Pressure vessels, wall thickness

[silver7767]

Homework Statement

20 m3 of gas at a pressure of 25 bar is to be stored in a cylindrical
pressure vessel 2 m long. Given the following information :
The yield strength of the vessel material is 14,000 psi
If a factor of safety of 5 is to be used, determine:
(a) Whether the vessel should be treated as a thin or thick cylinder.
(b) The wall thickness required for the pressure vessel.

Hi , so far i got,

radius;
r=1.784

hoop stress
Qc=19.3*10^6 pa

wall thickness
t=0.231 m

inner radius
Ri=1.553

thickness ratio
6.72

So this vessel should be treated as a thick wall vessel and minimun wall thickness should be 0.231 m

have i got it right. please let me know.

Thank you all in advance

 

[silver7767]

Anyone ?

 

[captain666]

I've got the same question as an assigmnent and am a bit lost. Just wondered how u got your answers - looking at the info they've given me I can't fit it to any formulas and without knowing whether the vessel is thin or thick walled I don't know which ones to use - that's obviously part of the question but i feel it's like 'chicken and egg' & without knowing nay radius' I'm in the dark.
Any help from yourself as to how u did it would be greatly appreciated.

 

[JimmyTheBlue]

He calculated the radius via the volume and the height. He converted the yield strength to PA then calculated the hoop stress from that using the safety factor. From that he used Hoop stress = pr/t to find the thickness. The rest is self explanatory.

He used the thin cylinder equations as I did to get to that point obviously which as you conclude may be an issue. However they just contain a degree of inaccuracy rather than complete inaccuracy...so having deduced it's a thick cylinder...maybe we're meant to recalc using the relevant related thick equations and find the true thickness?

I also think the inner radius was 1.74 and the outer 1.74 + 0.231. Though that still implies it's thick walled via the ratio consideration.

 

[captain666]

I did the question differently in the end & here's what I did :
Volume of air in vessel = 20m^3.
p1 = air pressure in vessel = 25 bar.
length = 2m.
yield strength = 14,000 PSI.
Factor of safety = 5.
Formula for compressed air in cylinders : P1V1 = P2V2.
P1 is pressure of compressed gas & 25 bar = 362.595 PSI.
V1 is internal volume of cylinder in litres.
P2 is atmospheric pressure (1 ATM = 14.7 PSI).
V2 is volume of gas at pressure p2 : 20m^3 = 20000 litres.

therefore as P1V1 = P2V2,
362.595 x V1 = 14.7 x 20,000
Transposes to V1 = (14.7 x 20,000) divided by 362.95.
Which ends up as V1 = 810.8219915 Litres = 0.811m^3.

And volume of cylinder = L x Pi x R^2
which goes to 0.811 = 2Pi x r^2
which ends up as Inside radius = 0.3593m or 14.15 inches.

Using this radius,if it is treated as a thick walled cylinder, the wall thickness ends up as 1.97m which using the ratio ends up as 7.18 which is less than 10 which indicates a thin walled cylinder.

using the radius and treating it as a thin walled cylinder,the thickness ends up as 1.83 inches which fed unto the ratio equation gives an answer of 7.722 which is again less than 10 therefore both answers indicate that it is a thin walled cylinder.

 

[LDC1972]

So who was correct?

I did the question differently in the end & here's what I did :
Volume of air in vessel = 20m^3.
p1 = air pressure in vessel = 25 bar.
length = 2m.
yield strength = 14,000 PSI.
Factor of safety = 5.
Formula for compressed air in cylinders : P1V1 = P2V2.
P1 is pressure of compressed gas & 25 bar = 362.595 PSI.
V1 is internal volume of cylinder in litres.
P2 is atmospheric pressure (1 ATM = 14.7 PSI).
V2 is volume of gas at pressure p2 : 20m^3 = 20000 litres.

therefore as P1V1 = P2V2,
362.595 x V1 = 14.7 x 20,000
Transposes to V1 = (14.7 x 20,000) divided by 362.95.
Which ends up as V1 = 810.8219915 Litres = 0.811m^3.

And volume of cylinder = L x Pi x R^2
which goes to 0.811 = 2Pi x r^2
which ends up as Inside radius = 0.3593m or 14.15 inches.

Using this radius,if it is treated as a thick walled cylinder, the wall thickness ends up as 1.97m which using the ratio ends up as 7.18 which is less than 10 which indicates a thin walled cylinder.

using the radius and treating it as a thin walled cylinder,the thickness ends up as 1.83 inches which fed unto the ratio equation gives an answer of 7.722 which is again less than 10 therefore both answers indicate that it is a thin walled cylinder.

So who was correct on this? I have only briefly looked so haven't much input yet, but the reason I "Googled" was because I took the obvious route (we have length and volume) so using these / ignoring pressure the Dia is 3.56m which is just mad! It'd be a big cumbersome flat tub...
So I got to thinking surely the gas is compressed and this reduces the physical volume, as the last poster has done.

 

[Chestermiller]

So who was correct on this? I have only briefly looked so haven't much input yet, but the reason I "Googled" was because I took the obvious route (we have length and volume) so using these / ignoring pressure the Dia is 3.56m which is just mad! It'd be a big cumbersome flat tub...
So I got to thinking surely the gas is compressed and this reduces the physical volume, as the last poster has done.

The problem statement clearly indicates that the compressed volume of gas within the cylinder is 20 M₃.

 

[LDC1972]

Thanks Chester, have clicked your thanks button.

The tutor also confirmed this yesterday...

 

[oxon88]

I did the question differently in the end & here's what I did :
Volume of air in vessel = 20m^3.
p1 = air pressure in vessel = 25 bar.
length = 2m.
yield strength = 14,000 PSI.
Factor of safety = 5.
Formula for compressed air in cylinders : P1V1 = P2V2.
P1 is pressure of compressed gas & 25 bar = 362.595 PSI.
V1 is internal volume of cylinder in litres.
P2 is atmospheric pressure (1 ATM = 14.7 PSI).
V2 is volume of gas at pressure p2 : 20m^3 = 20000 litres.

therefore as P1V1 = P2V2,
362.595 x V1 = 14.7 x 20,000
Transposes to V1 = (14.7 x 20,000) divided by 362.95.
Which ends up as V1 = 810.8219915 Litres = 0.811m^3.

And volume of cylinder = L x Pi x R^2
which goes to 0.811 = 2Pi x r^2
which ends up as Inside radius = 0.3593m or 14.15 inches.

Using this radius,if it is treated as a thick walled cylinder, the wall thickness ends up as 1.97m which using the ratio ends up as 7.18 which is less than 10 which indicates a thin walled cylinder.

using the radius and treating it as a thin walled cylinder,the thickness ends up as 1.83 inches which fed unto the ratio equation gives an answer of 7.722 which is again less than 10 therefore both answers indicate that it is a thin walled cylinder.

is the above approach correct?

 

[LDC1972]

is the above approach correct?

Nope!

It is a big flat tub if memory serves. I got it right anyway. (In the end LOL)

You'll get there, the info's there and if I remember rightly, there are online calculator to check your results. But all this was ages ago!

 

[LDC1972]

He calculated the radius via the volume and the height. He converted the yield strength to PA then calculated the hoop stress from that using the safety factor. From that he used Hoop stress = pr/t to find the thickness. The rest is self explanatory.

He used the thin cylinder equations as I did to get to that point obviously which as you conclude may be an issue. However they just contain a degree of inaccuracy rather than complete inaccuracy...so having deduced it's a thick cylinder...maybe we're meant to recalc using the relevant related thick equations and find the true thickness?

I also think the inner radius was 1.74 and the outer 1.74 + 0.231. Though that still implies it's thick walled via the ratio consideration.

This is basically what to do

Use the thin walled system - get your answer.

Then re-do with thick walled equations with now known figures and get precise thickness.

Cheers!

 

[oxon88]

ok i will give it a go. thank you for the response.

 

[oxon88]

can you provide any guidance with calculating the hoop stress?

 

[LDC1972]

can you provide any guidance with calculating the hoop stress?

V = ∏r^2 x length

simplify to r^2 = v / ∏ x length, that's your radius.

σ1 = yield strength / factor of safety

and as σ1 = Pr / t then t = Pr / σ1 and that's your wall thickness using thin wall.

Cool?

Once you get 231mm or so you've cracked it, then move onto thick walled with now known values...

 

[Chestermiller]

can you provide any guidance with calculating the hoop stress?

The equation for the hoop stress is obtained by integrating the stress-equilibrium equation (differential force balance), subject to appropriate boundary conditions.

 

[oxon88]

Many Thanks. just one question.

The thickness ratio for thin walled: r / t ≥ 10 or d / t ≥ 20

i've calculated r to be 1.784m. Is this the inner radius?

I see you have subtracted the calculated wall thickness, then calculated the ratio as:
(1.784 - 0.231) / 0.231 = 6.723.


Is this correct? Or should the ratio be:
1.784 / 0.231 = 7.723

 

[oxon88]

can anyone help with my last question?

 

[Big Jock]

I got the radius to be 1.784 M also Oxon88 but that's as far as I have got so far. Do you have any more light to shed on these two questions?

 

[oxon88]

m still pondering about what the correct ratio should be...

 

[Big Jock]

I can't seem to calculate the hoop stress. Trying to find a formula where I can use the safety factor to find the hoop stress to then work out the wall thickness as I don't fully believe or follow some of the workings above...

 

[Big Jock]

Oxon88 I got the wall thickness to be 0.231m and got 6.72 which indicates a thick walled vessel. Hope that helps

 

[oxon88]

still trying to get my head around this...

so I've got 0.231m as the wall thickness. and therefore the ratio is 6.72, which means its thick walled.

what do i need to do next?

 

[Chestermiller]

still trying to get my head around this...

so I've got 0.231m as the wall thickness. and therefore the ratio is 6.72, which means its thick walled.

what do i need to do next?

See this link: http://courses.washington.edu/me354a/Thick Walled Cylinders.pdf

 

[oxon88]

still struggling with the thick walled part. what exactly am i looking to calculate?

 

[Big Jock]

You have answered the questions asked. 1 was to indicate whether it was thick or thin wall and 2 was the wall thickness for the vessel...

 

[oxon88]

Yes but the result for wall thickness is based on thin walled equations. I think Thick walled equations need to be used to get a more accurate result for the wall thickness.

 

[Big Jock]

I got my wall thickness from subtracting the inner radius from the outer radius of the vessel so am fairly confident that the measurement of 0.231m is correct...

 

[RuBear]

Yes but the result for wall thickness is based on thin walled equations. I think Thick walled equations need to be used to get a more accurate result for the wall thickness.

Any success with this Oxon? Using the thick walled equation I got 0.74m as wall thickness but this seemed quite large?

 

[oxon88]

No, I am still struggling with this. how did you get to 0.74m?

 

[Big Jock]

Cracked it yet oxon88??

 

[RuBear]

0.74 was an error in my maths!
I had the assignment back and got the question right.
Persevere with the thick walled equations and you'll get there.
Use the examples in the workbook to guide you.

 

[Big Jock]

Rubear I found it to be thick walled and a minimum thickness off 231mm would this be correct??

 

[RuBear]

Yes but that's using the thin walled equation isn't it? You need to redo using the thick walled equation for greater accuracy I think.

 

[oxon88]

no not cracked it yet. I am stuck trying to apply thick walled equations...

 

[Big Jock]

I got the thick walled equation to = 6.71
And the thin walled equation to =7.71...