Cylinder volume and compression problem: helium cylinder with dimensions 51.5" H x 9D

Shawn L

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Cylinder volume and compression problem: helium cylinder with dimensions 51.5" H x 9D

This question deals with basic volume calculation and compression ratios. Please don't be turned off thinking it's a chem question because of the talk of helium!

I have a large helium cylinder with dimensions 51.5" H x 9D.

It stores compressed Helium. The amount of helium in that tank, if uncompressed* is 330 cubic ft.

A balloon takes 0.5 cubic ft of uncompressed helium.

If we had to compress the helium of one balloon into a new small cylinder, what would be the height of that cylinder at Diameter= 0.5"

I attempted to solve this by first finding the volume of the large cylinder in order to determine the compression rate. Then I applied that compression rate to the volume of the balloon to get the volume of the small cylider but I end up with what seems like an astronomically high number for the height. I must be doing something wrong!

Thanks in advance.

*I know compression is relative but to get the compression ratio, assume there's a state of compressed and uncompressed.
 
This question deals with basic volume calculation and compression ratios. Please don't be turned off thinking it's a chem question because of the talk of helium!

I have a large helium cylinder with dimensions 51.5" H x 9D.

It stores compressed Helium. The amount of helium in that tank, if uncompressed* is 330 cubic ft.

A balloon takes 0.5 cubic ft of uncompressed helium.

If we had to compress the helium of one balloon into a new small cylinder, what would be the height of that cylinder at Diameter= 0.5"

I attempted to solve this by first finding the volume of the large cylinder in order to determine the compression rate. Then I applied that compression rate to the volume of the balloon to get the volume of the small cylider but I end up with what seems like an astronomically high number for the height. I must be doing something wrong!

Thanks in advance.

*I know compression is relative but to get the compression ratio, assume there's a state of compressed and uncompressed.

Please show your actual calculations and results, so we can see if you did something wrong.

My first concern is that the dimensions you gave are probably outside height and diameter; you need the inside dimensions to find the compressed volume. It's not clear that the wall thickness would be proportional in a much smaller cylinder.
 
Thanks for raising the issue of wall thickness. I will try to find the wall thickness of both cylinders but for now let's assume they are proportional as I can accept answer that's +/- 10%.

Here's my calculation (forgive my poor format and notation):

V Large cylinder:
=Pi(4.5)2 (51.5)
=3276.29 In3

Uncompressed Volume:
330 Ft3 = 570240 In3

Compression Rate:
=570240/3276.29
=174.05X

Volume of Balloon:
0.5Ft3 = 864In3

Compressed Balloon Volume:
=864/174.05
=4.96In3

Small Cylinder:
D=0.5in
H=V/Pi(r)2
=4.96/Pi(.25)2
=25.26

Here is why I am questioning my math: I am imaging if the gas were stored in the small cylinders uncompressed that you would need 174 of these 1/2"x25" cylinders to store the contents of one single balloon. By visualizing it that seems way off. So either my math is wrong, my logic is wrong or my visualization is just wrong.

scale-model.jpg

Please show your actual calculations and results, so we can see if you did something wrong.

My first concern is that the dimensions you gave are probably outside height and diameter; you need the inside dimensions to find the compressed volume. It's not clear that the wall thickness would be proportional in a much smaller cylinder.
 
Here's my Calculation

Thanks for raising the issue of wall thickness. I will try to find the wall thickness of both cylinders but for now let's assume they are proportional as I can accept answer that's +/- 10%.

Here's my calculation (forgive my poor format and notation):

V Large cylinder:
=Pi(4.5)2 (51.5)
=3276.29 In3

Uncompressed Volume:
330 Ft3 = 570240 In3

Compression Rate:
=570240/3276.29
=174.05X

Volume of Balloon:
0.5Ft3 = 864In3

Compressed Balloon Volume:
=864/174.05
=4.96In3

Small Cylinder:
D=0.5in
H=V/Pi(r)2
=4.96/Pi(.25)2
=25.26

Here is why I am questioning my math: I am imaging if the gas were stored in the small cylinders uncompressed that you would need 174 of these 1/2"x25" cylinders to store the contents of one single balloon. By visualizing it that seems way off. So either my math is wrong, my logic is wrong or my visualization is just wrong.

scale-model.jpg
View attachment 9503

Please show your actual calculations and results, so we can see if you did something wrong.

My first concern is that the dimensions you gave are probably outside height and diameter; you need the inside dimensions to find the compressed volume. It's not clear that the wall thickness would be proportional in a much smaller cylinder.
 
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