design calculations for pressure vessels

Inputs

Dsign Code: ASME Sec VIII, Div.1, 2004

Cylinder Construction Material

See Section II Part D for other materials

Internal Design Pressure P 100.00 psi

Inner Diameter of Head L 2438.40 mm

Design Temperature Temp 650.00 °F

Corrosion Allowance CA 3.18 mm

Knuckle radius r 152.40 mm

0

15000.00 To be entered by user

Radiography Type Full

Joint Efficiency E 1.00

Ratio L/r 16.00

Case 1: when L/r= 16

Thickness per UG-32

This Formula Is Valid

Result:

t = 17.5762 mm

0.300 mm

to= 17.8762 mm or

14.2875 mm

9/16 in Recommend a higher thickness

Case 2: when L/r < 16

Thickness per UG-32

This Formula Is Not Valid

THICKNESS OF TORISPHERICAL HEAD(Internal Pressure & Inside Dimensions)

As Desired

Allowable Stress S psi

Min. Req. Design Thickness of Head

Mill Undertolerence per UG-16

Min. req'd thickness of Head

Select Head thickness

Torispherical Head

)1.0(

885.0

PSE

PLt

PSE

PLMt

2.02

Result:

M= 1.75 mm

t = 17.41 mm

0.300 mm

to= 17.71 mm or

14.2875 mm

SA-516 Gr. 70 9/16 in Recommend a higher thickness

SA-106 Gr. B

Case 3: SA-285 Gr. C

when L/r > 16 SA-240 Gr. 304

Thickness per UG-32As Desired


Result:

Factor M M= 1.75 mm

t = 17.41 mm

0.300 mm

to= 17.71 mm or

14.2875 mm


Stress Releif per UCS-79

Nominal thickness of Vessel tnom= 17.88 mm

Final Centre Linre Radius Rf= 170.28 mm

Original Centreline radius Ro= infinity for straight plate

7.87%

Stress Releif Required. To Avoid Stress Releif Increase The Thickness




Percent Extreme fiber Elongation

Factor M






PSE

PLMt

2.02

)3(4

1

rLM

PSE

PLMt

2.02

Do not print this sheet, it contains only information

as how to design elements of pressure vessel

INPUT CELLS (UNLOCKED) Drop down selection

CALCULATIONS BY PROGRAM

RESULTS

STEPS

1 Select sheet what you need to design (e-g: For shell design select shell sheet)

2 Input values in yellow cells -----> or thru cells

3 Results are shown for every item at end of the sheet

Histroy:

0 Reviewed with ARC USA 05.11.07

INPUTS

Select sheet what you need to design (e-g: For shell design select shell sheet)

INPUTS

Inputs


Cylinder Construction MaterialSee Section II Part D for other materials


Inner Diameter of Shell Di 4580.00 mm



20000

20000.00



Shell thickness per UG-27

Result:

t = 15.2910 mm

0.300 mm

to= 15.5910 mm or

16.0000 mm Recommended thickness is adequate





0.348% Stress Releif Not RequiredPercent Extreme fiber Elongation

Min. Req. Design Thickness of Shell

Min. req'd thickness of Shell

Select shell thickness

(Internal Pressure & Inside Dimensions)

THICKNESS OF CYLINDRICAL SHELL

SA-516 Gr. 70



Cylindrical Shell

)6.0(2 PSE

PDt i

Inputs




Inner Diameter of Shell Do 219.00 mm



17115

20000.00



Shell thickness per UG-27

Result:

t = 11.9131 mm

1.489 mm

to= 13.4023 mm or






6.809%


SA-106 Gr. B

(Internal Pressure & Outside Dimensions)

THICKNESS OF CYLINDRICAL SHELL



Min. Req. Design Thickness of Shell

Min. req'd thickness of Shell

Select shell thickness


Cylindrical Shell

)4.0(2 PSE

PDt o

Inputs




Inner Diameter of Shell Di 1524.00 mm

Height of Liquid Level in Boot H 3.00 ft



Total Internal Pressure in Boot Pi 351.30 psi

0




Thickness per UG-27

Result:

t = 16.5271 mm

0.300 mm

to= 16.8271 mm or



Nominal thickness of Boot tnom= 17.00 mm



1.10% Stress Releif Not Required




Min. Req. Design Thickness of Boot

Min. req'd thickness of Boot

Select Boot thickness

As Desired


THICKNESS OF BOOT

Boot

)6.0(2 PSE

DPt ii

Inputs




Inner Diameter of Head Di 3300.00 mm



20000

20000.00

Radiography Type Spot


Thickness per UG-32

Result:

t = 145.1705 mm

0.300 mm

to= 145.4705 mm or

14.0000 mm

Recommend a higher thickness






SA-516 Gr. 70


THICKNESS OF ELLIPSOIDAL HEAD







Ell

ipso

idal

H

ead

Ell

ipso

idal

H

ead

PSE

PDt i

2.02

Inputs




Inner Diameter of Head D0 273.00 mm



20000

20000.00



Thickness per UG-32

Result:

t = 12.2271 mm

0.300 mm

to= 12.5271 mm or






21.52%







SA-516 Gr. 70




Ell

ipso

idal

H

ead

Ell

ips

oid

al

H

ead

PSE

PDt o

8.12

Inputs


Cylinder Construction Material Add SA 105 as Boot capSee Section II Part D for other materials





0




Thickness per UG-32

Result:

t = 7.4297 mm

0.300 mm

to= 7.7297 mm or


5/16 in





7.53%








As Desired



Boot

PSE

PDt i

2.02

Inputs







0




Thickness per UG-32

Result:

t = 3.0495 mm

0.300 mm

to= 3.3495 mm or







As Desired


THICKNESS OF HEMISPHERICAL HEAD







Sp

he

ric

al

H

ea

d Sp

he

ric

al

H

ea

d

)2.02(2 PSE

PDt i

Inputs

Note: α to be less than 30 degree




Inner Diameter of Conical section Di 2438.40 mm



Cone Half Apex Angle α 35.00 Degree

17115

20000.00



Thickness per UG-32

Result:

t = 8.7270 mm

1.091 mm

to= 9.8179 mm or

7.9375 mm







S psi


Min. Req. Design Thickness of Conical section

Min. req'd thickness of Conical section

Select Conical section thickness

SA-106 Gr. B


THICKNESS OF CONICAL SECTION


Formula is not valid. See Div I for

special analysis

Allowable Stress

α Conical Section

)6.0(2 PSECos

PDt i

Inputs


Cylinder Construction Material

See Section II Part D for other materials


Inner Diameter of Head L 2438.40 mm



Knuckle radius r 152.40 mm

0




Ratio L/r 16.00

Case 1: when L/r= 16

Thickness per UG-32

This Formula Is Valid

Result:

t = 17.5762 mm

0.300 mm

to= 17.8762 mm or

14.2875 mm


Case 2: when L/r < 16

Thickness per UG-32







THICKNESS OF TORISPHERICAL HEAD


As Desired

Torispherical Head

)1.0(

885.0

PSE

PLt

PSE

PLMt

2.02

Result:

M= 1.75 mm

t = 17.41 mm

0.300 mm

to= 17.71 mm or

14.2875 mm

SA-516 Gr. 70 9/16 in Recommend a higher thickness

SA-106 Gr. B

Case 3: SA-285 Gr. C

when L/r > 16 SA-240 Gr. 304

Thickness per UG-32As Desired


Result:

Factor M M= 1.75 mm

t = 17.41 mm

0.300 mm

to= 17.71 mm or

14.2875 mm






7.87%











Factor M

PSE

PLMt

2.02

)3(4

1

rLM

PSE

PLMt

2.02

Inputs







FALSE




Required thickness of Shell tr -505.00 mm

Actual thickness of Shell ts -505.00 mm

Thickness per UG-34

Result:

C= 0.33 mm

t = 45.8892 mm

0.300 mm

to= 46.1892 mm or

46.0000 mm

Recommend a higher thickness




C Factor





As Desired


THICKNESS OF HEMISPHERICAL HEAD

Circular Flat Head

SE

CPDt

s

r

t

tC 33.0



10.56%



Dia of Max.Weight Dist. Of centre Bolt Dist. Bolt Dia

Vessel of Vessel Length Width Thickness Height Thickness Width Thickness Width Thickness from Base Plate

(mm) (Kg) A (mm) C (mm) G (mm) (mm) H (mm) D (mm) K (mm) (mm) H (mm) (B) E (mm) (mm)

304.8 19,051 266.7 101.6 6.35 6.35 101.6 6.35 304.8 88.9 12.70

355.6 22,680 317.5 101.6 6.35 6.35 101.6 6.35 330.2 101.6 12.70

406.4 25,402 355.6 101.6 6.35 6.35 101.6 6.35 355.6 127 12.70

457.2 28,123 393.7 101.6 6.35 6.35 101.6 6.35 381 152.4 12.70

508 31,752 444.5 101.6 6.35 6.35 101.6 6.35 406.4 165.1 12.70

558.8 34,474 482.6 101.6 6.35 6.35 152.4 6.35 431.8 177.8 12.70

609.6 38,102 533.4 101.6 6.35 6.35 152.4 6.35 457.2 190.5 12.70

660.4 40,824 571.5 101.6 6.35 6.35 152.4 6.35 6.35 482.6 203.2 12.70

711.2 44,453 622.3 101.6 12.7 6.35 152.4 6.35 6.35 508 215.9 12.70

762 47,174 660.4 101.6 12.7 6.35 152.4 6.35 6.35 533.4 228.6 12.70

812.8 50,803 711.2 101.6 12.7 6.35 152.4 6.35 6.35 558.8 241.3 12.70

863.6 58,061 736.6 152.4 12.7 6.35 279.4 6.35 6.35 584.2 254 12.70

914.4 60,782 774.7 152.4 12.7 6.35 279.4 6.35 6.35 609.6 279.4 12.70

965.2 65,318 838.2 152.4 12.7 6.35 279.4 6.35 6.35 635 304.8 19.05

1016 95,256 889 152.4 12.7 9.525 279.4 9.525 9.525 660.4 330.2 19.05

1066.8 99,792 927.1 152.4 12.7 9.525 279.4 9.525 9.525 685.8 355.6 19.05

1219.2 114,307 1066.8 152.4 19.05 9.525 279.4 9.525 9.525 762 406.4 19.05

1371.6 127,915 1193.8 152.4 19.05 9.525 279.4 9.525 9.525 914.4 457.2 19.05

1524 141,523 1320.8 152.4 19.05 9.525 279.4 9.525 9.525 990.6 508 19.05

Ribs

SADDLE DIMENSIONS

Base Plate Web Plate Wear Plate

1676.4 156,038 1460.5 152.4 19.05 9.525 279.4 9.525 9.525 1066.8 558.8 19.05

1828.8 182,347 1587.5 228.6 19.05 9.525 457.2 9.525 9.525 1143 609.6 19.05

1981.2 197,770 1727.2 228.6 19.05 12.7 457.2 9.525 12.7 1219.2 660.4 19.05

2133.6 213,192 1854.2 228.6 19.05 12.7 457.2 9.525 12.7 1295.4 711.2 25.40

2286 227,707 1981.2 228.6 19.05 12.7 457.2 9.525 12.7 1371.6 762 25.40

2438.4 243,130 2120.9 228.6 25.4 12.7 457.2 9.525 12.7 1447.8 812.8 25.40

2590.8 344,736 2247.9 228.6 25.4 12.7 457.2 12.7 12.7 1524 863.6 25.40

2743.2 365,602 2374.9 228.6 25.4 12.7 457.2 12.7 12.7 1600.2 914.4 25.40

2895.6 386,467 2527.3 228.6 25.4 19.05 609.6 12.7 19.05 1676.4 965.2 25.40

3048 406,426 2641.6 228.6 25.4 19.05 609.6 12.7 19.05 1752.6 1016 31.75

3200.4 426,384 2781.3 228.6 25.4 19.05 609.6 12.7 19.05 1828.8 1066.8 31.75

3352.8 447,250 2908.3 228.6 25.4 19.05 609.6 12.7 19.05 1905 1117.6 31.75

3505.2 467,208 3048 228.6 25.4 19.05 609.6 12.7 19.05 1981.2 1168.4 31.75

3657.6 488,074 3175 228.6 25.4 19.05 609.6 12.7 19.05 2057.4 1219.2 31.75

LATERInputs

* Wind Load (From PVElite) P 8500.00 lbs

* Height of Vessel H 58.00 ft

* Moment MT 493,000.00 lbs-ft

* Outside Radius of Skirt R 28.00 in

* Joint Efficiency E 0.70

* Stress Value of Head or Skirt 20000.00 psi

Mat. Whichever is smaller

* Weight of Tower above Skirt W 78000.00 lbs

Temp(F) S (psi)

(-20) 20,000

Formula used : 50 20,000

100 20,000

200 20,000

Resuslt: 300 20,000

400 20,000

Required Thickness of Skirt 0.30 in 500 20,000

600 19,400

650 18,800

Required Thickness of Skirt 7.58 mm 700 18,100

750 14,800

800 12,000

850 9,300

516 Gr-70

THICKNESS OF SKIRT

Skirt

RSE

W

SER

Mt T

2

²

12

900 6,700

950 4,000

1000 2,500

Note: For other materials

see section 2 part D

Nozzle Size : NB 3/4" (DN 20) Nozzle on Sump of PV-221 ( R22 Receiver ) LATER

Inputs Inputs

UG-45 b(1) for Internal Pressure UG-45 b(2) for External Pressure

Internal Design Pressure P 300.00 psi External Design Pressure P 15.00 psi

Diameter of Shell/Head D 3000.00 mm Diameter of Shell/Head D 3000.00 mm

Design Temperature Temp 200.00 F Design Temperature Temp 200.00 F

Allowable Stress of Shell S 20000.00 psi Allowable Stress of Shell S 20000.00 psi

Joint Efficiency E 1.00 Joint Efficiency E 1.00

Corrosion Allowance CA 3.00 mm Corrosion Allowance CA 3.00 mm

Formula used Formula used

Result Result

Thickness t 25.7043 mm Thickness t 4.1255 mm

Inputs Inputs

UG-16(b) UG-45 b(4)

Minimum thickness t 1/16 in Standard Wall Thk of pipe t 2.87 mm

Minimum thickness t 1.59 mm Minimum thickness t 2.5113 mm


Result Result

Thickness t 4.5875 mm Thickness t 5.5113 mm

Final Result Inputs

UG-45 a for Internal PressureStep 1: Max ( UG 45b(1) , UG 16b) t 25.7043 mm


Step 2: Max ( UG 45b(2) , UG 16b) t 4.5875 mm Diameter of Pipe D 20.00 mm

Design Temperature Temp 200.00 F

Step 3: Max ( Step1 , Step 2) t 25.7043 mm Allowable Stress S 17100.00 psi


Step 4: Min ( Step3 , UG-45 b(4)) t 5.5113 mm Corrosion Allowance CA 3.00 mm

Step 5: Max ( Step4 , UG-45 (a)) t 5.5113 mm Formula used

Result

t 5.5113 mm Thickness t 3.1773 mm

THICKNESS OF NOZZLE AS PER UG-45

Sch

Min Required thickness of

Nozzle

)6.0(2 PSE

PDt

)6.0(2 PSE

PDt

)6.0(2 PSE

PDt

Nozzle Size : 11.75 in ASME Section VIII Index L-7.2 Example 2 LATER

Inputs Inputs

UG-45 b(1) for Internal Pressure UG-45 b(2) for External Pressure

Internal Design Pressure P 400.00 psi External Design Pressure P 15.00 psi

Diameter of Shell/Head D 60.00 in Diameter of Shell/Head D 60.00 in

Design Temperature Temp 250.00 F Design Temperature Temp 250.00 F

Allowable Stress of Shell S 14300.00 psi Allowable Stress of Shell S 14300.00 psi

Joint Efficiency E 1.00 Joint Efficiency E 1.00

Corrosion Allowance CA 0.00 in Corrosion Allowance CA 0.00 in

Formula used Formula used

Result Result

Thickness t 0.8535 in Thickness t 0.0315 in

Inputs Inputs

UG-16(b) UG-45 b(4)

Minimum thickness t 1/16 in Standard Wall Thk of pipe t 9.57 mm

Minimum thickness t 1.59 mm Minimum thickness t 8.3738 mm


Result Thickness t 4.5875 mm Result Thickness t 8.3738 mm

Thickness t 0.1806 in Thickness t 0.3297 in

Final Result Inputs

UG-45 a for Internal PressureStep 1: Max ( UG 45b(1) , UG 16b) t 0.8535 mm


Step 2: Max ( UG 45b(2) , UG 16b) t 0.1806 mm Diameter of Pipe D 11.75 in

Design Temperature Temp 250.00 F

Step 3: Max ( Step1 , Step 2) t 0.8535 mm Allowable Stress S 16600.00 psi


Step 4: Min ( Step3 , UG-45 b(4)) t 0.3297 mm Corrosion Allowance CA 0.00 in

Step 5: Max ( Step4 , UG-45 (a)) t 0.3297 mm Formula used

Result

t 0.3297 mm Thickness t 0.14 in

Actual Thickness of Pipe = Pipe Schedule Thickness x 0.875 (12.5% Undertolerance )

Actual Thickness of Pipe should be greater than Minimum Required Thickness

THICKNESS OF NOZZLE AS PER UG-45

Min Required thickness of

NozzleSch

)6.0(2 PSE

PDt

)6.0(2 PSE

PDt

)6.0(2 PSE

PDt

ND OD Sch Sch. Sch. Std. Sch. Sch. Extra Sch. Sch. Sch. Sch. Sch XX ND

(in) 10 20 30 Wall 40 60 Strong 80 100 120 140 160 Strong

0.50 21.30 2.77 2.77 3.73 3.73 4.75 7.47 1/2

0.75 26.70 2.11 2.87 2.87 3.91 3.91 5.54 7.82 3/4

1.00 33.4 2.77 3.38 3.38 4.55 4.55 6.35 9.09 1.00

1.25 42.2 2.77 3.56 3.56 4.85 4.85 6.35 9.7 1 1/4

1 1/2 48.3 2.77 3.69 3.69 5.08 5.08 7.14 10.16 1 1/2

2.00 60.3 2.77 3.91 3.91 5.54 5.54 8.71 11.07 2.00

2 1/2 73 3.05 5.16 5.16 7.01 7.01 9.52 14.02 2 1/2

3.00 88.9 3.05 5.49 5.49 7.62 7.62 11.13 15.24 3.00

3 1/2 101.6 3.05 5.74 5.74 8.08 8.08 16.15 3 1/2

4.00 114.3 3.05 6.02 6.02 8.56 8.56 11.3 13.49 17.12 4.00

5.00 141.3 3.4 6.55 6.55 9.52 9.52 12.7 15.87 19.05 5.00

6.00 168.3 7.11 7.11 10.97 10.97 14.27 18.24 21.95 6.00

8.00 219.1 6.35 7.04 8.18 8.18 10.34 12.7 12.7 15.06 18.24 20.62 23.01 22.22 8.00

10.00 273.1 6.35 7.8 9.27 9.27 12.7 12.7 15.06 18.24 21.41 25.4 28.57 10.00

12.00 323.9 6.35 8.38 9.57 10.31 14.27 12.7 17.45 21.41 23.8 28.57 33.32 12.00

14.00 355.6 6.35 7.92 9.52 9.52 11.12 15.06 12.7 19.05 23.8 27.76 31.75 35.71 14.00

16.00 406.4 6.35 7.92 9.52 9.52 12.7 16.66 12.7 21.41 26.19 30.94 36.53 40.46 16.00

18.00 457.2 6.35 7.92 11.12 9.52 14.27 19.05 12.7 23.8 29.36 34.92 39.67 45.24 18.00

20.00 508 6.35 9.52 12.7 9.52 15.06 20.62 12.7 26.19 32.54 38.1 44.45 49.99 20.00

22.00 558.8 6.35 9.52 12.7 9.52 15.87 22.22 12.7 28.57 34.92 41.27 47.64 53.97 22.00

24.00 609.6 6.35 9.52 14.27 9.52 17.48 24.59 12.7 30.94 38.89 24.00

26.00 660.4 7.92 12.7 9.52 12.7 26.00

28.00 711.2 7.92 12.7 15.87 9.52 12.7 28.00

30.00 762 7.92 12.7 15.87 9.52 12.7 30.00

32.00 812.8 7.92 12.7 15.87 9.52 17.48 12.7 32.00

34.00 863.6 7.92 12.7 15.87 9.52 17.48 12.7 34.00

36.00 914.4 7.92 12.7 15.87 9.52 19.05 12.7 36.00

PIPE SCHEDULE CHART

LIFTING LUG DIMENSIONS

Vessel Weight Dia of Hole Thickness of Lug Radius of Outer Height of Lug Length of Lug Weld

(Kg) D (mm) T (mm) arc R (mm) H (mm) L (mm) (Min)

5,443 25.4 12.7 38.1 127 254

9,072 28.702 19.05 50.8 152.4 254

13,608 35.052 25.4 54.102 152.4 254

22,680 41.402 31.75 63.5 177.8 304.8

31,752 54.102 31.75 88.9 203.2 304.8

45,360 63.5 38.1 114.3 228.6 406.4

68,040 76.2 44.45 127 254 406.4

90,720 101.6 50.8 152.4 304.8 457.2

113,400 107.95 50.8 165.1 330.2 457.2

136,080 114.3 63.5 177.8 355.6 508

12.7 mm Full Penetration Fillet

19.05 mm Full Penetration Fillet

LATER

Butt Weld Input Pressure Conditions

Thickness of the Plate t 16.00 mm Design Pressure P 400.00 psi

Bevel Angle Theta 56.00 degree Diameter D 1375 mm

Diameter to be Weld D 1375.00 mm Area for Pressure A 1484140.63 mm2

Total Area of Weld A 539867.88 mm2

Area for Pressure A 2300.42 in2

Total Area of Weld A 836.80 in2

Load induced F 920169 lbs

Allowable Stress of Material S 20000.00 psi

Bearable Load for Butt Weld F 16735938 lbs

Strength of Weld 1718.79 %

Result Weld is O.K.

LATER

InputsBolt Area Bolt Size

Wind Load (From PVElite) P 3000.00 lbs in2

in

Height of Vessel with Skirt H 21.00 ft 0.126 0.500

Moment M 63,000.00 lbs-ft 0.202 0.625

Weight of Vessel W 11000.00 lbs 0.302 0.750

Bolt Circle 84.00 in 0.419 0.875

Area within Bolt Circle AB 5,538.96 in2

0.551 1.000

Circumference of Bolt Circle CB 264 in 0.693 1.125

Maximum Tension T 94.78 lb/in 0.89 1.250

Allow. Stress Value of Bolt Mat. SB 15,000.00 psi 1.054 1.375

No. of Anchor Bolts N 8.00 1.294 1.500

Req.Area of one Bolt BA 0.21 in2

1.515 1.625

Dia of Bolt from Table against Root Area d 0.63 in 1.744 1.750

Induced Stress in Anchor Bolts Sind 10,191.08 psi 2.049 1.875

Corrosion Allowance for Bolt CA 0.13 in 2.3 2.000

3.02 2.250

Formulas Used 3.715 2.500

4.618 2.750

i Maximum Tension ( lb/in ) 5.621 3.000

ii Req. Area of One Bolt ( Sq.in )

iii Stress in Anchor Bolt ( psi )

Resuslt:

Required Diameter of Anchor Bolt 0.75 in

Required Diameter of Anchor Bolt 19.05 mm

ANCHOR BOLT DESIGN

Table

BB C

W

A

MT 12

NS

TCB

B

BA

NB

TCS

A

BB

LATER

Nominal Thickness Nominal Thickness Temperature (F)

(in) (mm)

0.1 2.54 -55 2.54 -55

0.2 5.08 -55 5.08 -55

0.3 7.62 -55 7.62 -55

0.4 10.16 -55 10.16 -55

0.5 12.7 -55 12.7 -55

0.6 15.24 -50 15.24 -50

0.7 17.78 -45 17.78 -45

0.8 20.32 -40 20.32 -40

0.9 22.86 -35 22.86 -35

1 25.4 -30 25.4 -30

1.3 33.02 -20 33.02 -20

1.5 38.1 -15 38.1 -15

1.7 43.18 -10 43.18 -10

2.2 55.88 0 55.88 0

2.5 63.5 5 63.5 5

2.9 73.66 10 73.66 10

3.4 86.36 15 86.36 15

3.8 96.52 20 96.52 20

4.2 106.68 25 106.68 25

4.7 119.38 30 119.38 30

5.3 134.62 35 134.62 35

5.4 137.16 35 137.16 35

6 152.4 38 152.4 38

0

0

0

0

0

0

Temp (F) Thickness

X1 -50 Y1 15.24

X ? Y 16

X2 -45 Y2 17.78

X -48.5

INTERPOLATION

X1 340.57 Y1 81.35

X ? Y 85

X2 359.93 Y2 85.95

X 355.9317

INTERPOLATION

design calculations for pressure vessels

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