lecture # 17: fluids i (statics)
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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 - PowerPoint PPT PresentationTRANSCRIPT
Lecture # 17: Fluids I (Statics)
Gases1. Ideal gas Law
Pressure ~ force/unit areadue to particle impacts.
P = nRT/Vn = # moleculesR = gas constantT = temperatureV = volume
2. Boyle’s Law
P1V1/T1 = P2V2/T2
Lecture # 17: Fluids I (Statics)
3. Additivity
PT = ppX1 + ppX2 …ppXn
ppXn = partial pressure of X1 = n(Xn)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
1 cubic meter of airweighs 12 Newtons
8,400 m of air over our headswould exert 1 atmosphere.
We live here: 101 kPascals
1 cubic meter of waterweighs 9,800 Newtons
10.3 m of water over our headswould exert 1 atmosphere.
lung volumedecreases by half
in 10 m
snorkel
10 m
Lung works against 2 atmospheres. To descend, you must expel gas in lung.
What about brontosaurs?
Lungs could never have generated enough force to fill
lungs.
Buoyancy
swimbladder
Most bio-matter denser than water.
F = ma = mgF = Volumefish (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.
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.
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’
5. Forces at air-water interface
H20 H20
H20
H20
H20
H20
hydrogen bondssurround each molecule
no hydrogen bondsat surface
Work is required to create air-water interface.
Work = = 0.073 Joules/m2
= 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.
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.
work
Surface Tension is same as surface energy.
Filmof area2 x L
, defined earlier = surface energy
Energy to move bar = 2x 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
forc
e
Length, x
Can we walk on water?
leg contact
length, L
Upward force due to surface
tension = L
Downward force due to gravity
= L3 g
Ratio = Je = / L2 gMust be sufficiently small to walk on water
force/length of leg