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