Diving Physics Jan 2009

Diving PhysicsJan 2009

M. David Henry PADI / California Inst. Of Technology Personal Introduction

Course Outline • Pressure and Force • Atmosphere and Depth • Regulators • Gas Physics • Ideal gas Law • Dalton’s Law • Henry’s Law • Diving Gases • Optics • Snell’s Law • Spectrum of light & eyes • Absorption of light • Buoyancy • Archimedes Principle

Pressure and Force Atmosphere and Depth If I am standing on the surface of the earth, on the edge of the ocean…. I have the weight of all the atmosphere (oxygen atoms, nitrogen atoms, CO2, etc) up to the edge of space wanting to fall down on me. This is a force. Force = mass * gravity So let’s take an really small area; the size of the area determines how many of the molecules I include above me (mass). mass = (area * height) * density Or after rearrangement area=mass / (height * density) From the area I can calculate the pressure on that area. P = F / A = gravity *height * density We call this 1 atmosphere, or 1 Ata, which is roughly 14.7 psi. Note that it is independent of the area I picked.

Pressure and Force Atmosphere and Depth Using the same technique, I find out how deep I have to go to get 14.7 psi. P = gravity *height * density = 14.7 psi = 101353 kg/m2 gravity = 9.8 m/sec2 density of seawater = 1025 kg/m3 So then the height of the seawater is 10.09 meters or 33.1 feet. Or every 33 fsw I descend, I add one more atmosphere of pressure. If we were to look at freshwater, since the density is less, the height is only 34 feet.

Pressure and Force The fundamental relationship between pressure and force is that pressure is force spread out over a total area. Example: We drop a sharp pencil and let it land on our foot, lead side pointing down. OUCH. Alternatively we can drop the same pencil, eraser side down. They both have the same force (force=mass * gravity), but the difference is that the tip of the lead is a very small area. So, let’s place a given pressure on the large side of the piston. Although the force is the same, the smaller side can push a greater pressure. The fundamental principle of regulators. F P2A2=P1A1 P2=P1A1/A2 F=P1A1 F=P2A2

Pressure and Force Pressure of seawater Tank Pressure Pressure from spring Intermediate Pressure *Remember, this little piston is what the pressure is acting on. If the piston is not moving, then the sum of the forces equal zero.

Pressure and Force So if the diver inhales from the second stage, the IP decreases. Now the Force on right side of the equation is greater than the left side and the piston moves left. This allows air to move from the tank to the IP chamber until the pressure rises in the IP chamber high enough to balance the forces. Pressure of seawater Tank Pressure Pressure from spring Intermediate Pressure Ptank*Area + PIP*Area = Psw*Area + Pspring*Area

Gas Physics – Ideal Gas Law • Incorporates Gay-Lussac’s Law, Sir Charles’ Law, and Boyle’s Law into a single law. • Derived from statistical mechanics. • Remember, the laws are only valid for moving from one equilibrium state to another. ie: • the end of a nice slow tank fill in a dive shop to: • leaving the tank in a hot car • jumping into cooler Catalina waters • DCS – ending a dive with a cooler core temperature • jumping into a Jacuzzi – bubble theory • Remember, temperature is in Kelvin… the numbers will be incorrect if F or C is used.

Gas Physics – Ideal Gas Law • How to use the gas law: • starting pressure & volume = starting number & temperature * Kb • final pressure & volume final number & temperature * Kb • or Now, think about your system. What stays the same? If you are using a scuba tank, you know the volume is always the same and if the valve is shut then the number of molecules never changes. So if V1 = V2, then V1 divided by V2 is one. If n1 is the same as n2, then n1 divided by n2 is also one.

Gas Physics – Ideal Gas Law 1 1 Let condition 2 be a normal 3000 psi fill in a dive shop at 85 F. Let condition 1 be after you jumped into the Catalina waters 68 F.

Gas Physics – Ideal Gas Law Your turn. You fill the tank to 3000 psi in a dive shop at 85 F. Then you leave it in the trunk of your car and it heats to 150 F. What is the final pressure? 1 1

Gas Physics – Ideal Gas Law Pressure in different sized tanks, filled to rating, after you jump in the water during the winter (60 F) after a fill which leaves the tank hot – x axis.

Gas Physics – Ideal Gas Law Energy of an ideal gas as derived from statistical mechanics: This is interesting because it shows the energy wrapped up in a fully filled scuba tank can be quite large….

Gas Physics – Ideal Gas Law

Gas Physics – Ideal Gas Law Constant temperature and constant molecule number: who’s law is this? Boyle’s Law • Recall all the reasons why this law is one of a diver’s favorite… • Pulmonary over-inflation syndrome – holding your breath when you rise to the surface could lead to AGE, mediastinal emphysema, or pneumothorax. • Why you need to dump air from your BCD when you go from practicing skills at 30 fsw and you are doing your safety stop at 15 fsw.

Gas Physics – Ideal Gas Law • Why you need to dump air from your BCD when you go from practicing skills at 30 fsw and you are doing your safety stop at 15 fsw. BCD volume expanded by ~1.3 times!!

Gas Physics – Dalton’s Law The total pressure exerted by a mix of gases is equal to the sum of pressures exerted by the individual gases. As we dive deeper, we know that the total pressure increases. Using Dalton’s law, we can see how the partial pressure also increases. PPN2 *Remember, physiologically the body responds to partial pressures, not percentages or absolute pressures. PPO2

Gas Physics – Dalton’s Law NITROX Equivalent Depth – One of the advantages of nitrox is that by increasing the percentage of oxygen, you consequently decrease the percentage of nitrogen that you breath and thus absorb (Henry’s Law). What is typically used to demonstrate the benefit is equivalent air depth; how much shallower would I need to go on standard air for a given depth on a nitrox mix. Let’s use 40% nitrox. If Depth40% = 70 fsw, then on air you would only be able to go to 45.2 fsw for the same nitrogen loading rate.

Gas Physics – Dalton’s Law NITROX • Oxygen Toxicity – using the 1.6 limit (Contingency), what is the maximum depth one can take: • standard air • pure oxygen standard air – 218 fsw pure oxygen – 20 fsw *Don’t do this unless properly trained!!!!!

Gas Physics – Henry’s Law At a given pressure and temperature, the amount of gas dissolved in a given liquid is directly proportional to the partial pressure of that gas in contact with the liquid. The most obvious example is the classic soda bottle which is under a few psi pressure of CO2. This allows the soda to fizz immediately after opening. But the most important aspect of this model is typically overlooked…. what happens to the bubbles over time? Note that if the bottle is immediately vented, the bubble rate is highest; but it still bubbles even after 6 hours albeit slowly. Gradient is what is truly important here. For a diver, the obvious application of this law is the explanation of nitrogen absorption into the tissues and DCS. Once again the gradient is of importance. Note that dive computers do not stop with this simple idea, transport time of gases through the circulatory system as well the ideal gas law also come into play here.

Gas Physics – Henry’s Law • Dissolved Gas Models – maintains the concept that gas diffuses into and out of tissues to equalize the gas tensions but that this is fast; instead perfusion rates dominate (time for blood to distribute the gas). • Haldanian Model (refined by Workman, then Buhlmann) – premise was that different body tissues on/off gas at different rates and set maximum gradients for the model’s tissue groups (parallel) • Delta P Technologies • Dive Rite / Tusa • Nexus (makers of the Inspiration rebreathers) • DSAT – Oceanic & Aeris • Scubapro / UWATEC – recently added microbubbles to the model. • USN Tables. • DCIEM Model (Kidd and Stubbs) – model’s tissue compartments were chained together in series. • Citizen

Gas Physics – Henry’s Law with Ideal Gas Law • Bubble Models – adds that besides dissolved gas, there is also microbubbles whose movement is dependant on the bubble size (pressure) and location. Control of the growth of the microbubbles can sometimes be more important than the dissolved gas diffusion and/or perfusion, but at other times less important. (The real power of this model) • VPM Model (Yont & Hoffman at University of Hawaii) • Maintains the perfusion model as before, but adds on bubble theory. The first run utilized the USN tables and halftimes and added bubble theory. • Reduced Gradient Bubble Model “RGBM” (Wienke) • Maintains perfusion, diffusion and bubble theory. Further reduces the gradient, G, for multiday and ‘riskier’ dives • Suunto – just added the latest research with the ‘deep stop’ algorithm. • Cochran – typically uses 16 compartment models and implements microbubble algorithm adjustments (linear off bubble decrease)

Gas Physics – Henry’s Law with Ideal Gas Law and Calculus The practical difference between diving tables and computers is the accuracy of the dive profile. Accuracy of the computer’s depth and time are very nearly the same as a mechanical gauge / watch. Max depth/time = 98 ft / 29 min with 3 min @15 ft safety stop PADI Tables – exceeds the NDL of 100 ft for 20 minutes by 9 minutes. (pink) PADI Wheel – 100 ft for 19 min, 70 ft for 5 min, 40 feet for 5 min. Ending pressure group is R. (grey). Suunto Cobra computer – tissue groups shown below. (blue)

Gas Physics – gases • Argon - Heat flow from a diver – Yes the ocean is a very big heat sink. But that is not really our problem, the problem is that water conducts our heat energy away from us much faster than air. Think of our body as a heat generator fueled by food and the ocean as an infinite heat sink. So the trick is to slow the rate at which we cool; if the rate is slow enough our bodies can keep up (assuming we keep eating). Q=k*DT where k=0.025 for air and k=0.6 for water -ratio = 24 Dry suits work by further reducing the thermal conductivity between the body and the ocean. Argon k=0.0177 – but narcotic at depth –ratio of air to argon = 1.41

Gas Physics – gases • Helium - Typically used to replace nitrogen in trimix or heliox since helium is mostly inert (things get crazy with He at high partial pressures). So it still acts as another non-biologically-useful gas like nitrogen but has the advantage of not being narcotic (again watch out with extreme pressure). Another disadvantage is that it diffuses into and out of the body about ~4 times faster than nitrogen (don’t waver on your deco stops) and it also conducts heat about 6 times faster than air. This means that you cool off much faster as you exhale and inhale. k = 0.1513

Gas Physics – gases • Oxygen - Most life needs a partial pressure of at least 0.16 to survive (low end of the estimate). Over 1.6 (generally agreed upon), the body risks going into seizures known as CNS O2 Hyperbaric Toxicity. Over 1.0 the body begins to degrade; lung tissues are scarred, etc. Nitrox increases the percentage of oxygen across the range of 21% to 40%. Over 40% special precautions must be taken with both cylinders and regulators. Although one of the big problems with higher oxygen percentages are the use of petroleum based o-rings (use synthetics such as Viton) another big problem is the titanium pistons in 1st stages of regulators. As the knife edge of the piston shuts into the seat, localized friction creates a very high temperature (although short lived); this is bad when surrounded by pressurized oxygen.

Gas Physics – gases • Nitrogen – Quoting John Chatterton, “Me and Ritchie believe that nitrogen is a bad gas.” Bad for DCS, bad for nitrogen narcosis (if you deem that a bad deal), but I believe the best dilutant to go with oxygen for recreational diving. • Carbon Dioxide – We all exhale this gas, but in high partial pressures it can be dangerous. A poorly functioning second stage will use this gas to give a diver problems at depth. This is also a well known greenhouse gas. Good news is that this gas is what signals our body to breathe, helping to prevent shallow water blackouts when freediving. • Carbon Monoxide – This gas mostly comes from burning hydrocarbons (cars, compressors, fires, etc) and is of real concern when getting your tanks filled.

Optical Physics – Snell’s Law This law explains how light bends as it passes from one medium to another. For divers, we see the manifestation of this effect when looking from water to the surface, from our mask out to the reef, and even across thermoclines. nair = 1.0002926 nvacuum = 1 nwater = 1.333 nglass = 1.460 nfw = 1.33157 nsw = 1.3423 *note that index of water changes with salinity, temperature, and wavelength.

Optical Physics – Snell’s Law Light crossing the barrier of air and water. If one reverses the arrows, it would be the what the diver sees when looking up from the bottom of the ocean. Air Water

Optical Physics – Snell’s Law If one reverses the arrows, it would be the what the diver sees when looking up from the bottom of the ocean.

Optical Physics – Snell’s Law Another example is the light going from your eyes across the lens of the mask. Mask lens Diver’s eyes This is why a fish looks bigger in the water (and closer) than reality. What happens when you don’t have a mask? Light from the water enters your eye from your cornea (lens) which is also mostly water. Hence, your lens doesn’t bend light without the index change. nwater/nvacuum = 1.33/1 = 33% larger or 25% closer

Optical Physics – radiation / absorption Visible light only spans a very small percent of the Electromagnetic spectrum. When considering light as a wave, we can see visible light from about 400 nm to 730 nm.

Optical Physics – radiation / absorption The human has 3 distinct types of cones to detect color. Each has its own spectrum of which it is sensitive. The cone absorbs the radiation, initiating a chain of ion transport. This signals the brain which interprets the signaling from each to determine the color of what we see. This is a typical rod cell (similar to cones).

Optical Physics – radiation / absorption Similarly, water also absorbs electromagnetic radiation. As light travels from the surface of the water, all light is absorbed but red is taken out most strongly… this is most clear by looking at the strength of the absorption coefficient. I=Ioe-ad

Buoyancy Physics Archimedes’ Principle – an object which is immersed wholly or partially in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. density = mass / volume weight = mass * gravity So Weight =density*vol*gravity Weight / Vol = density *gravity

Buoyancy Physics • Divers utilize this principle to become neutrally buoyant. Without their weights, divers’ bodies displace enough water, beyond their weight, to make themselves float. • Another facet of buoyancy is how to use a lift bag to raise something off the bottom of the ocean. Weight per unit volume of seawater = 64 lbs per cuft Weight per unit volume of freshwater = 62.4 lbs per cuft If the object is neutrally buoyant, the force of gravity matches the buoyant force. So m*g = r * vol * g or m = r * vol. Neutral buoyancy is invariant (does not depend on) location in a gravitational field.

Buoyancy Physics Solving the lift bag problem Let’s suppose we have an object which weighs 20 lbs and is sitting at 66 fsw. The object displaces 0.1 cu. ft. of seawater. How much lift does it take to raise the object to the surface? 64 lbs/cuft * 0.1 cuft = 6.4 lbs Buoyancy is forcing the object up! The object weights 20 lbs. 6.4 lbs – 20 lbs = -13.6 lbs Hence 13.6 lbs of buoyancy is needed to make the object neutral. This requires us to displace 13.6 lbs / (64 lbs/cuft) =0.2125 cuft. *** note that we are exactly neutral at this point ***

Buoyancy Physics Solving the lift bag problem – back to ideal gas What is the volume displaced once the lift bag reaches 33 fsw and how much lift does it have? P1V1=P2V2 (remember this one?) 3 ata * 0.2125 cuft = 2 ata * V2 So V2 = 0.31875 cuft Going back to the previous equation…. 64 lbs / cuft * 0.31875 cuft = 20.4 lbs WOW, now the object is being forced up!!!!!!! * Ever see a new diver trying to work out their buoyancy issues and pop to the surface?

Buoyancy Physics Solving the lift bag problem This is why buoyancy is so difficult to master. If we are neutrally buoyant at a depth, and drop down just a few feet, ideal gas shows us that the air in the BCD compresses. This means we displace less water and so become negatively buoyant. Now we drop down faster!!!!! The same goes in reverse; if we raise just a bit, the air expands, displaces more water and we raise more AND FASTER!!!! POSITIVE FEEDBACK

Buoyancy Physics Buoyancy Check – does this make sense??? One way to check for neutral buoyancy on the surface is submerge up to your eyes with no air in your BCD while holding a normal breath of air. Average head circumference = 56.5 cm Distance from eyes to top of head = 4 inches Volume of head from eyes to top of head which is out of the water during the check = 2581 cu cm or 0.091 cu ft. Total lung capacity is approximately 6 liters or 0.212 cu ft. The additional air that can be forced in the lungs after a tidal (normal) inhalation is 3.6 liters. This means a normal inhalation displaces 2.4 liters or 0.0848 cu ft; pretty close to the amount of your head but don’t forget weight of the head. Forced vital capacity( amount of air that can be maximally forced out of the lungs voluntarily) is 4.8 liters or 0.1695 cu ft… This is 10.85 lbs of lift in the ocean!!!

Whew!!!! Anyone still awake???

Course Review • Pressure and Force • We know that every 33 fsw change equates to one atmosphere and that pressure doesn’t depend on the area! • We know that by balancing the force on the first stage piston of a regulator we can get air after a breath. • Gas Physics • One law saves us from learning 3 laws!! And we know how a hotfill will change our tank pressure when we jump into the water. • Nitrox rocks! Air is good to 218 fsw and pure oxygen is good to 20 fsw (don’t test this unless your are trained to do so… then still don’t do it!) • Our bodies are like soda bottles… after a good dive, don’t go up too fast! • Argon is warm, oxygen trades problems with DCS for problems with CNS, carbons aren’t just bad for global warming but also are bad for breathing, and NITROGEN IS A BAD GAS…. but better than any alternative… for now. • Optics • Without a mask in the water, our eyes effectively can’t focus. • Our eyes have detectors which pick up three different spectrums, but don’t worry we can’t see red at depth unless we bring lights anyway. • GPS or radios won’t work underwater! • Buoyancy • Positive feedback make buoyancy difficult, and my lungs can lift 10 lbs!!!!! Physics is actually really useful for divers!!!!

Cheers!

Diving Physics Jan 2009