This article is reprinted from the October 1996 issue of the EDA digest
Pressurization
ABSTRACT/SUMMARY
Pressurized containers store enormous amounts of potential energy which can be dangerous. The rupture and total energies of a cylinder are analyzed with a sample calculation provided.
A pressurized container, usually a cylindrical vessel, can be quite dangerous. The compressed Gas Association in New York is a good source of information on working pressures of gases. Some bottles have test pressures up to 43,000 psi. A cartridge of carbon dioxide can be pressurized to 835 psi. A one inch diameter HiPac CO2 cylinder for life belts, with internal pressure of 1,000 psi, are capable of soaring 200 feet into the air when punctured. However, aerosol pressures rarely exceed 100 psi. Specifications and standards for pressurized containers are numerous and are provided by organizations which include the ICC, ASME, Marine Engineering, and the National Board of Fire Underwriters. Compressed gas stores a lot of energy. Proof testing of storage containers can be done utilizing gas, but it is usually done with liquids. The energy contained in a pressurized fluid, whether liquid or gas, added to the energy contained in the expansion of its container can be very dangerous if released abruptly through rupture or puncture of the container. Liquids do compress. The bulk modulus, B, is the parameter of the liquid describing its compressibility. As an example, water up to 300,000 psi between 32°F and 150°F, has a bulk modulus of elasticity approximately 300,000 psi. Oils, over a lesser environmental span, average 200,000 psi. When a technical question arises, the operating conditions must be identified, and the fluid known, to properly apply its compression factor.
The following equations derive the energy contained in a hypothetical pressurized cylinder
The stored energy in a fluid under pressure is
At rupture, P1=0 and the released energy is
The cylinder, by itself, when analyzed through the analogy of a spring in tension, has a total energy of
and
To appreciate the amount of energy available, for useful work or released upon rupture, the following example is used: A cylinder containing 10,000 in3 of water at 5,000 psi. This steel cylinder has a SH=50,000 psi and a poisson's ratio of .25. The potential energy is found as follows The fluid energy is
The total energy available is
For those who have a better feel for electrical units, in this example, if the cylinder ruptures and its contents are released over a period of 1/2 second, 280,000 watts of power would be expended.
In aerosols and many kinds of gas cylinders, a change of state from liquid to gas takes place as the contents of the container are depleted. In state changing pressurized cylinders, a constant pressure is maintained until all of the liquid within the cylinder has turned to gas. The equations are somewhat different in that in that situation.
Sam Goldfarb, President of Mechanical Consulting Co., specializes in the packaging of optics and electronics, and the analysis of shock, vibration and thermal designs. Sam holds BME and MME degrees from City College and is a registered Professional Engineer. Sam can be reached at (516) 432-1174.
EDA has continuously published the ,EDA digest, a quarterly minitechnical journal since July, 1983. EDA maintains Copyrights to all articles from the EDA digest. No part of the EDA digest can be reproduced without written approval.  
Electronic Development Associates, Inc.
All rights reserved. |
