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Opus in profectus

# Pressure

## Discussion

### definition

Pressure is the ratio of force applied per area covered…

 P = F A

The unit of pressure is the pascal

 ⎡⎣ Pa = N = kg m/s2 = kg ⎤⎦ m2 m2 m s2

The pascal is also a unit of stress and the topics of pressure and stress are connected.

• Bed of nails (not really pressure but shear strain, which has the same units)
• Finger bones are flat on the gripping side to increase surface area in contact and thus reduce compressional stresses

### gauge vs. absolute

atm kPa device, event, phenomena, process
200 20,000 pressurized breathing apparatus
150 15,000 milk homogenization
110 11,000 rupture compression strength of vertebral disks
7–14 700–1400 puffed cereal manufacture
9 900 espresso machine
4–7 400–700 bicycle tire
> 4 > 400 oxygen poisoning and nitrogen narcosis for dives > 30 m
2.7–4.1 275–415 champagne at serving temperature (10 ℃)
2.7 275 carbonated soft drinks
2.0–2.5 200–250 car tire
> 4 > 400 blast wave, 100% lethality
2.3–4.0 230–400 blast wave, 50% lethality
1.6–2.3 160–230 blast wave, 1% lethality
1.02 103 typical household pressure cooker
1 101.325 one standard atmosphere over environment
47 bottom of feet while standing
20 lungs, extreme exhalation
17 sustained pressure, eardrum ruptures
8 sustained pressure, eardrum senses pain
13–19 blood pressure, arterial, systolic (during a heartbeat)
8–12 blood pressure, arterial, diastolic (between heartbeats)
7–14 aircraft shock wave
11 eye, severe glaucoma
1.6–3.0 eye, normal
4.0 blood pressure, capillary, arterial end
1.3 blood pressure, capillary, venous end
3 bladder, micturition reflex ("gotta go urge")
1.3–2.6 gastrointestinal tract
0.6–1.6 cerebrospinal fluid
0.4–0.9 blood pressure, venous
0.6–0.8 interstitial fluid (osmotic pressure)
2 acoustic pressure, eardrum ruptures (160 dB)
0.02 acoustic pressure, eardrum senses pain (120 dB)
2 × 10−8 acoustic pressure, threshold of hearing (0 dB)
0 0 environmental pressure
−1.3 lungs, resting
−1.5 lungs, drinking through a 15 cm straw
−25 lungs, extreme inhalation
−1

−101.325

one standard atmosphere below environment
a perfect vacuum in a standard atmosphere environment
Selected gauge pressures (black–positive, red–negative)
atm Pa device, event, location, phenomena, process
3.4 × 1011   center of the sun
????   center of Jupiter
3.6 × 106   center of earth
1070   Marianas Trench, Pacific Ocean (-10,924 m)
160   Lake Baikal, Asia (-1620 m)
140   Lake Tanganyika, Africa (-1470 m)
40   Lake Superior, North America (-406 m)
????   record dive by a human
90   surface of Venus
26   helium freezes at about 1 K
> 5   oxygen poisoning and nitrogen narcosis for dives > 30 m
108,380 record high, altitude adjusted (Siberia, 1968)
1 101,325 sea level, standard atmosphere
90,000 atmospheric pressure at 1,000 m, interior of concorde
87,000 record low, altitude adjusted (Typhoon Tip, 1979)
80,000 atmospheric pressure at 2000 m, interior of typical jet aircraft
52,000 La Paz, Bolivia (5200 m)
~ ½ 51,000 maximum altitude of permanent human habitation (5500 m)
~ 40,000 ~ vertical limit of human survivability (~7000 m)
~ ⅓ 31,000 Mount Everest (8848 m)
~ ⅕ 19,000 altitude of typical commercial jet aircraft (12,000 m)
0.062 6,3000 Armstrong limit, exposed body liquids boil (19,000 m)
> 0.033  > 3,300 > "low vacuum"
< 0.033  < 3,300 < "medium vacuum"
0.025 2,200 altitude of reconnaissance plane (SR-71, 26,000 m)
0.011 1,100 altitude of highest skydive (1960, 31,330 m)
0.006 600 altitude of highest manned balloon flight (1961, 34,668 m)
0.007   surface of Mars
~ 10−5   surface of Pluto, maximum (late 1990s)
< 10−6    "high vacuum"
< 10−9    "very high vacuum"
~ 10−13   surface of the moon, daytime
< 10−12    "ultra high vacuum"
~ 10−15   surface of the moon, nighttime
< 10−15    "extreme ultrahigh vacuum"
~ 10−17   I am told that below this value all vacuum equipment leaks.
Selected absolute pressures

### the atmosphere

Standard Atmospheric Tables

Chemical composition of the atmosphere Source: US Standard Atmosphere, 1976
gas formula molecular weight
(g/mol)
fraction
nitrogen N2 028.0134000 0.78084
oxygen O2 031.9988000 0.209476
argon Ar 039.9480000 0.00934
carbon dioxide CO2 044.0099500 0.000314
neon Ne 020.1830000 0.00001818
helium He 004.0026000 0.00000524
methane CH4 016.0430300 0.000002
krypton Kr 083.8000000 0.00000114
hydrogen H2 002.0159400 0.0000005
xenon Xe 131.3000000 0.000000087
overall 028.9644253 0.999997147

### fluids

Pressure in a uniform fluid.

• The gauge pressure in a uniform fluid at a particular depth is directly proportional to…
• the density of the fluid ρ,
• the acceleration due to gravity g, and
• the depth h.

The absolute pressure in a uniform fluid at a particular depth is given by…

P = P0 + ρgh

The absolute pressure in a uniform or nonuniform fluid at a particular depth h measured along the vertical or z-axis is given by…

 h P = P0 + ⌠⌡ ρ(z)g(z) dz 0

### devices

barometer

barometer, manometer, Hare's apparatus

The atmosphere as a unit.

 1 atm = 101,325 Pa (by definition) = 760 torr (by definition) = 763.43… mm Hg (approximately) = 1.03… kg/cm2 (approximately) = 10.3…tonnes/m2 (approximately) = 14.7… psi (approximately) = 1.06… tons/ft2 (approximately)

### physiology

blood pressure

ear pressure in the middle ear: eardrum at end of outer ear connected to smaller oval window at beginning of inner ear. 15-30 times greater pressure. combination of difference in membrane diameters and lever effects of middle ear bones.

eye pressure and glaucoma

Circulatory pressures (mm Hg, a.k.a. torr) Source: Physics of the Body
location systolic diastolic mean
aorta 120 80 100
left ventricle 120 8
left atrium 7 10 4
pulmonay artery 15 7 12
right ventricle 15 2
right atrium 4 4 0
pulmonary capillary wedge 7 10 4

### pascal's principle

• Pascal's principle: Pressure changes applied to the surface of an enclosed fluid are transmitted evenly throughout the fluid.
• Water seeks its own level. That's one of the realities of life.
• hydraulics
• Queckenstedt's maneuver - barbaric medical test from the early 20th Century to test for spinal stenosis