The Physics of Diving & Laws

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The Physics of Diving

Diving physics are the aspects of physics which directly affect the underwater diver. Physics explain the effects that divers and their equipment are subject to underwater while diving. These effects usually differ from the normal human experience out of the water.

The effects are mostly consequences of immersion in water, the hydrostatic pressure of depth and the effects of the pressure on breathing gases, the diver and the diving equipment.

An understanding of physics is useful when considering the physiological effects of diving and the hazards and risks of diving (full article).

Archimedes’ Law

Archimedes of Syracuse (287 – 212 BC) was a Greek mathematician, physicist, engineer, inventor and astronomer. Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola (full article).

Archimedes’ law or Archimedes’ principle states that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.

Read more about buoyancy and Archimedes’ principle in the following post: Let’s Talk About Buoyancy.

Boyle’s Law

Robert Boyle (1627 – 1691) was an Anglo-Irish natural philosopher, chemist, physicist, and inventor. Boyle is largely regarded today as the first modern chemist, and therefore one of the founders of modern chemistry, and one of the pioneers of modern experimental scientific method (full article).

Boyle’s law sometimes referred to as the Boyle–Mariotte law, or Mariotte’s law is an experimental gas law that describes how the pressure of a gas tends to increase as the volume of the container decreases.

Read more about pressure volume relationships and Boyle’s law in the following post: Pressure Volume Relationships in Diving.

Charles’ Law

Jacques Alexandre César Charles (1746 – 1823) was a French inventor, scientist, mathematician, and balloonist. Charles wrote almost nothing about mathematics, and most of what has been credited to him was due to mistaking him with another Jacques Charles, also a member of the Paris Academy of Sciences. Charles and the Robert brothers launched the world’s first unmanned hydrogen-filled gas balloon in  1783. Charles and his co-pilot Nicolas-Louis Robert ascended to a height of about 1,800 feet (550 m) in a manned gas balloon. Their pioneering use of hydrogen for lift led to this type of balloon being named a Charlière (full article).

Charles’s law, describing how gases tend to expand when heated, was formulated by Joseph Louis Gay-Lussac in 1802, but he credited it to unpublished work by Jacques Charles.

Charles’s law also known as the law of volumes is an experimental gas law that describes how gases tend to expand when heated.

Read more about pressure volume temperature relationships and Charles’ law in the following post: The Ideal Gas Law and the General Gas Equation.

Dalton’s Law

John Dalton (1766 – 1844) was an English chemist, physicist, and meteorologist. He is best known for introducing the atomic theory into chemistry, and for his research into colour blindness, sometimes referred to as Daltonism in his honour (full article).

In chemistry and physics, Dalton’s law also called Dalton’s law of partial pressures states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases.

Read more about partial pressures and Dalton’s law in the following post: Partial Pressure Implications.

Gay-Lussac’s Law

Joseph Louis Gay-Lussac (1778 – 1850) was a French chemist and physicist. He is known mostly for his discovery that water is made of two parts hydrogen and one part oxygen, for two laws related to gases, and for his work on alcohol-water mixtures, which led to the degrees Gay-Lussac used to measure alcoholic beverages in many countries (full article).

This law is often referred to as Gay-Lussac’s law of pressure–temperature. The pressure of a gas of fixed mass and fixed volume is directly proportional to the gas’s absolute temperature.

Gay-Lussac’s law can refer to several discoveries made by the French chemist and other scientists in the late 18th and early 19th centuries pertaining to thermal expansion of gases and the relationship between temperature, volume, and pressure.

Read more about pressure volume temperature relationships and Gay-Lussac’s law in the following post: The Ideal Gas Law and the General Gas Equation.

Henry’s Law

William Henry (1774 – 1836) was an English chemist. He was the son of Thomas Henry and was born in Manchester England. He developed what is known today as Henry’s Law (full article).

In chemistry, Henry’s law is a gas law that states that the amount of dissolved gas is proportional to its partial pressure in the gas phase.

Read more about dissolution of gases in liquids and Henry’s law in the following post: Decompression Theory Basics.

 Snell’s Law

Snell’s law is also known as Snell–Descartes law or the law of refraction.

Although named after Dutch astronomer Willebrord Snellius (1580–1626), the law was first accurately described by the Persian scientist Ibn Sahl at the Baghdad court in 984. In the manuscript On Burning Mirrors and Lenses, Sahl used the law to derive lens shapes that focus light with no geometric aberrations.

The law was rediscovered by Thomas Harriot in 1602, who however did not publish his results although he had corresponded with Kepler on this very subject. In 1621, Willebrord Snellius (Snell) derived a mathematically equivalent form, that remained unpublished during his lifetime. René Descartes independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 (full article).

The index of refraction of water is similar to that of the cornea of the eye, one third greater than air. This is the reason a diver cannot see clearly underwater without a diving mask with an internal airspace.

Read more about refraction of light and Snell’s law in the following post: How We See Things Underwater: It’s All About Light.

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Beware of Hyperthermia

Unknown 1Overheating is rarely an issue during diving because even relatively warm tropical water cools the body since its temperature is less than the normal temperature of a human body. But too much heat is a common problem before and after a dive especially in areas with hot climates and cool water thus requiring thick exposure suits or tropical areas with very warm waters.

When your body temperature rises either through exposure to a warm environment, heavy exercise or a combination of these, several physiological cooling processes begin to protect your core body temperature from rising.

Initially your skin capillaries dilate allowing heat from the blood to radiate through your skin. Next you begin to perspire cooling the skin and thus your blood through evaporation. If your core temperature remains high your heart rate and pulse accelerate
to circulate blood more rapidly to your skin for cooling accompanied by a breathing increase.

These responses remain until the core temperature returns to normal which usually means when you stop exercising or reach a cooler environment, for example entering the water. If this doesn’t happen soon enough your body can only continue its cooling efforts to your physical limit. The more physically fit you are and the less body fat you have the better you can handle hyperthermia, but beyond the limits of the human body’s cooling system you can experience heat exhaustion or heat stroke.

Hyperthermia or Heat Exhaustion

Thermoregulation is the ability of the human body to keep its temperature within certain boundaries even when the surrounding temperature is very different. When the surrounding temperature is high the body’s thermoregulation system is working at full capacity to cool.

Hyperthermia or heat exhaustion is elevated body temperature due to failed thermoregulation that occurs when a body produces or absorbs more heat than it dissipates.

Signs and symptoms of hyperthermia include weak rapid breathing, weak rapid pulse, cool clammy skin, profuse sweating, dehydration, nausea, etc.

A diver with heat exhaustion should remove the exposure suit, seek shade, drink non alcoholic fluids and rest until they cool off.

Extreme Hyperthermia or Heat Stroke

If a diver with hyperthermia remains hot or continues to heat the physiological control mechanisms will eventually fail and result in heat stroke.

Heat stroke is a type of severe heat illness that results in a body temperature greater than 40 °C.

Symptoms of heat stroke include red dry or damp skin, headache and dizziness. The pulse is strong and rapid, perspiration ceases and the skin is flushed and hot. At this point, the core temperature rises because the body’s cooling mechanisms have failed. Without medical attention, heat stroke can cause brain and organ damage, and even death is possible.

A diver with heatstroke should remove exposure suit, rest in a cool environment and contact emergency medical care immediately.

Heat Loss in Diving or How to Keep Warm

What is Heat?

In thermodynamics, heat is energy transferred from one system to another as a result of thermal interactions. Energy exchanged as heat changes the internal energy of each system by equal and opposite amounts (full article).

Heat Transmission

Heat transmission or transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy or heat between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation and others.

The fundamental modes of heat transfer are:

Conduction. The transfer of energy between objects that are in physical contact.

Thermal conductivity is the property of a material to conduct heat and evaluated primarily in terms of Fourier’s Law for heat conduction.

Convection. The transfer of energy between an object and its environment, due to fluid motion.

The average temperature is a reference for evaluating properties related to convective heat transfer.

Radiation. The transfer of energy by the emission of electromagnetic radiation.

A good way to imagine what radiation is that you can feel heat without touching the object emitting the heat.

Diving and Heat Loss

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Hypothermia

Water compared to air is a very good heat conductor. Water will transfer heat 24.17 times faster than air. The thermal conductivity of water is .598 (W/mK) and the thermal conductivity of air is .0259 (W/mK) watts per meters kelvin (at 20 °C).

Water removes body heat much faster than air. For the purposes of dive theory we simplify that water conducts heat 20 times a better than air. Water is 770 times more dense than air and 3.200 times more heat is required to raise to same temperature in water than it is in air of the same volume.

Any water that is cooler than the body temperature (even tropical waters with 28 °C to 30 °C) has the potential to eventually chill a diver or even induce hypothermia. If the water temperature is lower the heat loss in a diver will be faster.

Wetsuits trap a thin layer of water against a diver’s body. While the diver still gets wet, his body heats up the trapped layer of water to nearly body temperature. If the wetsuit fits properly the layer of water does not circulate away from the diver’s body and prevents more rapid heat loss.

For diving in colder waters (colder that 16 °C) a drysuit should be used. A drysuit traps air instead of water and insulates even better. It also allows the diver to wear undergarments that will keep him or her warmer during diving.

Physiology & Hypothermia

The environment exposes human physiology to a wide temperature range so our physiology has temperature maintenance mechanisms. The normal core body temperature is critical to the normal chemical processes continuously taking place in
the human body. A deviation above or below core temperature more than a few degrees for more than a short period may be life threatening.

Human body has physiological responses to protect against a drop in core temperature. This means that temperatures that we find comfortable and warm in the air quickly become uncomfortable and cool in water. Without an insulating exposure suit the average diver will be dangerously cold in half an hour in 16 °C water.

Hypothermia is reduced body temperature that happens when a body dissipates more heat than it absorbs. In humans, it is defined as a body core temperature below 35 °C.

If a diver looses a significant amount of heat during diving hypothermia may occur. The typical symptoms of hypothermia include shivering, numbness in the extremities, blueness in the fingers, lips and toes, etc. A diver experiencing these symptoms should end the dive, get out of the water and seek warmth.

Advanced Hypothermia

Advance or extremely advanced hypothermia can occur when then diver ignores uncontrollable shivering and lets his body continue to cool.

At a certain point the body heat loss is so severe that the temperature regulation mechanisms fails and the body core temperature drops even more.

The diver stops shivering, sluggish thinking and amnesia start to appear. Inability to use hands and stumbling are also usually present. Cellular metabolic processes shut down.

As the temperature decreases, further physiological systems falter and heart rate, respiratory rate, and blood pressure all decrease. Advanced hypothermia leads to unconsciousness, coma and death when body temp reaches around 30 °C.

Advanced hypothermia is a medical emergency and requires immediate emergency care.

Let’s Talk About Buoyancy

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Physics: Archimedes’ Principle

Diving is all about buoyancy. It is one of if not the most important skill to master in scuba diving.

At first glance, buoyancy control looks like a simple matter of balancing the downward force of your weights against the upward force of the gas in your BCD. When the two are equal, you’re neutrally buoyant and can hover in midwater.

Since the weight on your weight system doesn’t change with depth, it seems as though you have only one variable to deal with and that is the amount of gas in your BCD, in other words the upward force of your BCD. It sounds easy, right, so why isn’t it?

To better understand buoyancy while diving we first have to talk about Archimedes’ principle and then add a little bit of explanation with simple physics.

Read more about buoyancy tips on scubadiving.com.

Archimedes’ Principle

In diving we should be familiar with Archimedes’ principle (the famous mathematician’s name is not so important, but the principle is), which states that:

A body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.

In other words, an object submerged in fluid is seemingly lighter for the weight of the fluid displaced.

To explain this principle and apply it to diving situations we have to talk about density. Density is a measurement that compares the amount of matter an object has to its volume or in other words how much mass do we have per volume.

An object with much matter in a certain volume has high density, i.e. lead (12.000 kg/m3). An object with little matter in the same amount of volume has a low density, i.e. air (1,3 kg/m3). Since cubic meter has 1.000 litres we could also write that the density of lead is 12 kg/l and the density of air is 0,0013 kg/l. Let’s have a look at density of some other things we usually talk about in diving theory: wood (average 0,4 to 0,7 kg/l), water (1 kg/l), stone (average 2 to 3 kg/l), aluminium (2,7 kg/l), iron and steel (8 kg/l).

Buoyancy

Everybody knows that wood floats on water, regardless whether it is fresh or sea water (1 kg/l is more than 0,4 to 0,7 kg/l). Wood weights less then the water it displaces. Stone and metals don’t float on water (1kg/l is less than 2 to 3 kg/l for stone or 3 to 12 kg/l for metals). Stone and metals weight more then the water they displace. In terms of buoyancy, wood is positively buoyant in water (floats) and stone and metals are negatively buoyant in water (they sink).

With density in mind we can easily say objects float in fluids that are more dense than the object immersed.

Let’s have a look at another not so common example. If we melt lead (melting at 330 degrees Celsius), iron or steel will float solid on the surface of melted lead, because the iron or steel floating on the surface weights less than the displaced lead. This means iron or steel are positively buoyant in liquid lead.

We express how much positive or negative buoyancy an object has with a number that tells us what the difference between the weight of the displaced fluid and the object is. If this difference is positive the object will have that much positive buoyancy. If the difference is negative, the object will have that much negative buoyancy. If the difference is zero the object will be neutrally buoyant. Adding or removing weight will make the object sink or float.

Fresh and Salt Water

Fresh and salt water have different densities because of the salt dissolved in salt water that makes it more dense. 1 litre of fresh water weights 1 kg. 1 litre of salt water weights 1,03 kg.

A rubber balloon filled with fresh water would float in salt water (positively buoyant), whereas a rubber balloon filled with salt water would sink in fresh water (negatively buoyant). A rubber balloon filled with fresh water would hover (be neutrally buoyant) in fresh water and a rubber balloon filled with salt water would hover (be neutrally buoyant) in salt water (density of rubber is very close to water +/- less than 10%).

If an object is either neutrally or positively buoyant in fresh water it will be positively buoyant in sea water.

If an object is neutrally buoyant in sea water it will be negatively buoyant in fresh water.

If an object is positively buoyancy in sea water you cannot tell what will happen to its buoyancy when it will be placed in fresh water without additional information.

Buoyancy and the Human Body

The average density of the human body is 0,985 kg/l and the density of seawater is about 1,03 kg/l. The average density of the human body after taking a deep breath of breathing gas changes to 0,945 kg/l. So you can see where this is going. Wearing only a swim suit most people if they inhale will be positively buoyant and if they exhale will be negatively buoyant.

Adding scuba gear will complicate things a bit. Most of the scuba gear except the exposure suit is more or less neutral or a little negative. Exposure suit is positively buoyant and changes buoyancy with depth. The scuba cylinder is negatively buoyant, but as the amount of gas in the cylinder changes so does it’s buoyancy. A 12 litre cylinder filled to 200 bar contains 2,4 m3 of gas which weights around 3kg. An aluminium cylinder could be positively buoyant towards the end of the dive. Divers can compensate the buoyancy of themselves with all gear in place by adding weights and later air in the BCD and their lungs. The amount of air in the lungs effects buoyancy only if we dive open circuit scuba.

Simple Buoyancy Calculations

When you do simple calculations in order to determine the buoyancy of an object suspended in fluid you need to know the weight of the object, the volume or weight of  water it displaces and the density of the fluid displaced.

Exercise 1: How much gas must you add to a lifting device to make a 300 kg object that displaces 100 l or fresh water neutrally buoyant?

The weight of the objects is 300 kg. The weight of the displaced water is 100 l x 1 kg/l = 100 kg. The object is 200 kg negatively buoyant. To make it neutral we have to displace 200 kg of water with the lifting device. The volume of  the gas to add is 200 kg / 1 kg/l = 200 l. So the answer to the question above is: we have to add 200 l of gas to the lifting device to make it neutrally buoyant.

Exercise 2: A diver weighting 90 kg dives in fresh water and displaces 100 litres.  How much lead weight must he wear to have 2 kg of negative buoyancy on the bottom?

The weight of the water the diver displaces is 100 l x 1 kg/l = 100 kg. The diver is 10 kg positively buoyant. To make him neutral, he needs 10 kg of weight. To make him 2 kg negatively buoyant, he has to wear a total 12 kg weights.

Exercise 3: An anchor weighting 450 kg is lying at the depth of 20 m in salt water. The anchor displaces 130 litres.  How much gas do we have to take from a scuba tank and transfer it to a lifting device to bring it to the surface?

The weight of the water the anchor displaces is 130 l x 1,03 kg/l = 134 kg which makes the anchor 316 kg negatively buoyant. To make it neutral we need to displace 316 kg of salt water. The volume of 316 kg of salt water is 316 kg / 1,03 kg/l = 307 l. The pressure at 20 m is 3 bar. We have to take 3 x 307 l from the tank and transfer it to the lifting device where the air will be compressed back to 307 l. So the answer to the question above is 921 l.

Starting with the Blog

For a while I was thinking of putting up my own blog. I decided to go for it and WordPress seemed like a good platform to use.

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Photo by S.N. (c) 2018

It is hard to say what kind of content I will be publishing on this blog. The topics will be connected one way or another with diving.  I will come up with new approaches as I go.

The basic idea is to use the blog to publish interesting topics that pop up during training and might also be interesting for other divers to read too.

The blog will also be a place to shortly document interesting moments during training and interesting stuff we do and I want to share online. It is supposed to have a little more content than the brief posts I have on the Facebook page. I plan to post once or twice a month just to see what response I will get and I am looking forward to the feedback and future interaction.

Now let’s get some real content on here!