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FLUID PRESSURE

FLUID PRESSURE. PRESSURE PASCAL’s LAW HYDRAULIC JACKS VARIATION WITH DEPTH ATMOSPHERIC PRESSURE PRESSURE MEASUREMENT COMPRESSIBILITY EFFECTS. FLUID PRESSURE. Solids resist compressive forces by developing compressive stresses and strains with in

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FLUID PRESSURE

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  1. FLUID PRESSURE PRESSURE PASCAL’s LAW HYDRAULIC JACKS VARIATION WITH DEPTH ATMOSPHERIC PRESSURE PRESSURE MEASUREMENT COMPRESSIBILITY EFFECTS KK's FLM 221 - WK3: PRESSURE

  2. FLUID PRESSURE • Solids resist compressive forces by developing compressive stresses and strains with in • Fluids develop a Pressure within them to resist the compressive loads • Pressure is ratio of NORMAL FORCE to AREA where the force is acting: • (3.1) Qu.2.1: What are the dimensions of Pressure? • Pressure is measured in Newtons per square metre (N/m2). This unit is called a Pascal (Pa). Bigger units are necessary to measure the normal pressures we encounter in practice: 1 kPa = 103 N/m2; 1MPa = 106 N/m2 = 1 N/mm2; 1 bar = 105 N/m2 =100 kPa; 1 atm = 1.01325 bar = 101.325 kN/m2 KK's FLM 221 - WK3: PRESSURE

  3. Atmospheric pressure Patm Force ‘F’ (N) Additional weight causing GAUGE pressure, Pg Area ‘A’ (m2) Total pressure = Absolute pressure = Pabs Pabs = Pg+Patm Pressure P = F/A N/m2 FIGURE 3.1: Pressure; absolute and gauge KK's FLM 221 - WK3: PRESSURE

  4. ABSOLUTE & GAUGE PRESSURE • The atmosphere exerts a pressure, Patmon all surfaces with in it including those on earth • All other pressures are additional to Patmand are called GAUGE pressures, Pg • The total pressure is called the absolute pressure, Pabs. (3.2) • If the absolute pressure is below Patm, Pg is negative, and then we refer to vacuum pressure, Pvac. (3.3) Pg Pabs Pvac Patm Pabs FIGURE 3.2: Illustrating gauge and Vacuum pressure KK's FLM 221 - WK3: PRESSURE

  5. PASCAL’S LAW • Pascal’s law relates the pressure in a fluid to the direction in which it acts, and also tells us about transmission of any extra pressure from outside the fluid “Pressure at a point in a static fluid is the same in all directions and acts perpendicular to any surface in the fluid; Any additional external pressure is transmitted equally in all directions” KK's FLM 221 - WK3: PRESSURE

  6. Fluid continuum P3L P1Lsinθ Fluid element of unit width θ Horizontal equilibrium of element – means: P1Lsinθ = P3Lsinθ; i.e P1 = P3 P2Lcosθ Vertical equilibrium of element – means: P2Lcosθ = P3Lcosθ; i.e. P2=P3 FIGURE 3.3: PASCAL’S LAW: P1 = P2 = P3 for all θ KK's FLM 221 - WK3: PRESSURE

  7. PASCAL’S LAW: application 1 – Hydraulic Jacks • A small force F1 can be used to act on a small piston area A1 to generate a large pressure P1 in the fluid. If the fluid is assumed incompressible, this pressure is transmitted equally in all directions – and can therefore be made to act on a piston of larger area A2 to overcome a very big force F2. (3.4) • Mechanical advantage MA = F2/F1 = A2/A1 • Velocity ratio VR = Effort dist: Load dist = A2/A1 (3.5) F1 F2 A1 A2 FIGURE 3.4: Hydraulic jack KK's FLM 221 - WK3: PRESSURE

  8. PRESSURE VARIATION WITH DEPTH • Pressure in a static fluid will vary with position depending on the weight of the fluid above the point • For constant density fluids, gauge pressure is given as: (3.6) Where ‘ρ’ is the fluid density, ‘g’ is the acceleration due to gravity and ‘h’ is the depth of the fluid. KK's FLM 221 - WK3: PRESSURE

  9. Depth h1 Depth h2 Pg1 = ρgh1 Lower pressure on this plane at depth h1 Higher pressure on this plane at depth h2 Pg2 = ρgh2 FIGURE 3.5: GAUGE PRESSURE VARIATION IN A FLUID KK's FLM 221 - WK3: PRESSURE

  10. THE ATMOSPHERE • Gaseous envelope surrounding the planet and shielding it from harmful solar radiation and charged particles • Made up of different layers, each of varying composition, density and other thermodynamic properties • Exerts Pressure on all surfaces within it • Atmospheric pressure varies with height above the ground; Air tends to behave as an ideal gas obeying the equation: • Some processes affecting weather in the troposphere are adiabatic – though not isentropic – causing air to behave in line with the polytropic equation: • The implication of all this is that atmospheric pressure, temperature and density vary with height above the earth’s surface. Pressure is then NOT a simple function of depth as for incompressible fluids. KK's FLM 221 - WK3: PRESSURE

  11. 1- TROPOSPHERE; 6 -20km from earth surface (Weather layer) 2- STRATOSPHERE; up to 50 km (contains ozone layer; ‘T’ increases then drops) 3- MESOSPHERE; up to 85 km (contains charged particles from the sun: ‘T’ increases 4- THERMOSPHERE; up to 690 km (‘T’ increases even up to 1500oC: Space station in this region) 5- EXOSPHERE; up to 10,000 km and beyond (Exiting the earth’s atmosphere into space 5 4 3 2 EARTH 1 FIGURE 3.6: EARTH’s ATMOSPHERE KK's FLM 221 - WK3: PRESSURE

  12. PRESSURE MEASUREMENTS • THE BAROMETER – measures atmospheric pressure; uses mercury in an inverted tube. QUESTION:Why Mercury? Work out what barometer height would be required if we used Ethanol (alcohol) in Addis-Ababa, Ethiopia where the atmospheric pressure is 0.65 bar. Take ρeth = 783 kg/m3. • THE MANOMETER – uses the principle that the pressure in a continuous fluid is the same for all positions at the same horizontal level. It is used to measure small to moderate pressures and employs relatively heavy liquids for higher pressures. It employs U tubes • HOMEWORK / ASSIGNMENT: Find out about other more modern pressure sensing and measuring instruments: In particular, look for digital units, understand how they work and their advantages over older units. Make a survey in Cape Town about their pricing. Make sure you do this assignment – as one of the tests / exams will include work on it! KK's FLM 221 - WK3: PRESSURE

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