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Lecture 11

LIFESCI 3J03 Lecture 11: Fluid Mechanics

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Life Sciences
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Life Sci 3J03 - Lecture 11 – Fluid Mechanics Buoyant Force: the resultant of all vertical forces exerted on a body by the fluid that it is immersed in - Depending on how density is distributed within the body, the centre of buoyancy can have a different location than the centre of gravity - Since the gravitational and buoyant forces are the only forces acting on a floating object, the object will orient itself such that the two forces have equal and opposite directions Archimedes Principle: the magnitude of the buoyant force is equal to the weight of the fluid displaced Density = mass/volume - Units: kg/m or kg/L - The density of fresh water is 1kg per litre or 1000kg per cubic meter - If an object has a density that is greater than the density of water, it will not float o Can only displace enough water that equals its own volume and since the weight of the water will not be equal to its own weight, the gravitational force will be greater than the buoyant force Example - How much mass can be added to a canoe that has a mass of 50kg and a volume of 400L before it will sink in fresh water o Canoe has a density of 50/400 = 0.125kg/liter  Much less than water and will float  Will only displace 50L of water to achieve a buoyant force equal to its weight o As mass is added to the canoe, the gravitational force pushes it lower in the water until the buoyant force is equal to the gravitational force o Mass can be added to the canoe until it displaces its entire 400L of water which means that 350kg of mass can be added to the 50kg mass of the canoe to equal 400kg of displaced water Specific Gravity and Human Body Composition - Specific gravity: the weight of an object in the air divided by the buoyant force (in fresh water) o Another term for density - One way to measure the buoyant force is to take the difference between the weight of the object in the air and the weight of the submerged object - Hydrostatic weighing is a common method to determine the density or specific gravity of the human body - Another method is to use an air chamber that measures the volume of the body which can then be converted to density by dividing the volume into the whole body mass - Human body is composed of various tissues of different densities such as bone, fat and lean tissues like muscle and organs - Fat is less dense than water but muscle (lean tissue) and bones have greater densities than water - Person’s ability to float has nothing to do with their swimming ability but is determined by their overall density - Infants have a large percentage of fat and float quite easily - As we age, percentage of fat decreases and muscle increases which causes an increase in density - Older adults have less muscle and their bones have lost density as well which increases their ability to float - Human body composition is concerned with quantifying the amount of body fat as a percentage of the total body mass o Done using a two-component model of the human body assuming a density value of fat and another density value for lean tissue - Common assumption for the density of fat is 0.89kg/l and 1.10kg/l for the lean tissues - If the whole body density has been determined from hydrostatic weighing or a volume measurement, the % body fat can be estimated using: - While this estimate has been considered the most valid measurement of body composition for many years, it, it must be recognized that it depends on the validity of the assumed tissue densities - Individuals with a higher ratio of bone to muscle mass should have a higher value than those with a low bone to muscle mass ratio o Yet the above method assumes a value of 1.10kg/l for both - Newer methods involving medical imaging like Dual X-ray Absorptiometry (DXA) allow the measurement of bone, fat and lean tissue more directly but it is n
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