Chapter 13. liquids. gases. 1) Fluids exert pressure. a) because they're made up of matter with forces applied between (I.M.F.)
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1 \ Chapter 13 Fluids 1) Fluids exert pressure a) because they're made up of matter with forces applied between (I.M.F.) liquids gases b) they are made of matter in constant motion colliding with other matter applying forces (Kinetic Molecular Th) Blaise Pascal 1650's Under Pressure Pascal Pressure absolute vs. gauge P = F w /A = F w /πr 2 F w = Pπr 2 = 1.01x10 5 Pa(.031m 2 ) = 3,100 N on your head Atmospheric Pressure 10N/cm x10 5 Pa your head(some bigger!) is about.2 m across therefore, A = πr 2 = π(.1m) 2 =.031m N of atmospheric pressure on your head about the weight of a kilogram 2.2 pounds a penny (1.9 cm diameter) (2.54 x 10 4 m 2 = 2.54 cm 2 ) 25.4 N 5.8 lbs 1
2 What pressure is exerted when Mr. G does a pushup? push up my weight (810 now!!!) 10 cm 10 cm P = 900 N 0.02 m 2 = 45,000 Pa 45 kpa 0.1 m x 0.1 m = 0.01 m 2 2 hands 0.02 m 2 two hands 2 fingertip + thumb push ups r = 1.0 cm A = πr 2 = π(.01 m) 2 = m 2 42 finger areas 6 fingers (2/hand) m 2 P = 900 N = 500,000 Pa m2 500 kpa plus thumb that's almost 11 x the pressure as doing regular puch ups! Pascal's Principle Pressure a fluid exerts is directly proportionate to the depth of the fluid shape of the container doesn't matter! P h physics.ucla.edu 2
3 Pascal's Principle At a given height the pressure in a fluid is the same everywhere (along that height) Pressure is exerted throughout the fluid undiminished! See how the fluid in each tube is at the same height!...regardless of the shape! 3
4 r1 = 0.5 cm r2 = 12 cm P 1 = P 2 r 2 = 24 x r 1 F 2 = 24 2 F 1 or, 100 N x 24 2 = 57,600 N F2 = 57,600 N 4
5 A small force at F 1 can produce a large force at F 2 if A 1 is smaller than A 2. Pascal's Principle states that the pressure is the same throughout a confined fluid (at the same height). Therefore, P 1 = P 2 F 1 /A 1 = F 2 /A 2 half my weight! 500 N 2 cm F 2 =? 5 cm F 1 /A 1 = F 2 /A N F 2 π(1cm) 2 = π(2.5cm) 2 F 2 = 3125 N r 2 = 2.5 x r 1 F 2 = F 1 or, 500 N x = 3125 N Note the difference in the size of the two cylinders second class lever calipher master cylinder car braking system! 5
6 big cylinder small cylinder If we take a small diameter cylinder with a small surface area and connect it to a cylinder with a large surface area, we do not need to exert much force on the smaller cylinder to create a large force on the larger cylinder. Thus the jackman on the race car pushes down on a small cylinder that transmits the pressure to a larger cylinder and thus raises the car. 6
7 P = F/A P = mg/a P = mg/a P = ρvg/a P = ρvg/a P = ρahg/a P = ρvg/a F = mg P = ρhg ρ = m/v m = ρv V = Ah A's cancel P ~ h vad P = ρvg/a a = v 2 /2d P = ρvv 2 /2dA P = ρvv 2 /2V P = ½ρv 2 P = ρhg = ½ρv 2 V = Ad 7
8 ρ a = 1.29 kg/m 3 ρ w = 1000 kg/m 3 How high is the air above your head? h = P/ρg 1 g/cm 3 P = ρhg this is an over simplification: acts as if the density of air is the same as height increases it isn't! h =? h = 1.01 x 10 5 Pa 1.29 kg/m 3 (9.8 m/s 2 ) h = 7990 m 3/4 within 11 km 120 km when we notice effect of reentry mass = 5 x kg 1000 kg/m 3 = 1 g/cm kg ( 1000g 1m 3 1 m 3 1 kg 10 6 cm 3 ( ( ( = 1 g/cm 3 1m 1m 1m 100 cm 100 cm 100 cm 1 m cm 8
9 What pressure does the water exert at the bottom of your 10 m pool? P = ρhg P = 1000 kg/m 3 (10 m) 9.8 m/s 2 P = 98,000 Pa P = 98 kpa. What change in pressure do you experience if your jet takes off (at sea level) and climbs to 30,000 ft above the ground? 9
10 What change in pressure do you experience if you're in a jet 30,000 ft above the ground? 30,000 ft ( 1 m/3.28ft) = 9100 m P =ρhg = 1.29 kg/m 3 (9100 m)9.81 m/s 2 P = 115,000 Pa How high would the atmosphere be if it were homogenous and of unchanging density?...how many miles is that? 10
11 How high would the atmosphere be if it were homogenous and of unchanging density?...how many miles is that?... feet? P =ρhg h = P/ρg = 1.01 x 10 5 Pa/(1.29 kg/m 3 x 9.81 m/s 2 ) h = 7980 m 7980 m (1mile/1610 m) = 4.96 miles 7980 m (3.28 ft/m) = 26,200 ft Aerospaceweb.org computes properties such as temperature, pressure, and density up to about 280,000 ft (86,000 m, 53 miles), and atmospheric tables in some textbooks go up to 350,000 ft (106,800 m). Even the above illustration of the layers of the atmosphere reaches an altitude of 120 km, or 75 mi, which is nearly 400,000 ft (122,000 m).in addition, various aerial vehicles can fly at altitudes of 80,000 ft or more. On average, however, a good number to use for the true height of the atmosphere is about 400,000 ft (122,000 m), or 76 miles. It is at this altitude that vehicles such as the Space Shuttle are said to make "atmospheric interface" when they re enter the atmosphere prior to landing. Another "official" value you might consider is 50 miles, or 264,000 ft (80,540 m). Anyone flying higher than this altitude is officially considered an astronaut by NASA and the US Air Force. 11
12 imgurl= TRSDBJ9cGFd5hOl2zSSthU8ZlUw=&h=623 &w=504&sz=91&hl=en&start=37&itbs=1&tbnid=qp30rtbj89x8zm:&tbnh=136&tbnw=110 &prev=/images%3fq%3dfluid%2bpressure%2bin%2ball%2bdirections%26gbv%3d2% 26ndsp%3D20%26hl%3Den%26safe%3Dactive%26sa%3DN%26start%3D b notes.notebook old school braking system! note the smaller cylinders at the brakes pads (these would be called drum a cylinder shaped drum in placed over the pads and the pads push outward) overview 12
13 7.0 cm 1.2 cm Archimede's Principle buoyancy force fendt.de/ph14e/buoyforce.htm 13
14 Fluids in Motion Bernoulli's Principle: perpendicular to a fast moving stream of a fluid is a low pressure area, or, as the velocity of a fluid increases the pressure exerted by that fluid decreases note lower level of fluid in tube "B" indicating a lower pressure in that region higher pressure lower pressure slower moving fluid faster moving fluid 14
15 P 1 = P 2 P = F/A P = mg/a P = ρvg/a P = ρahg/a P = ρhg F = mg ρ = m/v m = ρv V = Ah A's cancel P = ρhg v 2 = 2ad...a = v 2 /2d P = ρhv 2 /2d h and d cancel P = ½ρv 2 P 1 = P 2 P 1 + ρhg 1 + ½ρv 2 1 = P 2 + ρhg 2 + ½ρv 2 2 P 1 + ρhg 1 + ½ρv 2 1 = P 2 + ρhg 2 + ½ρv P 1 = P 2 top and bottom both open to atmospheric pressure difference in air pressure from position 2 to 1 is almost nothing (outside pressure) v 2 = 0 compared to v 1 2 not moving thererfore ½ρv 2 2 = 0 1 ρhg 1 + ½ρv 2 1 = ρhg 2 ½ρv 2 1 = ρhg 2 ρhg 1 ½ρv 2 1 = ρg(h 2 h 1 ) v = 2gΔh hummm! 15
16 airfoil (wing) The shape of the wing causes the air going over the top of the wing to travel faster (because it has to travel farther) than the air going under the bottom of the wing. The faster air (going over the top) sets up a lower pressure a bove the wing. The higher pressure under the wing pushes upward in an attempt to equalize the difference in pressure causing a net upward force known as the lift force. What is the pressure difference if air passes over the top of the wing at 415 m/s and under the bottom at 350 m/s? h1 = h2 the difference in height of air because of the shape of the wing causes no real change in pressure, h 1 = h 2 16
17 Steamline (laminar) vs Turbulent laminar flow turb.html < turb.html> turbulent flow Forces within Liquids Surface Tension and Capillarity The surface of most liquids acts significantly different than its interior. The surface behaves almost like a stretched membrane with a tension applied to it This phenomenon is called "surface tension (γ gamma) This seeming tension acts parallel to the surface pulling molecules together by cohesive forces. γ = F/L F/L is the "force per unit of length" that acts across any line in a surface tending to pull it closed < Note the net downward pull of the molecules at the surface of the liquid compared to balanced pull of the molecules beneath the surface producing equilibrium. This net downward force at the top tends to compress the liquid. 17
18 This compressive force at the surface of a liquid tends to cause it to minimize its shape (surface area and volume) hence the spherical shape of water droplets (sphere is smallest possible shape) This compressive force at the surface of a liquid tends to cause it to To increase the surface area of a liquid work (and minimize force) must its be shape used to move molecules from the interior to the surface. This (surface work area increases and volume) the molecules PE and is called "surface energy" The greater hence the spherical surface area shape the greater the surface energy. of water droplets (sphere is smallest possible shape) astr.gsu.edu/hbase/surten.html < 18
19 imgurl= CapillaryAction.svg.png&imgrefurl= cm3emrozmp0batsh1ebzxpaoatk=&h=180&w=180&sz=2&hl=en&start=19&itbs=1 &tbnid=8iki_evdh2s3fm:&tbnh=101&tbnw=101&prev=/images%3fq%3dcapillary% 2Baction%26hl%3Den%26safe%3Dactive%26gbv%3D2%26tbs%3Disch:1 13.1b notes.notebook dyne = force acting on a gram, increases its velocity by one cm/s 2 erg = unit of energy and work equal to 10 7 joules. g(cm 2 /s 2 ) Capillary Action Caused by adhesion and cohesion. Adhesive forces are attractive forces that exist between particles of different substances (like glass and water). When you put a glass tube in water the glass pulls the water up the tube. Cohesion is also necessary because adjacent water molecules pull each other along with them as they rise in the tube. The water will rise until the weight column of water is equal to the strength of the adhesive forces. water mercury 19
20 13.1b notes.notebook lizards588.jpg +tension&source=lnms&tbm=isch&sa=x&sqi=2&pjf=1&ved=0ahukewip5nt1gr3tahwk5ymkhsksbnqq_auibigb&biw=1024&bih=638&safe=active&ssui=on#imgrc=bekb2ytlks5c8m: Expires= &Signature=bjJ021BFxcyKMybyfY imgurl= CapillaryAction.svg.png&imgrefurl= cm3emrozmp0batsh1ebzxpaoatk=&h=180&w=180&sz=2&hl=en&start=19&itbs=1 &tbnid=8iki_evdh2s3fm:&tbnh=101&tbnw=101&prev=/images%3fq%3dcapillary% 2Baction%26hl%3Den%26safe%3Dactive%26gbv%3D2%26tbs%3Disch:1 20
21 Evaporation and Condensation The particles in the liquid are in constant motion. If they have enough KE (from collisions or added TE) to overcome the surface tension at the surface and cohesive forces of other molecules they can pass through and be liberated from the liquid and become a gas (vapor). The Microscopic View of Evaporation Microscopic view of a liquid Microscopic view after evaporation. The Microscopic View of Condensation Microscopic view of a gas Microscopic view after condensation 21
22 imgurl= m.georgetown.edu/s02/lect30/lect30.htm&usg= TlOCX3 Zy179Iiw4QP5X nuklxi=&h=305 &w=675&sz=190&hl=en&start=27&itbs=1&tbnid=zz3jzrsdfp0ogm:&tbnh=62&tbnw=138 &prev=/images%3fq%3dcrystaline%2bsolids%26start%3d20%26hl%3den%26safe% 3Dactive%26sa%3DN%26gbv%3D2%26ndsp%3D20%26tbs%3Disch:1 13.1b notes.notebook 22
23 13.1b notes.notebook amorphous 23
24 24
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