View Full Version : Boyle's Law

Capt Nemo
09-06-2012, 10:02 PM
In this thread, I'm going to talk about things that most dive instructors won't talk about for legal reasons. "You can't change the laws of physics, but lawyers love to try!" However, I will talk about ALL the implications of the law, and what it can allow.

Moderators, please sticky this thread. This is important for not only scuba divers, but for freedivers and mermaids as well.

Boyle's Law

If the temperature remains constant, the volume of a gas will vary inversly as the absolute pressure and density will vary directly.


P1 * V1 = P2 * V2

P1 = Initial Pressure
V1 = Initial Volume
P2 = Ending Pressure
V2 = Ending Volume

Broken down this gives us three possibilities.

P1 > P2 and V1 < V2 Pressure decreases, volume increases.
P1 = P2 and V1 = V2 Pressure and volume stay the same.
P1 < P2 and V1 > V2 Pressure increases, volume decreases.

This law is very important to anyone who enters the water.
It is the cause of most diving related injuries.

At sea level, you are breathing air at 14.7 psi. 14.7 psi is considered as 1 atmosphere (ATM). As it's all around us, it is considered as ambiant pressure or absolute pressure. It only takes 33 feet of saltwater (34 freshwater) to equal 14.7 psi. So, for each 33 feet of depth, we gain 1 atmosphere of pressure. Hence, at 33 feet, we are at a total of 2 atmospheres ambiant pressure. This will continue as we decend.


From the chart, we can see how the pressure increases the deeper we go. We can also see what happens to a 100 cu/ft volume of air that started at 1 atmosphere. As we can see, the volume decreases until at 132 feet it is only 20 cu/ft or 20% of it's original volume. This volume change with pressure change is what causes the pressure related injuries. On descent, the air cavities in the human body will decrease in size as pressure increases. If the cavity, cannot be equalized, tissue damage will occur.

In the last column of the chart, we can see what happens to the same 100 cu/ft volume of air at 132 feet 5 ATM. Notice that as we ascend, the volume of air increases until at the surface, it now occupies 500 cu/ft. In the human body, this expansion creates the most serious injuries, and equalization becomes extremely important.

For snorkeling, the pressure change is the reason you don't see snorkel tubes longer than about 1 foot. On the surface, you have 14.7 pounds of pressure over every square inch of your chest. Altogether, that can equal hundreds of pounds! However, you have air in your lungs that's pushing back, and counteracts all that pressure. In the case of a long snorkel tube, the air in your lungs stays at 14.7 psi, but say at 4 feet of depth, there's an extra 2 psi of ambiant pressure for 16.7 psi. The pressures become unequal, and the extra 2 psi will feel like there's an elephant sitting on your chest. You could say the average human chest area is about 3 square feet. So at 14.7 psi, that's 6350 lbs, and at 16.7 psi, 7214 lbs, for a differance of 864 lbs. So you see why there are no long snorkel tubes!

For scuba, this pressure differance is why we must breathe compressed air on a regulator, or why mermaids breathe compressed air from hoses. We have to breathe air at ambiant pressure in order to breathe at all!

For freedivers, they too breathe compressed air! The air naturally compresses in their lungs due to Boyle's Law as they decend. However, they are not normally subject to ascent type injuries, as the volume they went down with is equal to what they surface with.

Divers and mermaids aren't so lucky! As they are submerged breathing air at increased pressure, they have to know the effects of Boyle's Law and how to prevent injury. Back at the table, look at the last column, and how a pressurized air volume expands as you ascend. A diver holding his breath and swimming to the surface from 132 feet would see that air expand to 5 times it's original volume. The differance in pressure would be 58.8 psi. Now the lungs can handle 2 psi before damage occurs, which is about the pressure differance of 4 feet of water. So our diver would most likely explode before reaching the surface. But before that, he would experience the worst injury that a diver could face, Air Embolism. Because our lungs are so fragile, divers came up with the first rule of scuba "NEVER HOLD YOUR BREATH."


If we take a good look at Boyle's Law, we will find that it actually allows us to hold our breath while breathing compressed air. It is only in the first instance of P1 > P2 and V1 < V2 that we have expansion of the air volume in our lungs over that of what we initially took in. With P1 being greater than P2, the volume must increase. And therefore, if a diver holds his breath and ascends, he will suffer overexpansion of the lungs.

With the second case of P1 = P2, we begin to see how we can hold our breath. In this case, P1 stays equal to P2, and causes V1 to stay equal to V2. There is NO expansion, and thus, NO expansion type injury can occur. However, temprature can cause some expansion to occur, but it would be small. Our bodies are very adept at warming and humidifying the air we take into our lungs, and so by the time we have finished inhaling, that air is almost at body temprature. So there would be negligible thermal expansion. Heliox and trimix divers may be more suceptable to thermal expansion as the helium in the mixes can absorb more heat than air.

In the third case of P1 < P2, there is no expansion at all! The volume must contract because the pressure is increasing. No expansion injury is possible!

So for the last two cases it is actually possible to hold your breath while breathing compressed air. As long as P2 stays greater than or equal to P1 there can be no expansion greater than the lungs can handle.


Does this mean a diver can do it in all situations? NO!!!

Normal scuba diving is generally changing depths throughout the entire dive. Even when neutrally buoyant, a diver rises when he inhales, and sinks when he exhales. Swimming around, it's very hard to keep track of depth, unless it's a very controlled situation. For normal diving practice, stick with the first rule of scuba, NEVER HOLD YOUR BREATH.

So when can you hold your breath? For modeling and performing.

For modeling, the model is usually weighted so she will stay put at constant depth. This keeps her in a P1 = P2 situation. However, when the model is changing depth, like going from a prone position to a standing position, the model may change depth enough to get her into trouble. So therefore, models should be breathing when changing positions (changing positions is usually a rest time for the model anyway). Some shots may require a model to change depth. As long as she decends, she may hold, and may return to the depth where she took her last breath from. If the model has to ascend from a deeper starting point, she must begin exhaling, or she will go into overexpansion.

For performance, the mermaids at Weeki Wachee hold their breath regularly. They also use their lungs as a buoyancy compensator to remain neutrally buoyant. This means that they are holding less than full lung volume. This gives them the ability to do things that seem impossible to scuba divers. They have room for limited expansion to occur, but generally, they operate from the P1 = P2 area and P1 < P2 areas where volume remains the same or decreases. In a way, it's like freediving, only the surface is 15' down.


09-07-2012, 02:13 AM
Very informative, Capt! That's pretty cool to know, especially to see the formula behind it.
I was always scared of diving because I always heard your lungs could explode xD
I never learned why so I just avoided it altogether.

Thanks for posting this, it's actually very essential if you're going to be freediving. Well,
if you actually have the skill to go down that deep!

Capt Nemo
09-07-2012, 10:30 PM
If I stay shallow do I still have to worry about this? YES!!!

As you can see from the chart, the greatest change in pressure occurs in the first 33 feet. The pressure doubles and volume decreases by 1/2! You could get an embolism on ascent in as little as 4 feet of water. After 33 feet, pressure won't double again for another 66 feet.

Why didn't we learn this much in scuba class?

Teaching about all the aspects of Boyle's Law has been severely curtailed due to the current legal enviroment. Insurance companies are also to blame. In order to get insurance coverage, PADI had to remove much about Boyle's Law, and go to scare tactics about the first rule of scuba, in order to have their resort course. The same is true for the other certification agencies. Now it's only really taught at the divemaster or instructor levels. European diving agencies, have fewer legal restrictions, and thus, are teaching much more about it.

Now that we have learned about how Boyle's Law works, let's talk about how it affects the body, and how to prevent injury.

The Squeezes

Mask Squeeze

Mask Squeeze occurs as the volume shrinks as pressure increases during descent. This causes the mask to begin to press against the face, and can press hard enough to rupture blood vessels around the eyes, and can also damage the eyes. To prevent this, divers blow air through their nose to equalize this airspace. Some freedivers will fill their mask with saline solution to eliminate this airspace, and remove the need to equalize. However, this will prevent clear vision unless special contacts or lenses are used.

Goggles or masks without nose pockets, put a diver at high risk for mask squeeze, as there is no way to equalize the pressure. As above, eliminating the air pockets in the goggles will make them safe. Other methods like "pipe" or "balloon" goggles have been used with some sucess. These goggles equalize with either a tube running to the mouth and blowing, or by ambiant pressure forcing air out of a balloon and into the goggles. Normal swimming goggles do not have any means of equalization, and should not be used for anything but surface swimming.

Here is a very good example of mask squeeze.

Sinus Squeeze

Sinus squeeze occurs when inflamed tissue or mucous block a sinus passage. As the diver descends, pressure transmitted through the blood forces blood into the sinus tissues which can rupture. This causes blood to take up the space as the air contracts. The primary symptom is usually a sharp pain or wedging sensation directly above the eyes, The pain may decrease as the tissue ruptures. If tissue damage occurs, there may be blood draining from the nose at the end of the dive.

This squeeze can also happen in reverse. The sinuses may also become blocked at depth, and upon ascent, the trapped air expands and forces it's way through the sinus passage. The force may tear the lining of the sinus passage and force it into the nasal cavity. Again there may be blood draining from the nose. Lesser blockages will blow mucous out of the nose in a sneeze like fashion. This can also cause sharp pain as above.

To prevent this, first, do not dive if you have a cold or congestion. Do not try to dive using decongestants unless a doctor permits it. Many drugs change under pressure or vacuum, and decongestants may stop working, or even become poisonous at depth. Very little pressure testing of medications have been done. Using the Valsalva technique will equalize the sinuses and ears at the same time. If pain begins that Valsalva cannot remedy, ascend and try to see if it will clear. If it does not, abort the dive. If a sinus squeeze occurs, generally, it is not required to seek medical attention, unless pain or congestion persists.

Ear Squeeze

Ear squeeze occurs as water pressure forces the ear drum inward as the air space behind it contracts as no air enters through the eustacian tube. As the pressure increases, you will begin to feel a pressure sensation, which will turn to pain, and eventually the eardrum will rupture. When rupture occurs, a diver may experiance nausea, dizziness and vertigo. A diver may also become unconscious. Medical attention should be sought if pain persists after a dive, or if there is any bleeding. Divers wearing ear plugs may also experience ear squeeze. In that case, air trapped between the plug and the eardrum will contract, and pull the eardrum outward rupturing it.

Prevention of ear squeeze can be as simple as swallowing, yawning, or rotating the jaw. If those do not work, use the Valsalva technique. You should begin equalizing as soon as you begin to decend. Waiting until things get painful may be already too late! If nothing seems to work, ascend a few feet until the pain subsides and try again. If that doesn't work, abort the dive. Do not dive with a cold or congestion, or ear plugs.

Note: There are ear plugs on the market that will prevent ear squeeze from the plugs. These are the only ones you can dive with.


Lung Squeeze

Lung squeeze can occur when the lungs are compressed below residual volume. Generally, this does not affect scuba divers, only freedivers. Originally, this was thought to occur at about 66 ft and deeper, as the lungs would be at residual volume at this depth. But as freediving has shown, this doesn't begin to occur until about 200 - 250 ft. It may also occur if a freediver were to dive and exhale on the bottom. Most divers do not realize it has occurred until ascent, or they cough up some blood, as there is usually little pain. Contact a physician as soon as possible if there is any evidence that lung squeeze has occurred.

Tooth Squeeze

Tooth squeeze can occur when there is a pocket of air between the tooth and filling. As the diver descends, the nerve gets pressed into the pocket causing pain in the affected tooth. Consult your dentist if this occurs, as the tooth may need refilling. And let the dentist know that you are a diver.

Intestinal Squeeze

Intestinal Squeeze is kind of a joke among divers, but it is very real. As you digest certain foods, they may create gas. When this occurs at depth, these bubbles begin to expand on ascent, causing pain, and in severe conditions intestinal rupture. Most often the pain may be relieved by flatulence. If the pain persists, descend and wait for it to pass before ascending. Do not eat foods that can cause gas before diving. And, DON'T OPEN THE DRYSUIT OF A DIVER THAT HAD BEANS! :lol:

Suit Squeeze

Suit squeeze generally occurs with drysuit divers only. In a drysuit, the suit is sealed so that there is a pocket of air between the suit and diver. This allows the diver to wear thermal undergarments beneath the suit to stay warmer. At depth, the water pressure may press or pinch the suit on the skin. This will break capillaries beneath the skin. Most drysuits have valves to allow air into the suit to relieve this pressure.

Ascent Injuries

The ascent injuries are the most serious ones that a person who breathes compressed air may encounter. Two or more of these injuries may occur at the same time. All are caused by overexpansion of the lungs. They may also occur in freediving if lung squeeze has occurred. While the lesser injuries do not require recompression, patients should still be taken to a recompression facility immediatly.

Subcutaneous Emphysema

This occurs when air forces it's way out of the lung, and moves up along the windpipe into the region around the collarbone and neck. This will cause swelling around the neck, voice changes, breathing difficulties, and crepitation (crackling sensation upon touching the affected area).

Mediastinal Emphysema

This occurs when air escapes the lungs and into the area of the heart. The air presses on the heart and surrounding vessels. This will cause chest pain, breathing difficulties, collapse, and cyanosis of the lips and nail beds. This may have to be treated prior to recompression for air embolism.


This occurs when air escapes the lung and moves between the covering of the lungs and ribcage. This will produce pressure on the lung and will tend to collapse it. It will show the same signs as mediastinal emphysema only breathing difficulties will be more pronounced, especially if both lungs are collapsed. Lung collapse will have to be treated before recompression for air embolism.

Air Embolism

THIS IS THE MOST SERIOUS INJURY!!! This occurs when air escapes the lung into the blood stream. Healthy lungs can withstand about 2 psi or 4' depth change before rupture. Smoking and disease may reduce this. When the bubbles escape the lungs, they will then pass through the heart and flow to the brain. The bubbles expand on ascent and block circulation in the brain, causing brain damage in 4-6 minutes. The diver may surface unconcious, or within 4-6 minutes after surfacing. The diver may also experiance, headache; vertigo; visual, auditory, and speech abnormalities; loss of small and large motor control and paralysis; unconsciousness and coma; respitory and circulatory distress and failure. There may be some blood at the mouth. Recompression must be immediate! If you survive, you can expect brain damage. This may also be caused by decompression sickness due to Henri's Law of dissolved gasses.


Almost all of the ascent injuries can be prevented by making sure that there is no expansion in the lungs over that of a full breath. For normal diving practice, this means breathing continously and not holding your breath. This keeps you as close as possible to a P1 = P2 situation. Fast ascent can also put you into serious expansion. Keep it slow!!! Breath holds should only be done under controlled conditions where depth is fixed, or referances are easily available as to where the last breath was taken.

Newbies should stay away from any ideas about using household compressors, or anything that could compress the air by Boyle's Law. NO ONE SHOULD ATTEMPT BREATHING COMPRESSED AIR UNTIL THEY ARE SCUBA CERTIFIED.

09-07-2012, 11:11 PM
fascinating. thanks for doing all this work

09-07-2012, 11:26 PM
Thanks for the diving tips Capt. Nemo. So from what I see here it is bad to hold your breath even when you are just swimming a few feet below the surface of the water?

Winged Mermaid
09-07-2012, 11:37 PM
Very interesting indeed! Thanks for taking the time to give us all this information!

Although I will ask.. what about freedivers? I know a few that can go 60-100ft down with dive times of 2-3 minutes down and back. People do freediving all over the world with no problem, and I've never heard anything about this kind of danger with breath holding before.

Capt Nemo
09-08-2012, 12:44 AM
Thanks for the diving tips Capt. Nemo. So from what I see here it is bad to hold your breath even when you are just swimming a few feet below the surface of the water?

Only if you are breathing compressed air. If you are freediving, the air compresses, but you come up with the same volume you went down with, so no overall expansion takes place. But on scuba, a submerged breath could kill if you held it all the way to the surface.

Let's say you were in a pool with a deep end. You set your cylinder on the bottom in the shallow end right where the bottom breaks to the deep end of the pool.
You could take a breath at the level of that cylinder, and then swim down to the bottom of the deep end, and return to that cylinder. If you have not gone above where you took that last breath, then no overall expansion has occured, and you are totally safe. But if you went above that point, you would have to begin exhaling air, as overall expansion is taking place. In this situation, you are working from a fixed air source at fixed depth, so it is easy to know the P1 = P2 point. However, when normal scuba diving, you are moving around too much to get an accurate depth of where you took the last breath from. So in that kind of situation, you always follow the never hold your breath rule.

I'm not done yet posting everything I want to in this thread. So stay tunned.....

Capt Nemo
09-08-2012, 01:09 AM
Very interesting indeed! Thanks for taking the time to give us all this information!

Although I will ask.. what about freedivers? I know a few that can go 60-100ft down with dive times of 2-3 minutes down and back. People do freediving all over the world with no problem, and I've never heard anything about this kind of danger with breath holding before.

Take a look at the chart! In the 4th column, look what happens to the 100 cu/ft of air that's at 1 ATM. At 33 feet, the volume has dropped 50 cu/ft and is now at 50 cu/ft. The same happens to a freedivers lungs at that depth. He only has half of the original lung volume that he had at the surface. But as the freediver returns to the surface, the air expands back to full lung volume.

The only seriously dangerous part of Boyle's Law for divers is when that full lung volume begins expanding beyond the original volume. With any compressed air diving, that can happen.


Here's the math for a freedive to 99 ft.

Start. surface 1 ATM lung volume 100 cu/in P1 = P2 V1 = V2

Mid point. 99ft 4 ATM lung volume 25 cu/in P1 < P2 V1 > V2

End point. surface 1 ATM lung volume 100 cu/in P1 = P2 V1 = V2

Capt Nemo
09-08-2012, 01:47 PM
Continuing with the math of the above post.

P1 = 14.7 psi, V1 = 100 cu/in, so P1 * V1 = 1470.

As the freediver descends P2 increases, so volume must decrease to remain equal to the product of P1 * V1.

At 0 ft. P2 = 14.7 psi, V2 = 100 cu/in, so P2 * V2 = 1470. (P1 = P2)
At 33ft. P2 = 29.4 psi, V2 = 50 cu/in, so P2 * V2 = 1470.
At 66ft. P2 = 44.1 psi, V2 = 33 cu/in, so P2 * V2 = 1470.
At 99ft. P2 = 58.8 psi, V2 = 25 cu/in, so P2 * V2 = 1470.

So we see no overall expansion in the case of a freedive. The air volume contracted and expanded back to it's original volume.

I saw a picture once of Tanya Streeter on a deep dive. Her lungs were so compressed that I could have put my fist between her ribcage and stomach and still not touch her. That gives you a real idea of how pressure can effect volume.

Now, let's look at the case of a scuba diver that holds his breath at 33 ft and ascends to the surface.

P1 = 29.4 psi, V1 = 100 cu/in, and P2 = 14.7 psi.

P1 * V1 = P2 * V2

29.4 * 100 = 14.7 * V2

2940 = 14.7 * V2

V2 = 2940 / 14.7

V2 = 200 cu/in

So the air in the diver's lungs has gained 100 cu/in of volume. If he doesn't exhale this extra volume out, it will kill him! If he breathed normally during the ascent, he keeps changing the P1 = P2 depth upward, so that any expansion during ascent is kept minimal, and well within the limits of what the body can handle.

Capt Nemo
09-14-2012, 02:20 PM
Yay finally finished the pressure injury part.

12-15-2012, 02:22 AM
Great post. But why did you start by saying most instructors don't talk about this? We talk about this all the time.

Capt Nemo
12-15-2012, 11:56 AM
Some instructors give the basics as per most dive courses, but rarely go in depth, and outright refuse to talk about all it's possibilities. When I had contacted a former NASDS Master Instructor/UW photographer, he told me about a few run-ins with models, who couldn't believe that their instructors refused to tell them everything. Even my instructor would cut me off and refuse to talk about it. The instructors at my current dive shop told me that this information isn't really covered until at least the divemaster/pre instructor course. Everything is geared toward the "first rule of scuba", and the rest is hidden. Most of it is fear of lawsuits, and the ability to get insurance. Outside the US, you don't have the pack of sharks waiting to pounce, and much more is taught.

It's my belief that knowing everything about Boyle's Law is safer than just the reason of the first rule of scuba. I've done a skip breathing ascent in a bad situation, and to do so, required total knowlege of the law, and that's more than what I was taught. My understanding came from understanding the mathmatics, which showed me that there was more to it than what I was taught. I realize too, that basic scuba courses are trying to change the students instincts. Their instinct is to try and hold their breath immediatly if anything goes wrong. This is why there is so much stress on never holding ones breath. And with the brevity of modern scuba courses, I can understand the brick wall that has formed. While scuba is relatively simple, I believe, that it is better taught with a longer 10-12 week course, rather than the short courses as taught today. The longer course prepares divers better because, the diver has had the time really learn it to the point of becomming automatic before hitting open water.

12-15-2012, 06:48 PM
I would think most entry level students don't really understand the topic and would just be confused by the whole discussion. I've had a few that wanted to know more and those divers usually went on to higher diver ratings. But the average person who just wants to dive for fun will get quickly confused and discouraged. A basic entry level course teaches the basics...then advanced courses teach more advanced topics. Studying the PPO2 is important for free divers as well. That's what causes the blackouts.

Capt Nemo
12-15-2012, 11:23 PM
PPO2 IS VERY IMPORTANT! And it's something for all divers, not just mixed gas scuba. It gets into some strange territory on fast ascents during freediving. It's one thing that's lacking in most courses when covering basic snorkeling/freediving.

12-15-2012, 11:35 PM
It's not taught in scuba classes because the freediving/snorkleing skills in those classes is designed for very shallow dives. I think it should be taught though. At least, introduced. The topic is covered thoroughly in freediving courses.

Capt Nemo
12-16-2012, 06:37 PM
And you wonder why I like the idea of 10 week scuba courses, rather than the 3 hour cruises! ;)

12-16-2012, 07:41 PM
10 weeks is too long for just an entry level course. But, I'm not a fan of the quick 3 day courses either. I like 6-8 weeks for divemaster courses. I know a friend that completed her divemaster course in 8 days. I can only imagine about the quality of that course.

Capt Nemo
12-16-2012, 11:39 PM
10 weeks is what I had to go through for advanced open water (basic was snorkeling which ended the 3rd week) with NASDS at the time. Then another 10 for the advanced gold card.

Many boat captains were relieved when they'd find out they had a boat full of NASDS or NAUI divers. It was the PADI ones they were always worried about!

The problem today is, no one wants to go that long, they want it NOW! It seems that planning ahead is a lost art these days.:rolleyes:

12-17-2012, 01:37 AM
Ironic...because around here, captains worry about the NAUI divers.