Diving Science Water & Gas Laws PDF

61. Diving Science Water and gas laws Core concepts At the end of this section, you should know and be able to demonstrate an understanding of, at least, the following: The relationship between the pressure, temperature, density and volume of air in a flexible container The chang...

61. Diving Science Water and gas laws Core concepts At the end of this section, you should know and be able to demonstrate an understanding of, at least, the following: The relationship between the pressure, temperature, density and volume of air in a flexible container The change of pressure in relation to change of depth below the sea surface as one ascends or descends The change in the volume of air as it is taken from one depth to another The gas laws of Boyle, Charles and Gay-Lussac How to use the pressure, volume and temperature equations How to change the subject of the formula in the above equations How to apply these calculations to diving contexts Fig 61.1: Dive Master Iain of Iain’s Scuba School, which operates at the Two Oceans Aquarium, illustrating perfect neutral buoyancy 61. Diving science 1 Introduction Diving in water is an adventure providing many opportunities for Marine Scientists to become familiar with underwater habitats and ecosystems. Physically being underwater is a vastly different experience to being on land. As one’s depth increases, you experience sensations from feelings of weightlessness and increased water pressure on your body at the various depths. Therefore, you need to understand that air functions differently in water as the depth changes. Also, the gases in the regulator through which you breathe has an effect on the air spaces in your body specifically your ears, the lungs and sinuses. In Topic 13, Energy transmission through water- Light, we studied how different parts of the light spectrum are absorbed at different depths below the surface and in Topic 40, Transmission of sound energy through water, we studied how sound travels and functions differently below the water surface, in this topic, we will focus on how air behaves under water. In order to spend time and move freely underwater, you need special breathing equipment called SCUBA (Self-Contained Underwater Breathing Apparatus) and to use this gear safely you need to understand the science of diving, which is mainly governed by the gas laws which show the relationship between gas temperature, water pressure and the volume of a parcel of air. Note: Although this topic will explain a great deal about diving, it is not a dive course. To learn to dive safely, you need to receive professional diving instruction from a registered organisation such as PADI (Professional Association of Diving Instructors). Air pressure At the sea surface, we are surrounded by air which presses against us. This air pressure is caused by the weight of the air column in the atmosphere above and around us. At sea level, air pressure is consistently the same from place to place and this air pressure is expressed as 1 bar (metric) or 1 atmosphere (imperial) – abbreviated as 1 ata. Fig 61.2: Weight of the air in the atmosphere 2 Marine Sciences Grade 12 Water pressure Water is more dense than air and therefore heavier. Unlike gases, water cannot be compressed into a smaller volume. Instead, its weight applies pressure to anything within it, including a parcel of air. Every metre below the surface, that pressure increases by one bar. Thus at 10 m below the water surface, the mass of that column of water adds one additional bar of pressure. And at every further 10 m of depth, an additional bar of pressure is added. Consequently, the accumulated pressure a diver experiences when descending is one bar of surface atmospheric pressure plus one additional bar of pressure for every 10 m of depth. Fig 61.3: Relationship between depth and water pressure Human body tissue is mostly made up of water, therefore the extra pressure at depth, although it is felt, does not impact much upon the body. The parts of the body that the pressure does affect are the spaces within the body where air is found. Those are the lungs, the sinuses and the tubes in the ears. Air pressure will also impact on the air in a diver’s face mask. Think heavier – water pressure is proportional to depth. Gas temperature Temperature affects both volume and pressure. This is a result of the energy transfer. An increase in temperature results in the increase in energy within the gas. That increased energy results in an increase of pressure within a rigid container as the molecules of gas will move around with greater energy as the heat is increased and vice versa. In a flexible container such as a balloon, that increased energy will result in increased volume. Similarly, if a dive cylinder is left in the sun and allowed to increase to over 35°C the pressure in the cylinder will increase significantly. Overheated cylinders have been known to burst. Volume Air or gases are compressible when exposed to an increase in pressure. This means that an increase in pressure on a parcel of air (or gas) affects its volume. A parcel of air/gas consists of a certain number of molecules. As the pressure on the parcel increases with depth, the pressure on the molecules within the parcel also increases, 61. Diving science 3 making less room (or less volume) for them to occupy. The molecules are thus compressed into a smaller volume. Therefore, we can say the change in air volume and density is inversely proportional to the change in pressure. As pressure increases, the volume decreases and the density (mass per unit volume) increases. Fig 61.4: Relationship between depth and volume Consequently, 1 litre of surface air behaves as follows at depth: At a depth of 10 m, 1 litre of air takes up ½ its original volume (½ ℓ = 500 ml) At a depth of 20 m, 1 litre of air takes up ⅓ its original volume (⅓ ℓ = 333.3 ml) At a depth of 30 m, 1 litre of air takes up ¼ its original volume (¼ ℓ = 250 ml) At a depth of 40 m, 1 litre of air takes up 1/5 its original volume (1/5 ℓ = 200 ml) For example, if a diver descends holding a balloon containing 12 litres of air at the surface, the balloon of air decreases in volume as follows: 0m depth (surface) 12 litres 10 m depth (12 ÷ 2) = 6 litres 20 m depth (12 ÷ 3) = 4 litres 30 m depth (12 ÷ 4) = 3 litres 40 m depth (12 ÷ 5) = 2.4 litres In another example, an inverted jar full of air shows a decreasing volume as depth increases. Fig 61.5: Density is inversely proportional to pressure Think thicker – air density changes proportionately when pressure changes. We have been discussing what happens to volume and pressure when a diver descends. What happens when a diver ascends? Volume and pressure behaviour when depth decreases is exactly opposite to their behaviour when depth increases. 4 Marine Sciences Grade 12 Take a flexible container of air/gas (e.g. a lung) ascending in a water column. The flexible container expands as it ascends. If this container is filled to its capacity with air at a depth and then brought to the surface, it will burst because the volume (expanding proportionately to the decreasing depth) has no space to expand into. This illustrates the danger of a scuba diver filling the lungs with air at a depth and not breathing out on the ascent. Holding your breath as you ascend is an extremely dangerous thing for a scuba diver to do. Fig 61.6: An ascending flexible container filled with air will burst if the volume is not decreased on the way up. With an open container, the excess expanding air simply bubbles out into the surrounding water. In a closed, flexible container the air volume grows proportionately with the decreasing pressure. If you inflate a sealed bag at 30 m, it will expand to four times the volume on the way to the surface – or burst during ascent if it cannot stretch that much. Buoyancy Divers need to understand and work with buoyancy. It is critical when at the surface after a dive, the diver needs to float on the surface to keep safe and breathe easily. Divers must also control their buoyancy during the dive. Diving deeper than planned is dangerous. An uncontrolled ascent could lead to a lung injury. Buoyancy control to ensure a slow and a gradual ascent is very important for a diver’s safety. When diving close to a reef, divers need to keep their body, equipment and fins/flippers away from the animals on the reef to prevent any damage both to themselves and the animals. Divers must constantly alter their buoyancy, particularly when on a reef and close to animals. An item that floats on water or is moving upwards in the water column is called a positively buoyant item. An item that is sinking in a water column is negatively buoyant. An item that is neither floating nor sinking in the water column but remains suspended in the water column at that depth is neutrally buoyant. 61. Diving science 5  Fig 61.7: Positive, negative and neutral buoyancy An item floats or sinks owing to its weight and the amount of fluid/water it displaces. It will float if it displaces a volume of water equal to or greater than its weight; it will sink if it displaces a volume of water less than its own weight. Example 1: A piece of plasticine clay rolled into a ball will sink to the bottom of a container of water. It sinks because it has weight, its density (mass per unit volume) is greater than water and it is not displacing sufficient water to be buoyant. If that plasticine is shaped like a boat, it will float because it displaces a volume of water equal to or greater than its own mass. Fig 61.8: Negative buoyancy when the weight is greater than volume of water displaced. Example 2: A boat weighing one ton will float as it displaces more than one ton of water. If there is a hole in the boat that allows in water, that water will keep replacing the displaced air until it no longer displaces one ton of water. At that point the boat will sink. Scuba divers can wear a buoyancy control device that allows them to float, be neutrally buoyant or to sink, depending on the amount of air they add or release. Fig 61.9: A buoyancy control device such as those used by the divers at the Two Oceans Aquarium The importance of understanding buoyancy for safe diving cannot be over-emphasised. If divers sink too deep, they could reach a depth beyond which they might not be able to return undamaged or even alive. If they change their buoyancy and rise through the water column too fast, the expanding air will place too much pressure on the lungs and will damage them. Fig 61.10: Divers at Two Oceans Aquarium wearing buoyancy control devices 6 Marine Sciences Grade 12 Safe diving Scuba diving is one of the most exciting and invigorating experiences to engage with the ocean and experience its inhabitants but it is an activity that must be approached with caution as it can be dangerous. All divers need to understand how pressure, volume and absolute temperature interact with each other so as to keep themselves and others safe at depth. Common dive accidents There are two broad categories of dive injuries, those caused by a) Decompression sickness (Nitrogen bubbles in a person’s body tissue) and b) Barotrauma (expanding or contracting gas, damaging the ears sinuses and or lungs) Dive accidents most commonly treated by medical personnel include barotrauma (gas pressure-related injury), lung overexpansion, decompression sickness, ear pressure trauma, and possible intake of poisonous gases such as Carbon monoxide if it is present in a scuba air cylinder. The bends occurs when a diver dives too deep or for too long and then does not allow enough time for coming up to the surface. A slow ascent will allow Nitrogen gas to diffuse out of the tissues without causing bubbles to develop. The physical presence of bubbles in the tissue damages the body tissue (for example a Nitrogen bubble in the spinal chord causes spinal chord damage). The Nitrogen in the body tissues is released as bubbles, which collect in joints and cause severe pain. In response to the pain the person bends over – hence the name. It is also referred to as decompression sickness. Nitrogen narcosis occurs when the partial pressure of Nitrogen becomes so high that it causes an effect similar to being intoxicated with alcohol. The deeper and faster the descent of the diver, greater the effect. The diver will show signs of euphoria similar to mild alcohol intoxication. An air embolism occurs when a diver holds his/her breath on their ascent. This causes a forcing of air into the veins of the lung which travels to the brain causing a stroke. A combination of “The Combined Ideal Gas Laws” guides divers to keep themselves safe. The combined and ideal gas laws In physics, a combination of gas laws governs the relationship between pressure, volume and temperature. These include Charles Law, Boyle’s Law and Gay Lussac’s Law to develop the Combined Ideal Gas Laws. With the addition of Avogadro’s Law, 61. Diving science 7 this became the Ideal Gas Law, giving a general gas equation. They are called the ‘ideal’ gas laws as their equations and relationships work at ideal and not extreme pressures and temperatures. The gas laws formula requires the temperature to be converted from degrees Celsius to Kelvin. You achieve this by adding 273 to the value of the Celsius reading. For example, 10 °Celsius = 273 + 10 = 283 Kelvin. Thus 10 °C = 283 K Boyle’s Law – If temperature is constant In a parcel of air in which the temperature is kept constant, the gas volume decreases as the air pressure increases, and vice versa. PV = k Charles’ Law – If pressure is constant The volume of the gas in a flexible container will increase proportionally in relation to the temperature expressed in Kelvin, and vice versa. This means:... A volume of gas expands when heated. Gay Lussac’s Law – If the volume is constant The pressure in a rigid container will change proportionally with absolute Kelvin temperature. This means: …In a rigid container, the pressure of a gas increases proportionately when heated. These two laws are very similar, the only difference being the container. In Guy- Lussac’s Law it is rigid, whereas in Charles’ Law the container is flexible. Dalton's law – one gas will not compress more than another gas In a container holding different gases, the total pressure exerted on the sides of the container will be equal to the partial pressures of the individual gases. This means: … the pressure of gas in a container is equal to the sum of the different pressures exerted by each individual gas. The biological effects on a diver depends upon the partial pressure, (i.e. the greater the partial pressure of a gas, the greater the effect it has upon the body). e.g. Total pressure = the partial pressure of Oxygen + the partial pressure of Nitrogen + the partial pressure of Helium + the partial pressure of Hydrogen … (and so on) Henry’s Law – If pressure increases The higher the pressure surrounding a body (e.g. a human body), the more gas is absorbed into the tissue of that body. The amount of dissolved gas in a liquid is proportional to the partial pressure exerted on that liquid. Avogadro’s Law – If pressure and temperature are constant At a constant pressure and temperature, the volume of any gas is proportional to the 8 Marine Sciences Grade 12 number of gas molecules present. If the number of gas molecules increases, then the volume that the gas occupies also increases. To apply these laws, Marine Sciences students are required to use the pressure, volume and temperature formula and calculate for the missing variable. In all calculations the temperature needs to be converted to absolute temperature, Kelvin. For all our calculations the following formula is used: P1.V1 = P2.V2 T1 T2 Example: A balloon at 12 m depth has a volume of 10 litres. What volume would the balloon have at 24 m? [In this example, T (temperature) remains constant. It is V (volume) and P (pressure) that change]. The pressure at 12 m depth (which is P1) will be: 1 bar (air pressure at surface) + 1.2 bar (water pressure at 12 m) = 2.2 bar Pressure, which is P2, at 24 m depth will be: 2.2 + 1.2 bar (another 12 m depth) = 3.4 bar. Use the formula: P1.V1 = P2.V2 T1 T2.. Because T is constant in this example, it is discarded for the calculation, leaving: P1V1 = P2V2 P1 = 2.2 bar and V1 = 10 litres Thus, P1 × V1 = 22 We want to find V2 so that needs to be subject of the formula: V2 = P1.V1 P2 = 22 3.4 = 6,470 litres (volume at 24 m) 61. Diving science 9 Additional resources You may find the following links useful: Videos Gas laws https://www.youtube.com/watch?v=robEY-idcLU https://www.youtube.com/watch?v=QhnlyHV8evY https://www.youtube.com/watch?v=TbZpW5pBBac Explanation of changing the subject of the formula in the Gas laws https://www.youtube.com/watch?v=UKUmYU6Q1cA https://www.youtube.com/watch?v=QhnlyHV8evY Websites Gay-Lussac's Law https://www.grc.nasa.gov/WWW/K-12/airplane/glussac.html Boyle’s Law http://physconcepts.co.uk/boyles.html 10 Marine Sciences Grade 12 Test your knowledge Gas law assessments will be marked as follows: Marks = 1 for all the PVTs correct + 1 for converting temp. + 1 for correct subject of the formula + 1 for correct answer. For each calculation it might be useful for you to fill in the following data. That will assist you to understand what is known, what is unknown; what will change and what will remain constant. P1 =______ V1 =______ T1 =______ P2 =______ V2 =______ T2 =______ 𝑃1𝑉1 𝑃2 𝑉2 Remember, the basic formula is: = 𝑇1 𝑇2 1. A balloon at 7 metres has a volume of 10 litres. What volume would the balloon have at 35 metres? 2. A balloon lying on the beach at dawn has a volume of 3 litres. The temperature is 12 °C. What is the volume at midday when the temperature rises to 38 °C? 3. A dive cylinder has 240 bars when filled at 17 °C. It lies in the boot of a car where the temperature rises to 45 °C. What is then the pressure in the cylinder? 4. A dive cylinder has been filled to 220 bars when the temperature is 42 °C. What will be the pressure when the temperature cools to 7 °C? 5. You have a balloon at 20 metres below the sea surface where the temperature is 17 °C and the volume is 15 litres. What would be the volume at 7 metres, where the temperature is 17 °C. 6. You have a balloon at 27 m with a volume of 10 litres. What volume would the balloon have at 5 metres? 7. You have a balloon at 30 metres where the temperature is 6 °C and the volume is 8 litres. What would be the volume be at 5 metres where the temperature is 16 °C? 8. You have a balloon at 32 m with a volume of 12 litres. What volume would the balloon have at 13 m? 9. You have a balloon at 34 metres, where the temperature is 6 °C. The balloon’s volume is 15 litres. What would be the volume at 7 metres, where the temperature is 18 °C? 61. Diving science 11 10. You have a balloon at 42 m with a volume of 10 litres. What volume would the balloon have at 8 metres? 11. Your dive cylinder has 230 bars when filled at 15 °C. You leave it in the boot of the car and the temperature rises to 38 °C. What now is the pressure in the cylinder? 12. A one-ton anchor is on the seabed at 30 m. What volume of air is required in a floatation bag to make the anchor neutrally buoyant? 12 Marine Sciences Grade 12 Marine Sciences Definitions These definitions are examinable and integral to your understanding of the topic. atmospheric the force exerted against a surface by the weight of the air above and pressure surrounding the surface, due to gravity buoyancy the capacity of a solid item to float on a fluid by displacing a volume of that fluid that is equal in weight to that item mass the measurement of the quantity or amount of material an object contains, causing it to have weight in a gravitational field pressure an action of force applied against a surface and expressed in force per unit area weight the force with which an object is attracted towards the centre of Earth or celestial body by gravitation; weight is equal to the product of the mass and the gravitational constant weightlessness a sensation of floating experienced when no external objects or contact forces are exerting a push or pull upon one’s body General terminology These words are terms commonly used in sciences and should be part of your general vocabulary. euphoria a heightened feeling of well-being 61. Diving science 13