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Date : (1C) 6 Feb (1D) 4 Feb (1E) 4 Feb (1F) 5 Feb Can you identify a common relation between Figure (a) & (b). The common properties between them is their ability to flow and can't take a fixed shape, but take the shape of the container Materials that exhibit these properties are called Fluids. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids. Difference between liquids and gases Gases can be compressed, but liquids are incompressible. Fluid Mechanics (Hydrostatics) Fluid At rest Fluid Dynamics (Hydrodynamics) Fluid in motion Students will be able to use pressure difference between two points of a fluid and Newton's laws to analyze behavior of that fluid. Concepts A. Fluids B. Pressure C. Manometer D. Pressure gauge E. Units of pressure F. Effect of atmospheric pressure on boiling point of water G. Change in atmospheric pressure with altitude H. Pressure difference and force I. Archimedes Principle Skills A. Determine pressure change as function of height in columns of fluid B. Explain how a mercury barometer measures atmospheric pressure C. Determine atmospheric pressure as a function of altitude D. Convert between different pressure units (such as: kPa, atm,mm Hg) E. Explain how a straw works F. Explain how a manometer works G. Measure the gauge pressure of a trapped gas H. Use manometers & barometers I. Explain different boiling points of water at different altitudes J. Measure the apparent weight of an immersed object. K. Determine the Buoyant force on a submerged, or floating object L. Use Archimedes principle to explain why large ships do not sink • Density • Pressure • Viscosity • Specific weight (unit weight) • Specific gravity (relative density) • Specific volume Density ‘𝝆’ • It is the ratio between mass (m) and volume (V). It’s unit is kg/m3 • If a fluid has more atoms/molecules and particles are placed close to each other, it is going to have a higher density. • The density of water 𝝆w= 1 g/cm3= 1000 Kg/m3 • The density of air 𝝆air= 1.21 Kg/m3 Specific Gravity (Relative Density) A) Pressure at a point: • When object is submerged in a fluid, fluid exerts a force on the object. • The force is perpendicular to the surface of the object at each point of the surface. • The magnitude of the perpendicular force on a surface per unit area is called the pressure of the fluid: F F P or P A A where P is the pressure of the fluid, F is the force exerted by the fluid on the object, A is the area of the object. The SI unit of pressure is Pascal (Pa) =1 N/m2. The Pascal is a small unit of pressure. • If the force acts at an angle, the force component along the direction perpendicular to the surface must be used to calculate pressure. F sin 𝛉 F F cos 𝛉 F 𝜃 𝜃 A A P= 𝐹 𝑠𝑖𝑛 𝜃 𝐴 P= 𝐹 𝑐𝑜𝑠 𝜃 𝐴 Factors affecting the pressure at a point Why do snowshoes keep you from sinking into the snow? Atmospheric (air) Pressure • The weight of air column over unit area of earth surface at sea level. 1 atm ≈1.01325×105 Pa. • It exerted due to collisions between the mixture of gases found in the air Fluids pays a pressure in every direction If air pressure always push us from outside, how come we keep balanced?! Unit Weight Length Conversion Newton/𝒎𝟐 1 atm = 101,325 = 1.013 x 𝟏𝟎𝟓 𝑵/𝒎𝟐 Pascal (Pa) 1 atm = 1.013 x 𝟏𝟎𝟓 𝑵/𝒎𝟐 1 𝑵/𝒎𝟐 = 1 Pascal Psi (lb/in2) 1 atm = 14.7 psi (Pound per square inch) Bar 1 atm = 1.013 bar 1 bar = 𝟏𝟎𝟓 𝑵/𝒎𝟐 cm Hg 1 atm = 76 cm Hg = 760 mm Hg = 29.92 inHg Torr 1 atm = 760 torr 1 torr = 1 mm Hg 1 Torr = 101325/760 Pascal (≈ 133.3 Pa) I. Converting between atmospheres and millimeters of mercury. 1 atm. = 760.0 mm Hg • Example 1: Convert 0.875 atm to mmHg. 0.875 atm x 760.0 mmHg / atm = 665 mmHg • Example 2: Convert 745.0 mmHg to atm. 745.0 mmHg x atm / 760.0 mmHg = 0.980 atm II. Converting between atmospheres and kilopascals. 1 atm. = 101.325 kPa • Example 3: Convert 0.955 atm to kPa. 0.955 atm x 101.325 kPa / atm = 96.76 kPa • Example 4: Convert 98.35 kPa to atm. 98.35 kPa x atm / 101.325 kPa = 0.970 atm III. Converting between millimeters of mercury and kilopascals. 760.0 mmHg = 101.325 kPa • Example 5: Convert 740.0 mmHg to kPa. 740.0 mmHg x 101.325 kPa / 760.0 mmHg = 9.609 x 10-3 kPa • Example 6: Convert 99.25 kPa to mmHg. 99.25 kPa x 760.0 mmHg / 101.325 kPa = 744.436 mmHg Absolute Pressure • A pressure measured relative to a perfect vacuum. • Explain the relationship among absolute pressure, gauge pressure, and atmospheric pressure Pabs Patm Pgage where Pabs : Absolute pressure Patm : Atmospheric pressure Pgage : Gage pressure = ρ g h Gauge Pressure • A pressure measured using a pressure measuring instrument . • Is the difference between the absolute pressure and the current atmospheric pressure. • It can be either positive or negative depending on whether the pressure is above or bellow the atmospheric pressure. Work with your group and try to deduce the main parameters that affecting the pressure of fluid Using this simulation • Static Fluid pressure: • Atmospheric pressure is a good example of static pressure as its ultimate source is gravity. • The pressure exerted by a static fluid depends only upon 1) The depth of the fluid (h) 2) The density of the fluid (ρ) 3) The acceleration of gravity (g) • Imagine a horizontal plate (x) of area (A) at depth (h) inside a liquid of density (ρ). • This plate acts as the base of a column of the liquid. • The force acting on the plate (x) is the weight of the column of the liquid whose height (h) and cross section area (A). • The force resulting from the liquid pressure balances with the weight of the column of the liquid. PL g h Pt Pa g h where: (Pa ) is the atmospheric pressure. • For a fluid whose density remains approximately constant throughout, the pressure increases linearly with depth: P = P0 + ρFg h where P is the pressure at the bottom of the column of the fluid, P0 is the pressure at the top of the column, g is the acceleration due to gravity, ρF is the density of the fluid = m/V h is the height of the column of the fluid. ▪ If you are in a car that is submerged in a flood, how hard will it be to open your door? Because water pushes immersed foam with upward force due to pressure difference across piece of foam. the an the the 1. Change in atmospheric pressure with density Density of a fluid decreases with increase in temperature. It increases with increase in pressure. Effect of atmospheric pressure on boiling point of water Is it easier or harder to boil water when on top of a very high mountain? • As altitude increases, atmospheric pressure and boiling point decrease because air is less dense at higher altitudes. • If the atmospheric pressure is exactly 1 atm, the boiling point of water is 100.0 degrees Celsius. This is because the vapor pressure of water is 1 atm at this temperature. • The boiling point decreases to 80.0 degrees at higher altitudes. • If you increase the pressure, the boiling point will increase because more energy will be needed to raise the vapor pressure to the increased atmospheric pressure. Likewise, if you decrease the pressure, the boiling point will decrease. • If you want water to stay a liquid, just pressurize it a lot. This is done in pressure cookers to allow food to cook more quickly in water at a temperature of several hundred degrees. 2. Change in atmospheric pressure with altitude/ depth Pressure increases with increase in depth . Pressure decreases with increase in altitude . The higher you go up above sea surface level, the lower the pressure. Pressure is equal at all the points that lie on the same level A B C Pressure is equal at point A, B and is smaller than that at point C What is the reason of building water tanks very height? • When a liquid is put in a Ushaped tube, the level of the liquid in the two branches is the same. • When another liquid is added in one branch of the tube (both liquids don’t mix). A B The pressure at point B = The pressure at point A (at the same level). Pa 1 g h1 Pa 2 g h 2 1 h1 2 h 2 2 h1 1 h2 If the 1st liquid is water, then the ratio (ρ2 / ρ1) represents the relative density of the 2nd liquid. How could you use the U-shaped tube to determine the specific density of some liquids? Specific gravity (relative density): Is the ratio of density of a fluid to density of water at 4ºC SG = ρ / ρw Unitless The relative density of oil • Oils relative density ranging from 0.7 to 0.98 g/cm3 so most are less dense than water . • For Petroleum ≅ 800 Kg/m3 or 0.8 g/cm3