Revised Version 2
Thanks to Jorge Carballeira who found the error
Consider a box. It is is h
high and has a top and bottom area of A units.
It is full of gas at pressure p and the height h is variable so as h varies so p varies.
The outside pressure is Pa
Let's be simplistic and use Charles's law
that states p*v is constant for a given volume of gas provided the temperature
So for a given starting pressure P0 and volume V0 we can deduce any later pressure as p = P0*V0 / v
But since the volume is v=h*A we can reason
p = P0*V0/(h*A)
Now if we let the gas expand just a teeny
bit (a distance dh) the work done (dW) is the distance moved multiplied by the
Force is (p - Pa) * A so
dW = ((P0*V0)/(h*A) - Pa) * A * dh
dW = (P0*V0/h - Pa*A) * dh
So now we want to sum all the dW for all the
dh for a range of h from our initial pressure/volume until the pressure reaches
So the initial limit is based on v=h*A giving h = V0/A
and the closing limit is based on p = P0 * V0 / (h * A) so for p=Pa we get h = P0*V0/(Pa * A)
W = integrate((P0*V0/h - Pa*A) * dh) using limits above
W = P0*V0 * integrate(h-1*dh) - A * Pa * integrate(dh)
W = P0*V0 * [logeh] - A * Pa * [h]
substitute in the initial and final values for h
W = P0*V0 * (loge(P0*V0/(A * Pa)) - loge(V0/A)) - A * Pa * (P0*V0/(A * Pa) - V0/A)
since log(a)-log(b) = log(a/b) we can simplify this a bit
W = P0*V0 * (loge((P0*V0/(A*Pa))/(V0/A)) - A*Pa*(P0*V0/(A*Pa)-V0/A)
now it all comes together with basic algebra
W = P0*V0 * loge(P0/Pa) - P0*V0 + Pa*V0
W = P0*V0 * (loge(P0/Pa)-1) + Pa*V0
Well I could use this but it's messy and I
only want a feel for the numbers. P0/Pa is the tank
pressure divided by normal air pressure and
loge of 200 is 5.3 and loge of 300 is 5.7 so I'll call it 5.5 also Pa*V0 is pretty trivial beside the first term so it all becomes:
W = P0*V0* 4.5
Great. Just need to sort out the units.
The world in general seems to have settled for MKS (Meters/Kilograms/Seconds) as a way to do business in physics but I'd prefer litres and bar here.
1 bar is 105 Newtons/square meter and 1 litre is 10-3 cubic meters so our formula becomes
W (in Joules) = P0*V0*450
So for a 230 bar 12L tank we have 230*12*450 Joules. 1242000 joules!
You're not impressed? You don't have a
feel for a joule perhaps?
A joule is one watt for one second. so 1242000 joules is 3 kilowatts for just under 7 minutes.
That would boil 3.5 litres of water and so make coffee for everybody on the boat?
Still doesn't seem much does it? The trick is to release it in an instant.
In a previous life (see CV) I used a unit of energy that was 4.184x1012 joules representing the energy released by 1000 tons of TNT.
That works out at about 1866000 joules per pound.
In metric units the tank contains the energy in 300 grams of TNT. A normal hand grenade has about 150 grams.
Hum. That works out at 650 grams for my
10L twins at 300 bar.
Just behind my head? Now I see why people worry about it.
This seems to be very
dependent on tank geometry but it can be estimated.
As before skip the analysis if you just want the numbers.
Consider a bit of tank wall.
The radius is R and the thickness is T. We will work on a slice of this W long
rather than do the whole tank.
We want the force that pulls left and right at the line A. I contend that this is half the total force pulling the left hand side to the left plus the force pulling the right hand side to the right. Half because the piece of wall opposite A is also being stretched.
The force on A can therefore be the sum of all the right hand components of the pressure on the wall for all values of θ from 0 to π/2
Well for a vanishing small slice of θ
ie. dθ we have an area W*R*dθ
so if the pressure difference across the wall is P a force of W*R*P*dθ
The horizontal component is then
so integrating from 0 to π/2 we get W*R*P*(-cos(π/2)+cos(0))) = 2*W*R*P
We want to use the Young's modulus values for the tank material and this is the ratio of the stress to the strain. ie: m = (force/unit area)/fractional increase in length
Now the piece of than wall this acts on is a
the a area at A which is W*T so the stress is 2*W*R*P/W*T giving 2*R*P/T
so the stretch is 2*R*P/(T*m)
Now the energy in a even stretch is ½ *
force * distance
The distance stretched is the circumference * the strain ie: D = 4*R2*π*P/(T*m)
giving an energy of E = 4*R3*π*P2*W/(T*m)
OK so lets try some numbers in MKS units
again using one of my 10L tanks.
R = 0.09 meters
P = 300x105N/sq meter (300 bar)
W = 0.45 meters
m = 2x1011 for steel
T is a problem but to a first order guess the tanks weigh 16Kg so that is virtually 2 Litres = 0.002 cu meters to make a cylinder 0.5m long by 0.5m circumference leaving 0.008m (0.8cms for the wall)
Bang all the numbers in and we get 2319
less than 0.2% of the air. So that's all right then I suppose.
Thanks to Nigel Hewitt firstname.lastname@example.org
Reprinted by permission from http://www.combro.co.uk/nigelh/diver/tank.html
One bar equals 14.504 psi.
3000 psi equals 206.8 bar(atmosphere)
An 80cubic foot American tank is equivalent to an 11 Liter European tank.
According the the US Department of Transport(DOT) In 1999, of the estimated 25 Million cylinders made of 6351 only 12 were reported to have ruptured.
Several people have said that there is no list of tanks made from the 6351-T6 alloy. This is not exactly correct. While it is true that there doesn't seem to be a nice cross referenced list of serial numbers available to the public, there is a "list" sufficient for most people to figure out if their tanks are made from the bad alloy. The following comes directly from the DOT Safety Alert Bulletin:
Here is "The List" of scuba tanks that the DOT says are most likely made from the 6351-T6 aluminum alloy:
Unless proven otherwise, all scuba tanks in the above list should be assumed as being made using the 6351-T6 alloy.
Note that many other types of cylinders (SCBA, Medical, Industrial, CO2, etc.) were also made from the 6351-T6 alloy. However, for brevity, only SCUBA type cylinders are listed above. See the DOT Safety Alert Bulletin for information on those.
Also, it should be noted that Catalina cylinders were NEVER made from the 6351-T6 alloy. They were made using alloy 6061-T6, which as of yet, has not been known to fail explosively. All of the manufacturers in the above list, except Walter Kidde, switched to the 6061-T6 alloy on the dates shown.
The DOT has not as of yet issued a recall of these tanks - only a safety alert. Essentially, if you own or use a scuba tank in the above list , you should consider it as being a time bomb waiting to explode. You should consider the tank unsafe until you learn for certain that it is made from the new alloy.
Reprinted by permission.
“The scuba tank was a 10.3 liter tank which holds about 72 cubic feet of air. It was manufactured by Gerzat (A French Company) in 1973 out of the 5283 aluminum alloy. The 5283 aluminum alloy is just as bad as the 6351 aluminum alloy. The scuba tank itself had been successfully hydrotested in December 1993. The tank had not been used since then and was holding a steady 2800 psi (180 BAR).” - From an article in the Norwegian magazine "Diving" written by Kai Garseg [4/97] “
The following photograph was taken on Saturday, 9/9/2001 at "Tjömetreffen2001", a dive camp held by Dag's diving club. dag.deberitz @c2i.net
Chris Hawkins, my 18 year old nephew, worked at the Force E dive shop located in Riviera Beach, FL as a technician. His job responsibilities included, among other things, filling scuba cylinders. On February 1, 1998, a regular customer came into the shop to have his aluminum Walter Kidde scuba tank topped off before going on another dive. Chris examined the tank and found current inspection stickers. He took the tank and placed it in the water tub and connected it to the fill station. Store policy requires that all cylinders have their pressure checked before actually adding any air. Chris opened the scuba valve and was attempting to check the pressure when he heard a hissing sound. He assumed that it was a leaky O-ring in the valve which he had seen many times before in other tanks. He then fully submerged the tank into the water to check for bubbles. Before Chris could determine the origin of the leak, the tank suddenly exploded. Absolutely no air was added to the tank and the tank was not mistreated at any time. There were two other witnesses to this event. Both have stated on record that Chris did nothing wrong. Photographic evidence clearly shows that the fill station valve was in the OFF position at the time of the blast indicating that no air was added to the tank before it exploded. Also, the fill equipment itself had a special regulator that prevented overfills.
Chris sustained severe injuries in the explosion. He lost the better part of his hand and his face was badly cut up. Ironically, the customer who owned the tanks and another employee (Paul) were standing less than six feet away from the tank when it suddenly exploded. Paul was blown about 20 feet backwards through the air, but was not seriously hurt. The blast from the explosion propelled another scuba tank right past Paul's head - luckily missing him. The customer was blown across a cluster of filled tanks and into a steel rail, but sustained only minor injuries. Chris was blown into a steel grate railing about 10 feet back from where the tank was. A large chunk of the exploded tank ripped a hole through the steel rail, ricocheted off a full oxygen tank, made a 90 degree turn and blasted out the front store window which was criss-crossed with commercial grade burglar bars. Fortunately, this failed to rupture the oxygen tank which could have killed them all.
Despite the fact that some officials are saying that Chris lost two fingers in the blast, they are not entirely accurate. Chris lost most of his hand in the blast including his thumb and index finger. If you draw a line on your hand, starting at the crack between your middle finger and your index finger, down your hand to the middle of your wrist and then over to the edge just under the base of the thumb, then you will have a better idea what he really lost. That is a lot more than just two fingers.
I went by the dive shop where this happened and the building was still standing, but messed up pretty bad. Due to a safety water tub that Chris had lowered the scuba tank into, most of the damage was confined to the roof and ceiling area although there were several windows blown out, torn metal, etc. The shop was, in fact, open for business the next day - minus their filling equipment which was destroyed in the blast.
Points to Remember:
The blast that ripped off the better part of Chris's hand was caused by a defective aluminum Walter Kidde scuba tank. It was made from an alloy, 6351-T6, that has been known to be inferior for use in scuba tanks for many years. This alloy was routinely used to make scuba tanks from the late 70's on up to 1990. The tank that exploded had its last hydrotest in 1994 and displayed current inspection stickers.
The explosion was roughly equivalent to several sticks of dynamite. According to one scuba tank inspection expert, "The explosive potential in a fully charged 80cf aluminum SCUBA cylinder is approximately 1,300,000 foot pounds -- enough to lift a typical fire department hook-and-ladder truck over 60 feet in the air!", stated by A. Dale Fox on his web page.
Walter Kidde is a leading manufacturer of fire extinguishers and other low pressure gas cylinders. They used to make Scuba tanks, including the one that nearly killed Chris, but sold their North Carolina scuba plant in 1989. In an interesting twist, Walter Kidde claims that Luxfer purchased their scuba division at that time and thus, assumed the liability for their tanks. Luxfer denies that they purchased the Kidde scuba division and claims that they only purchased its assets.
Here is the interesting part. The DOT has already issued a safety alert bulletin for tanks made with alloy 6351-T6 way back in 1994. They stopped short of requiring the tanks to be removed from service or ordering a recall. It seems that Chris was not the first victim of these defective tanks. The first tank that exploded was actually a SCBA tank (self-contained breathing apparatus) - like what firemen wear. This explosion occurred at a chemical plant in Deer Park, Texas. The tank was manufactured in 1977 and exploded while being filled to its rated pressure of 2216 psig. Fortunately, there were no reports of serious injury in that explosion.
On June 4, 1994, a second explosion reported to the DOT seriously injured Arnie Hubber, who was the fill station technician at the Scuba Sports Dive Store located in North Miami, Florida. He lost his right thumb and both his right arm and left leg were broken in addition to other injuries. The scuba tank in that explosion was manufactured in 1982, and had a current hydro (less than two years old) and a current VIP. It exploded while being filled to its rated pressure of 3000 psig. Arnie Hubber actually came to visit Chris in the hospital. In all of these previous explosions, a piece of the cylinder neck separated from the tank.
According to the DOT's safety alert in the Federal Register (Volume 59, No. 142, pages 38028-38030), the problem originates from the use of an inferior aluminum alloy to build these tanks. Alloy 6351-T6 has been used in the manufacture of seamless aluminum cylinders marked "DOT 3AL", and some composite cylinders. The DOT estimates that approximately seven million tanks have been manufactured using this alloy, with about two million being scuba tanks.
With that many tanks currently out there right now and only about ten exploding, the DOT has not seen fit to order a mandatory recall. With the cost of such a recall being into the millions of dollars, the scuba manufacturers have not seen fit to voluntarily recall these cylinders. Meanwhile, as the cylinders get older, more and more of them will explode. However, according to my preliminary findings, DOT 3AL aluminum tanks made from 6351-T6 may possibly be safe if less than 10 years old and inspected by a qualified inspector annually. Even still, it makes you wonder just who will be next.
Why is this alloy unsafe if only ten out 7,000,000 tanks have exploded? The reason is that many, many tanks are condemned every year because they either fail their hydrotest or their visual inspection. If testing wasn't required, many more scuba cylinders would have exploded and killed or injured people. Annual inspections catch most of these defective tanks before they actually explode, but in so doing, they make the tanks look safer (statistically) than they really are. For this reason, if your visual inspector fails your tank, you should thank him because it is better to lose your tank than your life. The odds get much worse when you consider that only about 400 fill stations fill approximately 80% of the scuba tanks in this country.
Points to Remember:
A photographer that was on the scene moments after the blast took these photos for Chris:
This is a new enhanced enlargement of one of the photographs. It shows that
the tank was visually inspected in August 1997. The tank exploded on February
1, 1998. The tank was inspected at another dive shop in the Force E chain. Shop
policy requires that all aluminum tanks be inspected for, in addition to other
things, neck cracks both inside and outside the tank. A special light and
mirror are used for this inspection. No cracks or deformities were detected
during this tanks last visual inspection. This does not suggest that annual
inspections are useless. On the contrary, most tanks that would normally
have exploded are caught and condemned by annual inspections. However, this
does suggest that hidden defects in tanks made from the 6351-T6 aluminum alloy
may be much harder to detect than previously believed.
Here is a view of the tank being reassembled by emergency workers.
Here is another angle of the tank being reassembled by emergency workers.
This is the fill station where the tank exploded. The work area is sunken
into the ground about three feet. The blue panel on the right was the fill
station. Under the fill station panel is the remains of the water tub. The red
stuff in the picture is blood.
Here is a new photo taken by a Riviera Beach Fireman who was on the scene.
This is what was left behind after Chris was taken away in the ambulance. The
injuries were so severe that his clothes had to be cut off to determine the
extent of his injuries before he could be moved. Most of the blood that Chris
lost was in the "pit" area where a tourniquet was placed around his
arm. He was able to stagger to this point and fall. The small red puddles are
blood that oozed out past the tourniquet.
Scuba Tank Storage
Several scuba experts have pointed out to me that proper scuba tank storage is very important even for new tanks. When storing tanks, they should be stored in an upright position with only about 50 PSI in them. They should not be emptied to zero PSI (unless you plan on discarding the tank). The reason for not going to zero PSI is to prevent the backflow of humid, unfiltered air into the tank. A pressure of 50 PSI in a tank hydrotested to 5,000 PSI is not a significant risk.
Reprinted by permission.