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

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

3. 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 1 cubic meter of water weighs 9,800 Newtons 10.3 m of water over our heads would exert 1 atmosphere. lung volume decreases by half in 10 m snorkel 10 m Lung works against 2 atmospheres. To descend, you must expel gas in lung.

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 = Volume fish (  fish –  H20 ) 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.

10. 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 PXPX [x] For Biologically relevant gases: k(NH 3 ) >>> k(CO 2 ) > k(O 2 ) > k(N 2 ) 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; (NH 4 + ) is too toxic.

11. Example: ‘The bends’ At depths, gases that are soluble at depth come out of solution at sea level. N 2 bubbles form in arteries – can lead to strokes & heart attacks ‘= the bends’

12. 5. Forces at air-water interface H20 hydrogen bonds surround each molecule no hydrogen bonds at surface Work is required to create air-water interface. Work =  = 0.073 Joules/m 2 = surface energy Energy/Area Force/Length Cavitation (bubble formation as fluid ruptures)  Column held together by molecular forces. At 28 MPa (tensile strength) starts to cavitate.

13. 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.

14. work Surface Tension is same as surface energy. Film of area 2 x L , defined earlier = surface energy Energy to move bar =  2  x L) = surface energy X  area What is the force required? = work/distance = (2  L  x )/  x = 2  L Therefore  is force/length (surface tension) L x force Length, x

15. Can we walk on water? leg contact length, L Upward force due to surface tension =  L Downward force due to gravity =  L 3 g Ratio = Je =  /  L 2 g Must be sufficiently small to walk on water force/length of leg 