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Semester 3 CB 306 HYDRAULIC Note Chapter 2 - Fluid Pressure

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- CHAPTER 2: FLUIDPRESSURE PREPARED BY : NOOR ASSIKIN BINTI ABD WAHAB
- Learn more about Fluids & TODAY’S GOAL PRESSURE
- PRESSURE Pressure is defined as a normal force exerted by a fluid per unit area. Units of pressure are N/m2 , which is called a pascal (Pa). Since the unit Pa is too small for pressures encountered in practice, kilopascal (1 kPa = 103 Pa) and megapascal (1 MPa = 106 Pa) are commonly used. Other units include bar, atm, kgf/cm2 , lbf/in2 =psi.
- Pressure Pressure is the force per unit area, where the force is perpendicular to the area. p= A m2 Nm-2 (Pa) N F This is the Absolute pressure, the pressure compared to a vacuum. pa= 105 Nm-2 1psi =6895Pa The pressure measured in your tyres is the gauge pressure, p-pa.
- Pressure Pressure in a fluid acts equally in all directions Pressure in a static liquid increases linearly with depth ∆p= increase in depth (m) pressure increase ρg ∆ h The pressure at a given depth in a continuous, static body of liquid is constant. p1 p2 p3 p1 = p2 = p3
- Pressure Pressure is the ratio of a force F to the area A over which it is applied: Pressure ; Force F P Area A = = A = 2 cm2 1.5 kg 2 -4 2 (1.5 kg)(9.8 m/s ) 2 x 10 m F P A = = P = 73,500 N/m2P = 73,500 N/m2
- The Unit of Pressure (Pascal): A pressure of one pascal (1 Pa) is defined as a force of one newton (1 N) applied to an area of one square meter (1 m2 ). 2 1 Pa = 1 N/mPascal: In the previous example the pressure was 73,500 N/m2 . This should be expressed as: P = 73,500 PaP = 73,500 Pa
- PRESSURE HEAD P(A) static pressure of system Column of water supported by this pressure Pressure Head hp = p ρg
- Fluid exerts forces in many directions. Try to submerse a rubber ball in water to see that an upward force acts on the ball. • Fluids exert pressure in all directions. F
- Pressure vs. Depth in Fluid Pressure = force/area ; ; mg P m V V Ah A ρ= = = Vg Ahg P A A ρ ρ = = h mg Area • Pressure at any point in a fluid is directly proportional to the density of the fluid and to the depth in the fluid. P = ρgh Fluid Pressure:
- Independence of Shape and Area. Water seeks its own level, indicating that fluid pressure is independent of area and shape of its container. • At any depth h below the surface of the water in any column, the pressure P is the same. The shape and area are not factors. • At any depth h below the surface of the water in any column, the pressure P is the same. The shape and area are not factors.
- PROPERTIES OF FLUID PRESSURE The forces exerted by a fluid on the walls of its container are always perpendicular. The fluid pressure is directly proportional to the depth of the fluid and to its density. At any particular depth, the fluid pressure is the same in all directions. Fluid pressure is independent of the shape or area of its container. The forces exerted by a fluid on the walls of its container are always perpendicular. The fluid pressure is directly proportional to the depth of the fluid and to its density. At any particular depth, the fluid pressure is the same in all directions. Fluid pressure is independent of the shape or area of its container.
- Example 2. A diver is located 20 m below the surface of a lake (ρ = 1000 kg/m3 ). What is the pressure due to the water? h ρ = 1000 kg/m3 ∆P = ρgh The difference in pressure from the top of the lake to the diver is: h = 20 m; g = 9.8 m/s2 3 2 (1000 kg/m )(9.8 m/s )(20 m)P∆ = ∆P = 196 kPa∆P = 196 kPa
- Atmospheric Pressure at m at m h Mercury P = 0 One way to measure atmospheric pressure is to fill a test tube with mercury, then invert it into a bowl of mercury. Density of Hg = 13,600 kg/m3 Patm = ρgh h = 0.760 m Patm = (13,600 kg/m3 )(9.8 m/s2 )(0.760 m) Patm = 101,300 PaPatm = 101,300 Pa
- Absolute Pressure Absolute Pressure:Absolute Pressure: The sum of the pressure due to a fluid and the pressure due to atmosphere. Gauge Pressure:Gauge Pressure: The difference between the absolute pressure and the pressure due to the atmosphere: Absolute Pressure = Gauge Pressure + 1 atmAbsolute Pressure = Gauge Pressure + 1 atm h ∆P = 196 kPa 1 atm = 101.3 kPa ∆P = 196 kPa 1 atm = 101.3 kPa Pabs = 196 kPa + 101.3 kPa Pabs = 297 kPaPabs = 297 kPa
- Pascal’s Law Pascal’s Law: An external pressure applied to an enclosed fluid is transmitted uniformly throughout the volume of the liquid. FoutFin AoutAin Pressure in = Pressure outPressure in = Pressure out in out in out F F A A =
- Example 3. The smaller and larger pistons of a hydraulic press have diameters of 4 cm and 12 cm. What input force is required to lift a 4000 N weight with the output piston? Fout Fin AouttAin ;in out out in in in out out F F F A F A A A = = 2 2 (4000 N)( )(2 cm) (6 cm) inF π π = 2 ; 2 D R Area Rπ= = F = 444 NF = 444 N Rin= 2 cm; R = 6 cm
- ABSOLUTE, GAGE, AND VACUUM PRESSURES Actual pressure at a give point is called the absolute pressure. Most pressure-measuring devices are calibrated to read zero in the atmosphere, and therefore indicate gage pressure, Pgage=Pabs - Patm. Pressure below atmospheric pressure are called vacuum pressure, Pvac=Patm - Pabs.
- Absolute, gage, and vacuum pressures
- PRESSURE AT A POINT Pressure at any point in a fluid is the same in all directions. Pressure has a magnitude, but not a specific direction, and thus it is a scalar quantity.
- SCUBA DIVING AND HYDROSTATIC PRESSURE
- PRESSURE MEASUREMENT Pressure is an important variable in fluid mechanics and many instruments have been devised for its measurement. Many devices are based on hydrostatics such as barometers and manometers, i.e., determine pressure through measurement of a column (or columns) of a liquid using the pressure variation with elevation equation for an incompressible fluid.
- PRESSURE Force exerted on a unit area : Measured in kPa Atmospheric pressure at sea level is 1 atm, 76.0 mm Hg, 101 kPa In outer space the pressure is essentially zero. The pressure in a vacuum is called absolute zero. All pressures referenced with respect to this zero pressure are termed absolute pressures.
- Many pressure- measuring devices measure not absolute pressure but only difference in pressure. This type of pressure reading is called gage pressure. Whenever atmospheric pressure is used as a reference, the possibility exists that the pressure thus measured can be either positive or negative. Negative gage pressure are also termed as vacuum pressures.
- MANOMETERS U Tube Enlarged Leg Two Fluid Inclined Tube Inverted U Tube
- THE MANOMETER 1 2 2 atm P P P P ghρ = = + An elevation change of ∆z in a fluid at rest corresponds to ∆P/ρg. A device based on this is called a manometer. A manometer consists of a U-tube containing one or more fluids such as mercury, water, alcohol, or oil. Heavy fluids such as mercury are used if large pressure differences are anticipated.
- MUTLIFLUID MANOMETER For multi-fluid systems Pressure change across a fluid column of height h is ∆P = ρgh. Pressure increases downward, and decreases upward. Two points at the same elevation in a continuous fluid are at the same pressure. Pressure can be determined by adding and subtracting ρgh terms. 2 1 1 2 2 3 3 1P gh gh gh Pρ ρ ρ+ + + =
- MEASURING PRESSURE DROPS Manometers are well-- suited to measure pressure drops across valves, pipes, heat exchangers, etc. Relation for pressure drop P1-P2 is obtained by starting at point 1 and adding or subtracting ρgh terms until we reach point 2. If fluid in pipe is a gas, ρ2>>ρ1 and P1-P2= ρgh
- THE BAROMETER C atm atm P gh P P gh ρ ρ + = = Atmospheric pressure is measured by a device called a barometer; thus, atmospheric pressure is often referred to as the barometric pressure. PC can be taken to be zero since there is only Hg vapor above point C, and it is very low relative to Patm. Change in atmospheric pressure due to elevation has many effects: Cooking, nose bleeds, engine performance, aircraft performance.
- Measuring pressure (1) Manometers h p1 p2=pa liquid density ρ x y z p1 = px px = py pz= p2 = pa (negligible pressure change in a gas) (since they are at the same height) py - pz = ρgh p1 - pa = ρgh So a manometer measures gauge pressure.
- Measuring Pressure (2) Barometers A barometer is used to measure the pressure of the atmosphere. The simplest type of barometer consists of a column of fluid. p1 = 0 vacuum h p2 = pa p2 - p1 = ρgh pa = ρgh examples water: h = pa/ρg =105 /(103 *9.8) ~10m mercury: h = pa/ρg =105 /(13.4*103 *9.8) ~800mm

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