 #VALUE!
52 (NO.12 - NO.13 - NO.14) (AS PER SPECIFICATION)
53 16. NPSH AVAILABLE AT PUMP BASE m #VALUE! 41. SHUTOFF DISCH. PRESS kg/cm^2[g] #VALUE!
54 PLATE (NO.15 x 10.2 / SpGr) (NO.39 + NO.40)
55 17. Estimated NPSH REQUIRED m #VALUE!
56 (N=10000 for water, 3550 rpm)
REVISION
DATE
BY/CHECKED / / / / / / /
GS ENGINEERING & CONSTRUCTION
NO
TE
- T
hese
dat
a ar
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nfid
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prop
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of G
SE
&C
and
sha
ll no
t be
disc
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oth
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or r
epro
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any
man
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or u
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for
any
purp
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wha
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n pe
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. JOB NO 111580 UNIT NAME 0 CASE 0
PROJECT RABIGH PHASE II MAIN CIRCUIT 0 REV 0
CLIENT ARAMCO SEG CIRCUIT 0 DATE 12/30/1899
PROCESS HYDRAULICS - PRESSURE PROFILE SUMMARY SHEET LOCATION RABIGH , KSA DESCRIPTION SR NAPHTHA FEED PUMP PAGE 1 OF 1
01
02 Ciruit Components Normal Maximum Minimum Nominal Sch Inside Equiv. Specific Velocity Static Nozzle Equip Flow
03 100.0 % 110.1 % 39.8 % Diameter No Diameter Length Press Head Elev Elev Rate
04 Inlet Press Press Drop Inlet Press Press Drop Inlet Press Press Drop Pipe Drop
05 kg/cm^2[g] kg/cm^2 kg/cm^2[g] kg/cm^2 kg/cm^2[g] kg/cm^2 in Class in m kg/cm^2/100m m/s mm mm mm kg/hr
06
07 1203F Splitter Receiver 1.00 0.00 1.00 0.00 1.00 0.00 6850
08 Section 1 1.00 #VALUE! 1.00 #VALUE! 1.00 #VALUE! 10 40 10.020 75 #VALUE! #VALUE! 391,000
09 Static Head -0.46 -0.46 -0.46 -6850
10 SPLIT #VALUE! 0.00 #VALUE! 0.00 #VALUE! 0.00 0
11 Section 2 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 6 40 6.065 3800 #VALUE! #VALUE! 391,000
12 Static Head 0.02 0.02 0.02 300
14 1214J/JA #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 300
15 Section 3 #VALUE! 0.00 #VALUE! 0.00 #VALUE! 0.00 4 40 4.026 0 0.00 0.0 0
16 Static Head -0.02 -0.02 -0.02 -300
17 FV315 #VALUE! 4.65 #VALUE! 0.00 #VALUE! 0.00 0
18 Section 3-1 #VALUE! 0.00 #VALUE! 0.00 #VALUE! 0.00 4 40 4.026 0 0.00 0.0 0
19 Static Head 0.00 0.00 0.00 0
20 B.L. #VALUE! 0.00 #VALUE! 0.00 #VALUE! 0.00 0
21 Section 4 #VALUE! 0.00 #VALUE! 0.00 #VALUE! 0.00 4 40 4.026 0 0.00 0.0 0
22 Static Head 0.00 0.00 0.00 0
23 1813C #VALUE! 0.58 #VALUE! 0.70 #VALUE! 0.11 0
24 Section 5 #VALUE! 0.00 #VALUE! 0.00 #VALUE! 0.00 4 40 4.026 0 0.00 0.0 0
25 Static Head 0.00 0.00 0.00 0
26 1811F #VALUE! 0.28 #VALUE! 0.34 #VALUE! 0.05 0
27 Section 6 #VALUE! 0.00 #VALUE! 0.00 #VALUE! 0.00 4 40 4.026 0 0.00 0.0 0
28 Static Head 0.95 0.95 0.95 14000
29 1806C #VALUE! 0.29 #VALUE! 0.35 #VALUE! 0.06 14000
30 Section 6-1 #VALUE! 0.00 #VALUE! 0.00 #VALUE! 0.00 4 40 4.026 0 0.00 0.0 0
31 Static Head -0.91 -0.91 -0.91 -13400
32 HV045 #VALUE! 0.00 #VALUE! 0.00 #VALUE! 0.00 600
33 Section 7 #VALUE! 0.00 #VALUE! 0.00 #VALUE! 0.00 4 40 4.026 0 0.00 0.0 0
34 Static Head 0.00 0.00 0.00 0
35 PV100 #VALUE! 0.00 #VALUE! 0.00 #VALUE! 0.00 600
36
37
38
39
GS ENGINEERING & CONSTRUCTION
NO
TE
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hese
dat
a ar
e co
nfid
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l and
the
prop
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of G
SE
&C
and
sha
ll no
t be
disc
lose
d to
oth
ers
or r
epro
duce
d in
any
man
ner
or u
sed
for
any
purp
ose
wha
tsoe
ver
exce
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y w
ritte
n pe
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or
as p
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in a
sig
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E&
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data
. JOB NO 111580 UNIT NAME CASE
PROJECT RABIGH PHASE II MAIN CIRCUIT REV 0
CLIENT ARAMCO SEG CIRCUIT DATE
PROCESS HYDRAULICS - HYDRAULIC CIRCUIT DIAGRAM LOCATION RABIGH , KSA DESCRIPTION SR NAPHTHA FEED PUMP PAGE 1 OF 1
BL
12"
SEC2
SEC1
16"STR0900A S030-P-0900A/B
Notes: 1
2
3
4
5
GS ENGINEERING & CONSTRUCTION
NAPHTHA REFORMER (R410)
T
Equivalent Summary SheetRev Date Made by Checked by
Client : ARAMCO JOB No.: 111580 Main Circuit 0
Location : RABIGH , KSA Unit No. : Circuit Description SR NAPHTHA FEED PUMP
RABIGH PHASE II Unit Name : 0
Line No. :
Stream No :
From : TIE-IN POINT S040-P-0810 A/B
To : S040-P-0810 A/B
Nominal Dia. 1 15 1 13 1
Straight Length [m] 75.0 3800.0
90° elbow Short Radius 0 0
Long Radius 2 15.4 2 12.2
45° elbow Short Radius 0 0
Long Radius 0 0
Tee Flow Branch 0 0
Flow Through 0 2 12.2
Glove Fully Open Valve
90%φ 0 0
60%φ 0 0
45%φ 0 0
Check Valve
Swing 0 0
Ball 0 0
Lift 0 0
Three Way Cock Valve Straight Flow 0 0
Flow Branch 0 0
Ball Valve Full Port 0 0
Reduced Port 0 0
Plug Valve Straight Full Port 0 0
Reduced Port 0 0
Straight Cock Valve 0 0
Butterfly Valve 0 0
Diaphram Valve 0 0
Gate Valve Fully Open 2 8 2 7
Angle Valve 0 0
180% Return bend Short Radius 0 0
Long Radius 0 0
90% Return bend Short Radius 0 0
Long Radius 0 0
45% Return bend Short Radius 0 0
Long Radius 0 0
90% Meter bend 3 meter 0 0
4 meter 0 0
Exit 0 0
Inward Projecting Entrance 0 0
Sharp edged Entrance 0 0
Slightly rounded Entrance 0 0
'Well rounded Entrance 0 0
Enlargers From 1 0 1 0 1 0 1
To 1 1 1 1
Reducers From 1 1 1 0 1
To 1 1 1 1
Calculated Equiv. Length (m) 98 3,831 -
Overdesign % is Applied ? (Y/N) N
Overdesign % if Applied ? 5
Project :
Section 1 Section 2
BL
Equivalent Summary SheetRev Date Made by Checked by
Client : ARAMCO JOB No.: 111580 Main Circuit 0
Location : RABIGH , KSA Unit No. : Circuit Description SR NAPHTHA FEED PUMP
RABIGH PHASE II Unit Name : 0 Project : Selected Equiv. Length (m) 75 3,800 -
Client : ARAMCO
Location : RABIGH , KSA
RABIGH PHASE II
Line No. :
Stream No :
From :
To :
Nominal Dia.
Straight Length [m]
90° elbow Short Radius
Long Radius
45° elbow Short Radius
Long Radius
Tee Flow Branch
Flow Through
Glove Fully Open Valve
90%φ
60%φ
45%φ
Check Valve
Swing
Ball
Lift
Three Way Cock Valve Straight Flow
Flow Branch
Ball Valve Full Port
Reduced Port
Plug Valve Straight Full Port
Reduced Port
Straight Cock Valve
Butterfly Valve
Diaphram Valve
Gate Valve Fully Open
Angle Valve
180% Return bend Short Radius
Long Radius
90% Return bend Short Radius
Long Radius
45% Return bend Short Radius
Long Radius
90% Meter bend 3 meter
4 meter
Exit
Inward Projecting Entrance
Sharp edged Entrance
Slightly rounded Entrance
'Well rounded Entrance
Enlargers From
To
Reducers From
To
Calculated Equiv. Length (m)
Overdesign % is Applied ? (Y/N)
Overdesign % if Applied ?
Project :
1
0
0
-
N
5
Client : ARAMCO
Location : RABIGH , KSA
RABIGH PHASE II Project : Selected Equiv. Length (m) -
Line Differential Pressure Calculation for Liquid Flow
ID Service Case
Flow rate Density Viscosity Pipe ID Rough F. Press. Temp. Press. Drop Velocity
Nre
Darcy Friction Factor Constant Pipe ID Flow rate
kg/hr cP Schedule inch ft m/sec m/sec F A B C inch
1 Section 1 1 391,000 692.0 0.400 16 40 #VALUE! 0.00015 40.0 0.12 #VALUE! #VALUE! 1.83 #VALUE! ### ### ### ### #VALUE! 565.0 ###
From : TIE-IN POINT 2 430,100 692.0 0.400 16 40 #VALUE! 0.00015 40.0 0.12 #VALUE! #VALUE! 1.83 #VALUE! ### ### ### ### #VALUE! 621.5 ###
To : S040-P-0810 A/B
Line No.:
Note :
2 Section 2 1 391,000 692.0 0.400 12 40 #VALUE! 0.00015 40.0 0.12 #VALUE! #VALUE! 1.83 #VALUE! ### ### ### ### #VALUE! 565.0 ###
From : S040-P-0810 A/B 2 430,100 692.0 0.400 12 40 #VALUE! 0.00015 40.0 0.12 #VALUE! #VALUE! 1.83 #VALUE! ### ### ### ### #VALUE! 621.5 ###
To : BL
Line No.:
Note :###
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Project No. : Revision No. :
Project Name : Revision Date:
Nominal size
Press. Drop limit
Velocity limit
Pipe IDkg/m3 kg/cm2 g oC
(kg/cm2)/ 100m
(kg/cm2))/ 100m
m3/hr M
Line Differential Pressure Calculation for Vapor Flow
ID Service Case
Flow rate
MW
Visco. Press. Press. Know P Temp. Pipe ID Press. Drop Velocity
Nre Ma out
Density
kg/hr cP Z Barg Schedule inch ft m/sec m/sec Barg m
3 1 11,561 14,396 18.00 0.010 1.00 1.30 2.65 2.7 1 149.0 12 40 #VALUE! 1.5.E-04 ### 0.10 #VALUE! ### 6~12 ### ### ### 100 1.88
From : 2 11,561 14,396 18.00 0.010 1.00 1.30 2.65 2.7 1 149.0 12 40 #VALUE! 1.5.E-04 ### #VALUE! ### ### ### ### 100 1.88
To : 3 1,324 1,649 18.00 0.010 1.00 1.30 2.65 2.7 1 149.0 4 40 #VALUE! 1.5.E-04 ### #VALUE! ### ### ### ### 100 1.88
Line No.: 4 1,324 1,649 18.00 0.010 1.00 1.30 2.65 2.7 1 149.0 4 40 #VALUE! 1.5.E-04 ### #VALUE! ### ### ### ### 100 1.88
Note :
4 1 #DIV/0! - #VALUE! ### #VALUE! #DIV/0! ### ### ### 100 #DIV/0!
From : 2 #DIV/0! - #VALUE! ### #VALUE! #DIV/0! ### ### ### 100 #DIV/0!
To : 3 #DIV/0! - #VALUE! ### #VALUE! #DIV/0! ### ### ### 100 #DIV/0!
Line No.: 4 #DIV/0! - #VALUE! ### #VALUE! #DIV/0! ### ### ### 100 #DIV/0!
Note :
Project No. : Revision No. :
Project Name : Revision Date:
Comp. Factor
specific heat ratio
Nominal size Rough F.
Press. Drop
(Calc'ed*1.2)
Press. Drop limit
Velo. Limit
Outlet Press.
Equi. Length
Nm3/hr k(Cp/Cv) kg/cm2 g 1-Up, 2-Down
oC bar/ 100m
barg/ 100m (kg/cm2)/L kg/m3
Line Differential Pressure Calculation for Mixed Flow
ID Service CasesFlow rate Density MW
Temp. Nominal Size PipeID Press Drop Pressure Drop(kg/cm2)
Schdule Homo. Method Duckler Homogeneous Duckler
kg/hr cPinch inch m/sec
Cal'ced Bar Regime x y dyne/cm kg/cm2 kg/cm2Barg - - -
5 1 L 2,055 902.4 0.179 161.4 100.0 44.9 3.0 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### 48.4 #VALUE! #VALUE!V 345 2.59 0.014 38.47 43.99 40.0 0.00015 #VALUE! #VALUE! #VALUE! #VALUE! ### ### ###
2 L 2,055 902.4 0.179 162.6 347.0 46.5 3.0 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### 48.4 #VALUE! #VALUE!V 345 2.59 0.014 59.39 45.59 40.0 0.00015 #VALUE! #VALUE! #VALUE! #VALUE! ### ### ###
3 L 2,055 902.4 0.179 166.3 308.0 44.0 3.0 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### 48.4 #VALUE! #VALUE!V 345 2.59 0.014 34.46 43.19 40.0 0.00015 #VALUE! #VALUE! #VALUE! #VALUE! ### ### ###
4 L 2,055 902.4 0.179 164.3 350.0 46.3 3.0 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### 48.4 #VALUE! #VALUE!V 345 2.59 0.014 58.07 45.39 40.0 0.00015 #VALUE! #VALUE! #VALUE! #VALUE! ### ### ###
6 1 L - #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### #VALUE! #VALUE!V #VALUE! #VALUE! #VALUE! #VALUE! ### ### ###
2 L - #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### #VALUE! #VALUE!V #VALUE! #VALUE! #VALUE! #VALUE! ### ### ###
3 L - #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### #VALUE! #VALUE!V #VALUE! #VALUE! #VALUE! #VALUE! ### ### ###
4 L - #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### #VALUE! #VALUE!V #VALUE! #VALUE! #VALUE! #VALUE! ### ### ###
Project No. : Revision No. :
Project Name : Revision Date:
Visc. Inlet Press.
Two Phase Velocity
Flow Regime, Horizontal Line (Baker Chart)
Average Density Surface
TensionInlet Press.
Roughness factor
Vapor Vol. Frac, Fv
Flow Regime, Vertical Line (G-W Chart)
Inplace Density
kg/m3oC
kg/cm2g Calc * 1.5 Bar kg/m3
From :
To :
Line :
Note :
From :
To :
Line :
Note :
Line sizing guideline LDM Parson
Type of service Velocity Velocity
ft/sec m/s psi / 100 ft ft/s m/s
Liquid lines
Pump Suction
Boiling liquid 2 6 0.61 1.83 0.5 0.12 0.11 4 1.22 0.01 0.06
Non-boiling liquid 4 8 1.22 2.44 1 0.23 0.23 5.2 1.58 0.05 0.22
Pump discharge 10 3.05 0.2 0.5
6 8 1.83 2.44 6 1.38 1.36
8 10 2.44 3.05 4 0.92 0.90
10 15 3.05 4.57 2 0.46 0.45
Bottom outlet 4 6 1.22 1.83 0.6 0.14 0.14
Reboiler trap out 1 4 0.30 1.22 0.15 0.03 0.03
Liquid from condenser 3 6 0.91 1.83 0.5 0.12 0.11
Liquid to chiller 4 6 1.22 1.83
Refrigent line 2 4 0.61 1.22 0.4 0.09 0.09
Gravity run lines 3 8 0.91 2.44 0.4 0.09 0.09
Liquid feed to towers 4 6 1.22 1.83
Steam condensate line 0.5 1 0.15 0.30
Drains 2 6 0.61 1.83
Waste water collection systems 3 8 0.91 2.44
Reboiler downcomer 3 7 0.91 2.13
Sidestream draw-off 4 1.22 0.06 0.1
Amine, Carbonate, Sour water 7 2.13
Sodium carbonate 4~6 1.22~1.83
Salt water 10 3.05
Erosion limit API-RP-14E
Water lines
General service 2 16 0.61 4.88 2 0.46 0.45
1 inches 2 3 0.61 0.91
2 inches 3 4.5 0.91 1.37
4 inches 5 7 1.52 2.13
6 inches 7 9 2.13 2.74
8 inches 8 10 2.44 3.05
10 inch 10 12 3.05 3.66
12 inch 10 14 3.05 4.27
16 inch 10 15 3.05 4.57
20 inches and up 10 16 3.05 4.88
Pump suction and drain 4 7 1.22 2.13
Pump discharge 5 10 1.52 3.05
BFW 8 15 2.44 4.57
Refinery water lines 2 5 0.61 1.52 2.5 0.58 0.57
Cooling water * 12 16 3.66 4.88 2 0.46 0.45
From condenser 3 5 0.91 1.52
Hydrocarbon vaporGeneral recommendation
Subatmospheric 0.1 0.1 0.02 0.02 0.02 0.02
0.15 0.15 0.03 0.03 0.03 0.03
0.3 0.3 0.07 0.07 0.07 0.07
0.6 0.6 0.14 0.14 0.14 0.14
1.5 1.5 0.35 0.35 0.34 0.34
2 2 0.46 0.46 0.45 0.45
Subatmospheric 250 76.20 0.01 0.06
~ 6.9 bara 200 60.96 0.06 0.13
~ 69 bara 150 45.72 0.13 0.5
> 69 bara 100 30.48 0.2%
Gas line within BL 0.5 0.5 0.12 0.12 0.11 0.11
Compressors piping suction 75 200 22.86 60.96 0.5 0.5 0.12 0.12 0.11 0.11
Reciprocating 20~40 6~12 0.1
Centrifugal 40~80 12~25 0.1
Compressors piping discharge 100 250 30.48 76.20 1 1 0.23 0.23 0.23 0.23
Refrigant suction lines 10 35 3.05 10.67
Refrigant discharge lines 35 60 10.67 18.29
Tower overhead
125 200 38.10 60.96 0.05 0.1 0.01 0.02 0.01 0.02
Atmospheric 60 100 18.29 30.48 0.2 0.5 0.05 0.12 0.05 0.11
0.2 0.5 0.05 0.12 0.05 0.11
Gas turbine inlet line 150 350 45.72 106.7
Vacuum exhaust lines 450 137.2
Two phase flow 35 75 10.67 22.86
Reboiler riser (liq./vap.) 35 45 10.67 13.72
High velocity flow (Pressure letdown) 0.9 Mach
Steam linesGeneral recommendation 0.02 0.6
0.25 0.06 0.06 d=inch d=inch
0.5 0.12 0.11
1 0.23 0.23
1.5 0.35 0.34
Saturated steam 200 60.96
Superheated steam 250 76.20
Feed lines to pumps & reciprocating engines 12.5 15 3.81 4.57
Power house equipment & process piping 100 170 30.48 51.82
115 330 35.05 100.6 0.3 0.07 0.07
Exhaust steam line for exhaust steam main 0.2 0.5 0.05 0.12 0.05 0.11
Exhaust steam line for leads to header 1.5 0.35 0.34
Steam line to drivers, heat exchanger and heating coils
0.5 1.5 0.12 0.35 0.11 0.34
1 2 0.23 0.46 0.23 0.45
1 2 0.23 0.46 0.23 0.45
1 3 0.23 0.69 0.23 0.68
Maximum DP Maximum DP
kg/cm2/100m bar / 100 m bar / 100 m
0-250 gpm, 0~ 57 m3/hr
250-700 gpm, 57~159 m3/hr
> 700 gpm, > 159 m3/hr
Max. 200 [100/(r)0.5] or Max.
50% sonic
~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
Vacuum ( < 10 psig, 0.7 kg/cm2g)
> 50 psig, 3.5 kg/cm2g, 3.5 barg
50(d)0.5 15(d)0.5
~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
Boiler & turbine leads (superheated > 200 psig, 14 kg/cm
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
EQUIVALENT PIPE LENGTH(m) for STEEL PIPE
Nominal Size(inches) 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 NONEInside Diameter(inches) 0.622 0.824 1.049 1.61 2.067 2.469 3.068 4.026 6.065 7.981 10.020 11.938 13.250 15.250 17.250 19.250 21.250 23.250 25.250 27.250 29.250 31.250 33.250 35.250 41.250 47.250 53.250 59.250 65.125 71.125 83.125 95.000 107.000 119.000 1/2
Schdule No. 30 30 20 20 20 20 3/490° elbow Short Radius 0.8 1.2 1.6 1.9 2.3 3.1 4.6 6.1 7.6 9.1 10.1 11.6 13.1 14.7 16.2 17.7 19.2 20.8 22.3 23.8 25.3 26.9 31.4 36 40.6 45.1 49.6 54.2 63.3 72.4 81.5 90.7 1
Long Radius 0.5 0.8 1.1 1.3 1.6 2 3.1 4.1 5.1 6.1 6.7 7.7 8.8 9.8 10.8 11.8 12.8 13.8 14.9 15.9 16.9 17.9 21 24 27.1 30.1 33.1 36.1 42.2 48.3 54.4 60.5 1 1/245° elbow Short Radius 0.4 0.7 0.8 1 1.2 1.6 2.5 3.2 4.1 4.9 5.4 6.2 7 7.8 8.6 9.4 10.3 11.1 11.9 12.7 13.5 14.3 16.8 19.2 21.6 24.1 26.5 28.9 33.8 38.6 43.5 48.4 2
Long Radius 0.5 0.6 0.7 1 1.5 2 2.5 2.5 3.5 3.5 4 4.5 5 6 2 1/2Tee Flow Branch 1.6 2.5 3.2 3.8 4.7 6.1 9.2 12.2 15.3 18.2 20.2 23.2 26.3 29.3 32.4 35.4 38.5 41.5 44.6 47.6 50.7 53.7 62.9 72 81.2 90.3 99.3 108.4 126.7 144.8 163.1 181.4 3
Flow Through 0.5 0.8 1.1 1.3 1.6 2 3.1 4.1 5.1 6.1 6.7 7.7 8.8 9.8 10.8 11.8 12.8 13.8 14.9 15.9 16.9 17.9 21 24 27.1 30.1 33.1 36.1 42.2 48.3 54.4 60.5 4 Glove Fully Open Valve 10.7 16.4 21 25.1 31.2 40.9 61.6 81.1 101.8 121.3 134.6 154.9 175.3 195.6 215.9 236.2 256.5 276.9 297.2 317.5 337.8 358.1 419.1 480.1 6
8.2 10.5 12.5 15.6 20.5 30.8 40.5 50.9 60.6 67.3 77.5 87.6 97.8 108 118.1 128.3 138.4 8 7.2 9.2 11 13.6 17.9 27 35.5 44.5 53.1 58.9 67.8 76.7 85.6 94.5 103.3 112.2 121.1 10
Check Valve Swing 4 5.5 7.1 8.5 10.5 13.8 20.8 27.4 34.4 40.9 45.4 52.3 59.2 66 72.9 79.7 86.6 93.4 100.3 107.2 114 120.9 141.4 162 12 Ball 6.1 7.9 9.4 11.7 15.3 23.1 30.4 38.2 45.5 50.5 58.1 65.7 73.3 81 88.6 96.2 103.8 14 Lift 12 27.5 46 76 107 137 168 199 16
Three Way Cock Valve Straight Flow 1.8 2.4 2.8 3.5 4.6 6.9 9.1 11.5 18 Flow Branch 5.7 7.4 8.8 10.9 14.3 21.6 28.4 35.6 20
Ball Valve Full Port 0.3 0.6 0.9 1 2 2.5 3 4 4.5 5 5.5 6 7.5 22 Reduced Port 2.5 3 6 14 17 20 24.5 29 33.5 24
Plug Valve Straight Full Port 0.6 0.9 1.5 2 3 4 5 5.5 6 7.5 8 9 11 26 Reduced Port 1.5 2 4.5 7.5 15 27.5 38 45.5 28
Straight Cock Valve 0.8 1.1 1.3 1.6 2 3.1 4.1 5.1 6.1 6.7 7.7 8.8 9.8 10.8 11.8 12.8 13.8 30 Butterfly Valve 1.9 2.5 3.1 4 4.5 6 8 9 10.5 11.5 12 13 14 17 21.5 29 36.5 40 32 Diaphram Valve 2.5 7 10 17 35 36.5 46 68.5 76 34
Gate Valve Fully Open 0.3 0.6 0.8 1 2 2 3 3.5 4 4 4.5 5 6 7.5 9.5 11 12 36 Angle Valve 5.3 10.5 15.6 20.5 30.8 40.5 50.9 60.6 67.3 77.5 87.6 97.8 108 118.1 128.3 138.4 42 180% Return bend Short Radius 1 1.6 1.9 2.2 2.5 3.5 5.5 7 9 10 12 13 15 16.5 20 25 29 35 40 45.5 51 56 61 70.5 80 86 86.5 48
Long Radius 0.8 2.5 3.1 3.7 5 6.5 9.5 12.5 15.5 18.5 20.5 23.5 26 30.5 37 44 52 60 68 77.5 87.5 93.5 101.5 116.5 129 144 158 54 90% Return bend Short Radius 0.8 1 1.1 1.5 2 3 3.5 4.5 5 6 6.5 7.5 8.5 10 60
Long Radius 1.3 1.6 1.9 2.5 3.5 5 6.5 8 9.5 10.5 12 13 15.5 18.5 66 45% Return bend Short Radius 0.4 0.5 0.6 0.7 0.9 1.5 2 2.5 2.5 3 3.5 4 4.5 5 72
Long Radius 0.7 0.8 1 1.5 2 2.5 3.5 4 5 5.5 6 6.5 8 9.5 84 90% Meter bend 3 meter 6.1 6.7 7.7 8.8 9.8 10.8 11.8 12.8 13.8 14.9 15.9 16.9 17.9 21 24 27.1 30.1 33.1 36.1 96
4 meter 5.5 6.1 7 7.9 8.8 9.7 10.6 11.5 12.5 13.4 14.3 15.2 16.1 18.9 21.6 24.3 27.1 29.8 32.5 108 Exit 0.6 0.8 1.2 1.9 2.8 4.3 6 10.3 14.5 18.9 23.3 26.7 31.2 36.5 41.4 46.1 50.9 56.3 61.8 66.9 72.2 77.5 82.9 97.9 118.8 133.9 150.5 165.4 180.7 211.1 241.3 271.8 302.3 120 Inward Projecting Entrance 0.5 0.7 0.9 1.5 2.2 3.4 4.7 8 11.3 14.7 18.2 20.8 24.4 28.5 32.3 36 39.7 43.9 48.2 52.2 56.3 60.4 64.7 76.4 92.7 104.5 117.4 129 140.9 164.7 188.2 212 235.8Sharp edged Entrance 0.3 0.4 0.6 1 1.4 2.2 3 5.1 7.2 9.4 11.7 13.4 15.6 18.3 20.7 23.1 25.5 28.1 30.9 33.5 36.1 38.7 41.5 49 59.4 67 75.2 82.7 90.3 105.6 120.7 135.9 151.1Slightly rounded Entrance 0.1 0.2 0.3 0.5 0.7 1 1.4 2.5 3.5 4.5 5.6 6.4 7.5 8.8 9.9 11.1 12.2 13.5 14.8 16.1 17.3 18.6 19.9 23.5 28.5 32.1 36.1 39.7 43.4 50.7 57.9 65.2 72.5Well rounded Entrance 0.05 0.1 0.2 0.2 0.4 0.6 0.8 0.9 1.1 1.2 1.5 1.7 1.8 2 2.3 2.5 2.7 2.9 3.1 3.3 3.9 4.8 5.4 6 6.6 7.2 8.4 9.7 10.9 12.1
NOTE 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 3/4 1 1 1/2 2 3 4 6 8 10 12 14 16 18 20 24d2 1/2 1/2 3/4 3/4 1 1 1 1/2 1 1/2 2 2 3 3 4 4 6 4 6 8 6 8 10 6 8 10 12 8 10 12 14 10 12 14 16 12 14 16 18 18 20
0.2 0.4 0.2 0.5 0.4 0.7 0.4 1.2 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 3.7
Enlargers d2/d1=1/2 0.3 0.9 2.0 3.0 5.0 5.5 6.0 9.0 12.0 16.5 20.0 26.0 32.0(gradual) d2/d1=3/4 0.3 0.3 0.3 0.9 0.9 0.9 1.0 1.0 2.0 3.0 3.0 4.0 4.5Reducers d2/d1=1/2 0.3 0.3 0.6 1.0 2.0 2.0 3.5 3.5 4.5 6.0 8.0 10.0 12.5(gradual) d2/d1=3/4 0.3 0.3 0.3 0.6 0.6 0.6 0.9 0.9 2.0 2.0 2.0 3.0 3.0
NOTE Length in terms of smaller diameter. For two phase flow, mutiply these values by factor of 2.0.
90%φ60%φ45%φ
3/8"wall 7/16"wall 1/2"wall
d2 d1 d2 d1
d1 d2 d1 d2
Nominal size(inches)
40
Enlargers### 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
NONE 3/4 0
1 0 0.21 1/2 0.7 0.4
2 0.7 0.43 1.2 0.94 1.5 0.96 2.4 1.28 3.7 2.2
10 4.6 4.3 212 5.8 4.6 214 6.7 3 4.6 1.916 9.1 3 4.6 2.218 9.1 7 4.6 1.220 9.1 6.4 4 1.524 7.6 3.7
Reducers### 3/4 1 1 1/2 2 2 1/2 3 4 6 8 10 12 14 16 18 20 24 26 28 30 32 34 36 42 48 54 60 66 68 72 84 96 108 120
NONE 1/2 0.2 0.3 3/4 0.2 0.31 0.3 0.4
1 1/2 0.4 0.82 0.7 13 1 1.64 1.3 2.2 2.56 2.2 2.9 3.7 4.38 1.9 3.7 4.3 5.2
10 2 4 5.2 5.812 1.9 4.6 5.8 7.114 4.6 7.116 1.3 418 1.5 7.620 4.5
PIPE ID OF STEEL PIPE
10 20 30 40 60 80 100 120 140 160
NONE
1/4 0.364 0.410
1/2 0.622 0.674 0.622 0.546 0.466 0.446 3/4 0.824 0.884 0.824 0.742 0.612 0.612
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 2.125
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 5.187
8 7.981 8.125 8.071 7.981 7.813 7.625 7.437 7.187 7.001 6.813
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 22.876 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
42 41.000 40.750 40.500
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
STD