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Lecture # 17: Fluids I (Statics)

2. Boyle’s Law P 1 V 1 /T1 = P 2 V 2 /T 2. Lecture # 17: Fluids I (Statics). 1. Ideal gas Law Pressure ~ force/unit area due to particle impacts. P = nRT/V n = # molecules R = gas constant T = temperature V = volume. Gases. Example 1. Bar Headed Goose

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Lecture # 17: Fluids I (Statics)

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  1. 2. Boyle’s Law P1V1/T1 = P2V2/T2 Lecture # 17: Fluids I (Statics) 1. Ideal gas Law Pressure ~ force/unit area due to particle impacts. P = nRT/V n = # molecules R = gas constant T = temperature V = volume Gases

  2. Example 1. Bar Headed Goose Yearly migration over Himalayas. Humans can barely breath at 8840m. Bar-headed goose has specialized blood chemsitry. Mt. Everest Lecture # 17: Fluids I (Statics) 3. Additivity PT = ppX1 + ppX2 …ppXn ppXn = partial pressure of X1 = n(Xn)RT/V

  3. snorkel 10 m Lung works against 2 atmospheres. To descend, you must expel gas in lung. 1 cubic meter of air weighs 12 Newtons 8,400 m of air over our heads would exert 1 atmosphere. We live here: 101 kPascals 10.3 m of water over our heads would exert 1 atmosphere. lung volume decreases by half in 10 m 1 cubic meter of water weighs 9,800 Newtons

  4. What about brontosaurs? Lungs could never have generated enough force to fill lungs.

  5. Buoyancy swim bladder Most bio-matter denser than water. F = ma = mg F = Volumefish (rfish – rH20) g Swim bladder allows fish to regulate mean density via change in volume. Evolved from invagination of esophagus. Evolved into lungs. Must be active: start to sink – bladder gets denser – sinks more. Rete mirabile – secretes gas in/out of bladder. Submarine and cuttlefish bladders are rigid.

  6. 4. Solubility Henry’s Law Px = K [x] P = pressure of gas in contact with fluid k = solubility of gas in liquid [x] = concentration of gas in fluid PX [x] For Biologically relevant gases: k(NH3) >>> k(CO2) > k(O2) > k(N2) Example: Nitrogenous waste: Protein metabolism generates nitrogenous waste: How do we get rid of it? Fish: ammonia – works because it is so soluble Mammals: urea; (NH4+) is too toxic.

  7. Example: ‘The bends’ At depths, gases that are soluble at depth come out of solution at sea level. N2 bubbles form in arteries – can lead to strokes & heart attacks ‘= the bends’

  8. w Cavitation (bubble formation as fluid ruptures) Column held together by molecular forces. At 28 MPa (tensile strength) starts to cavitate. 5. Forces at air-water interface Work is required to create air-water interface. Work = g = 0.073 Joules/m2 = surface energy Energy/Area Force/Length no hydrogen bonds at surface H20 H20 hydrogen bonds surround each molecule H20 H20 H20 H20

  9. Example: tree circulation Water must get from roots to leaves. ‘pump’ is transpiration at leaf. Works because of high failure tension of water. Water lost at leaf, creating negative pressure to pull water up through column. Channels in xylem help recover from cavitation events.

  10. Surface Tension is same as surface energy. G, defined earlier = surface energy Energy to move bar = g (2 Dx L) = surface energy X D area What is the force required? = work/distance = (2 g LDx )/ Dx = 2 g L Therefore g is force/length (surface tension) Film of area 2 x L x L force work Length, x

  11. force/length of leg ga Upward force due to surface tension = g L Downward force due to gravity = r L3 g Ratio = Je = g/r L2 g Must be sufficiently small to walk on water Can we walk on water? leg contact length, L

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