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This 36 page Class Notes was uploaded by Jada Daniel on Wednesday September 23, 2015. The Class Notes belongs to MEM220 at Drexel University taught by YoungCho in Fall. Since its upload, it has received 16 views. For similar materials see /class/212396/mem220-drexel-university in Mechanical Engineering at Drexel University.
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Date Created: 09/23/15
Chapter 2 Fluid Statics Objective to understand how pressure varies as we go up or down Why does pressure increase as we go down in water 53mm sinus i 0 mm Aircraft Submarine Blood Pressure Pascal s Law Free surface pressure 10 Figure 23 p 42 Notation for pressure variation in a fluid at rest with a free surface Objective to derive pressure variation with respect to height or depth 75 p may I I fX I I 8 5 3 567 39 I I t 5X52 gt 0 lt39 I 0 2 x h E V s s I I 5X y5x by b E 5y 39 I X Xdx 7 7 5x5 fxdx fx Fig 22 p40 Figure 24 p 43 Fluid equilibrium in a container ofarbitrary shape Liquid surface Specific weighty Hypnosrnics 39 How do we lift a car at Pep Boys What is the principle of hydraulic jack F1pA1 F2pA2 Figure 25 p 45 Transmission of fluid pressure 11320 Tun Fleur J acke 24 Standard Atmosphere What is the pressure outside an aircraft cruising at normal altitude Figure Lb p 47 Variation of temperature with altitude in the US standard atmosphere 50 40 E 30 3 U 3 lt7 20 Stratosphere 10 O Troposphere O 1OO 80 473 km p 01 kPa 445 0C 322 km 17 09 kPa 201 km p 55 kPa 565 0C 110 km 1 226 kPa p 1013 kPa abs 15 C What is the benefit of flying at that high altitude 60 40 20 0 Temperature C Less pressure 9 Less air 9 Less 9 Less fuel consumption 9 more What about an orbiting space station What is the benefit of flying at the orbit No pressure 9 No air 9 No Figure 26 p 47 Variation of temperature with altitude in the US standard atmosphere 50 473 km 2 01 kPa 9 40 LQ ltr it 322 km 7 09 kPa E 30 g 390 E 7 20 g 201 km p 55 kPa Stratosphere L b 10 39 110 km 7 226 kPa 7 1013 kPa abs Troposphere 15 0C 0 100 80 60 40 20 0 Temperature C 9 No fuel consumption 9 25 Measurements of Pressure Gage Pressure and Absolute Pressure 1 atm 101000 Pa 147 psia 760 mmHg 760 Torr 2992 in Hg What is a vacuum pressure A Pressure below zero gage pressure Pressure Gage pressure 1 Local atmospheric pressure reference 2 Gage pressure 2 Absolute pressure 7 8 suction or vacuum Absolute pressure Absolute zero reference Figure 27 p 48 Graphical representation of gage and absolute pressure How do we measure the atmospheric pressure mm Who did it for the first time Torricei 1644 Invert PB Patm What is PA Objective to determine the height h Construct a force balance Figure 28 p 49 Mercury barometer 26 Manometry Objective to determine gas pressure P1P2 P2P3 P3P atm Open Figure 210 p 51 Simple Utube manometer Example 24 Objective to determine the pressure reading In psi Given 6 of Hg 136 Density of water 194 slugft3 Gravity constant 32174 fts2 h1 36 in h2 6 in h3 9 in P1P2 P2P atm Figure E24 p 52 Pressure gage Example 25 Flow meter using an orifice nozzle How does it work Flow rate N pressure difference Flow rate N PA PB gtp nwk Flow nozzle Figure E25 p 53 263 Inclinedtube manometer Why do we use it What is the benefit Figure h p 54 Inclined tube manometer Conventional Pressure gage What is the principle How does it work Figure 213 p 55 a Liquidfilled Bourdon pressure gages for various pressure ranges b Internal elements of Bourdon gages The quotC shaped Bourdon tube is shown on the left and the quotcoiled spring Bourdon tube for high pressures of 1000 psi and above is shown on the right Photographs courtesy of Weiss Instruments Inc Digital Pressure gage What is the principle How does it work Bourdon Ctube Core Mounting Pressure line A ll Input Figure 214 p 56 Pressure transducer which combines a linear variable differential transformer LVDT with a Bourdon gage From Ref 4 used by permission StrainGage Pressure Transducer What is the principle How does it work Diaphragm stop Armature Diaphragm Link pin Beam strain gages deposited on beam Figure 215b p 57 b Schematic diagram of the P23XL transducer with the dome removed Deflection of the diaphragm clue to pressure is measured with a silicon beam on which strain gages and an associated bridge circuit have been deposited How to measure blood pressure Listen heart beat using a Stethescope cu ff pressure equot auger so no sound Korotkoff sounds no sound 28 Hydrostatic Force on a plane surface What is the pressure at the bottom if h 3 m What is the total force acting on the bottom Bottom area 4 m2 Free surface Free surface a Pressure on tank bottom b Pressure on tank ends Figure Z1b p 58 a Pressure distribution and resultant hydrostatic force on the bottom of an open tank b Pressure distribution on the ends of an open tank What happens if the bottom is a curved surface pair 2 40 psi Task to estimate the force acting on the bottom 2 Liter Coke bottle How lt 43 in diameter Hemisphere Water it ti i it A i WarmestI is it F ritttftmE jwatertight map a Figure P294 p 89 28 Hydrostatic Force on a plane surface Inclined surface Free surface n V a u Locauon of I resulmnl farce Center nl pressure cm Figure a p 58 Notation for hydrostatic force on an inclined plane surface of arbitrary shape 28 Hydrostatic Force on a plane surface Inclined surface Air v Objective to estimate the force acting on T a square window 4 m x 4 m Water 3 m Air 28 Hydrostatic Force on a plane surface Inclined surface Air Water 3 m Air Objective to estimate the force acting on a circular window with a diameter of4 m 28 Moment created by Hydrostatic Force on a square window 4 m x 4 m Air Hinge What is zero at hinge Objective to estimate the force F1 required to keep the window closed 28 Moment created by Hydrostatic Force on a square window 4 m x 4 m HW 261 Given Width 4 ft gate weight 800 Ibf Objective to determine tension in cable Figure P261 p 85 211 Buoyancy Why does a light object float Why does a heavy object sink Centroid of displaced volume d Centroid Consider a force balance 0 Fma 39 What kinds of forces do you see Figure 224 p 69 Buoyant force on submerged and floating bodies 211 Buoyancy Derivation of buoyancy force Example 210 Buoyancy Given Buoy diameter 15 m weight 85 kN Objective to determIne the ten5on In cable Figure E240 p 71 9 7 v Consider a force balance Pressure envelope F ma Seawater What kinds of forces do you see Cable a Volume of sphere dz HW 2105 Buoyancy Consider a force balance F ma What kinds of forces do you see Figure P2105 p 90 E En PLASTIC HYDROMETERS w aw m m139ruum n wmuvmu m mum m moan venuequot arm nvwam my sum mm mm mumquot smmuw 9 1 Jimmy among Hog mm m nigh on can mumls 1 0023 Fluid surface HW 2102 Buoyancy Inverted test tube partially filled with air floats in water When we squeeze the plastic bottle The test tube sinks 9 Why 5 V All quotThe test tube sinksquot means 9Bu0yancy force decreases or increases TeSt tUbe Mathematically Aueeze Can we explain the situation g Water Plastic bottle Figure P2102 p 90 ARCHIMEDES theFirstStreaker 2 V Serendipity VArchimzdz discovers luzw ta mauurz the volume of an irregqu abject mch as a crown 212 Linear Motion Carrying fuel in a container truck Example 211 Stability problem Is the truck accelerating or decelerating Direction of a truck gt v Vent gt i1 03ft Transducer Figure 211 p 74 212 Linear Motion Carrying fuel in a container truck Derivation of Eq228 for an inclined surface Accelerometer a lent P Flylkl I I dP y I 05 ft l 2 1 Transducer l7 075 ft n o75 ft Hl Water to tame wind atop new skyscraper It is Believed to be the largest in the world GIIIIIIIIE Will I Holds 300000 gallons of water Maiionaarilag Liberty Fmpany Trus HDEEBTWESTI Inqmrnr stalimu A 300000gallon doublechambered tank of water is going in near the top of the Comcast Center a creative solution by engineers to keep Philadelphia s tallest building from swaying too much in the wind 2122 Rigid Body Rotation Objective to find a mathematical equation of the curved surface Derivation P Prz Along the curved surface what is constant s P constant 2 dP O Axis of rotation d d ppar 20er p lt 1er dr dz L w dp prwzdr pgdz Figure 230 p 75 Rigidbody rotation of a liquid in a tank