\ Chapter 13 Fluids 1) Fluids exert pressure a) because they're made up of matter and therefore forces are applied to them 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 Apr 18 10:26 AM 1
Pressure 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 is @ 10N/cm 2 your head(some bigger!) is about.2 m across therefore, A = πr 2 = π(.1m) 2 =.031m 2 about the weight of a kilogram 2.2 pounds a penny is about 2.3 cm 2 Apr 10 7:42 AM 2
What pressure is exerted when Mr. G does a pushup? push up my weight 10 cm 10 cm P = 900 N 2 = 45,000 Pa 0.02 m 45 kpa 0.1 m x 0.1 m = 0.01 m 2 2 hands 0.02 m 2 two hands 2 fingertip push ups r = 1.0 cm A = πr 2 = π(.01 m) 2 = 0.0003 m 2 4 fingers (2/hand) 0.0012 m 2 42 finger areas P = 900 N 0.0012 m 2 = 750,000 Pa 750 kpa that's almost 17 x the pressure as doing regular puch ups! Apr 18 12:10 PM 3
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 Apr 18 10:48 AM 4
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! Apr 18 12:10 PM 5
See how the fluid in each tube is at the same height!...regardless of the shape! Mar 27 1:48 PM 6
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r1 = 0.5 cm r2 = 12 cm P1 = P2 F2 = 57,600 N Apr 18 12:49 PM 8
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 F 1 /A 1 = F 2 /A 2 F 2 =? 5 cm 500 N F 2 π(1cm) 2 = π(2.5cm) 2 2 cm F 2 = 3125 N Mar 24 10:52 AM 9
Note the difference in the size of the two cylinders second class lever master cylinder calipher car braking system! Mar 24 10:52 AM 10
big cylinder small cylinder Apr 10 11:11 AM 11
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. http://mw.concord.org/modeler1.3/mirror/fluid/pascal.html Apr 10 11:13 AM 12
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P = F/A P = mg/a P = mg/a P = ρvg/a P = ρvg/a P = ρahg/a F = mg P = ρhg ρ = m/v m = ρv V = Ah A's cancel P ~ h Apr 19 10:41 AM 14
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 10 18 kg Apr 17 11:08 AM 15
1000 kg/m 3 = 1 g/cm 3 1000 kg/m 3 (1000g/1kg)(1m 3 /10 6 cm 3 ) = 1 g/cm 3 1m 1m 1m 100 cm 100 cm 100 cm 1 m 3 10 6 cm Apr 3 10:19 AM 16
What pressure does the water exert at the bottom of your 10 ma pool? P = ρhg P = 1000 kg/m 3 (10 m) 9.8 m/s 2 P = 98,000 Pa P = 98 kpa Apr 19 10:44 AM 17
What change in pressure do you experience if you're jet takes off (at sea level) and climbs to 30,000 ft above the ground? Apr 17 8:33 AM 18
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 Apr 19 1:45 PM 19
How high would the atmosphere be if it were homogenous and of unchanging density?...how many miles is that? Apr 17 8:33 AM 20
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 Apr 17 8:27 AM 21
Aerospaceweb.org computes properties such as temperature, pressure, and density up to about 280,000 ft (86,000 m), 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. Apr 17 8:36 AM 22
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old school braking system! overview http://images.google.com/imgres? imgurl=http://boomeria.org/physicslectures/pascal/hydrauliclift.jpg&imgrefurl=http://boomeria.org/physicslectures/pascal/pascal.html&usg= 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%3D20 Mar 24 10:39 AM 24
Archimede's Principle buoyancy force http://www.walter fendt.de/ph14e/buoyforce.htm Mar 24 10:49 AM 25
Fluids in Motion Bernoulli's Principle: perpendicular to a fast moving steam 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 Apr 13 9:32 AM 26
lower pressure higher pressure slower moving fluid faster moving fluid Apr 13 9:42 AM 27
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 Apr 13 9:43 AM 28
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. Apr 13 9:36 AM 29
Steamline (laminar) vs Turbulent laminar flow www.engineering.uiowa.edu/.../lim turb.html <http://www.engineering.uiowa.edu/~cfd/gallery/lim turb.html> turbulent flow Apr 13 9:47 AM 30
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 )" 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 www.chem1.com/acad/sci/aboutwater.html <http://www.chem1.com/acad/sci/aboutwater.html> 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. Apr 13 9:48 AM 31
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) To increase the surface area of a liquid work (and force) must be used to move molecules from the interior to the surface. This work increases the molecules PE and is called "surface energy" The greater the surface area the greater the surface energy. Apr 13 10:47 AM 32
www.chem1.com/acad/sci/aboutwater.html <http://www.chem1.com/acad/sci/aboutwater.html> Apr 13 10:48 AM 33
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 http://www.lhup.edu/~dsimanek/museum/captube.gif http://images.google.com/imgres? imgurl=http://img.search.com/thumb/8/85/capillaryaction.svg/180px CapillaryAction.svg.png&imgrefurl=http://www.search.com/reference/Surface_tension&usg= 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 Apr 13 10:50 AM 34
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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). Apr 14 10:54 AM 37
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 http://www.chem.purdue.edu/gchelp/liquids/condevap.html Apr 14 10:55 AM 38
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