Presentation on theme: "Liquids and Gasses Matter that “Flows”"— Presentation transcript:
1Liquids and Gasses Matter that “Flows” Fluid MechanicsLiquids and GassesMatter that “Flows”
2Density and Specific Gravity Density is mass per unit volumeSI unit isBut this is also used
3Specific Gravity Ratio of density to the density of water at 4oC. Density of water at 4oC=1 g/cm3The 4oC is important since water’s density changes with temperatureIt has nothing to do with gravityRelative density would be a better term
4PressureA static fluid will exert a force perpendicular to any surface it is in contact withPressure is defined as Force per unit AreaNote this is scalarSI unit of N/m2=pascal=pa
5Atmospheric PressureThe big volume of air above us exerts pressure downwards.Pressure at sea levelChanges depending on elevation, temperature, weather condition etc.
6Pressure at depth Assume that is constant all throughout the liquid. Fluid is incompressibleForce is from weight of liquid
7Pressure at depthIf fluid is compressible (gasses) density changes with height and equation is only valid for very thin slices.
8Pascal’s Law Equations independent of Area, only height matters. Pressure is the same at any two points at the same level of the fluid.If pressure is applied to one end it is distributed throughout the fluid and to the walls of the container
9Pascal’s Law Application Hydraulic LiftHowever, volume of the liquid remains the same
11ExampleA car lift used in a service station uses compressed air to exert a force on a small piston with a circular cross section of radius 5.00cm. The pressure is transmitted by a liquid to a second piston of radius 15.0 cm. What force must the compressed air exert to lift a car weighing 13300N? What air pressure produces this force?
12ExampleNote: no need to convert to meters since units cancel
13Absolute Pressure and Gauge Pressure Total Pressure within a vesselGauge PressureExcess Pressure above atmospheric pressureGauge Pressure – Ex. A tire shows 220kPaAbsolute Pressure of tire is 220kPa+1atm=320kPAFlat tire actually has 1 atm of pressure inside
14Pressure Gauges - Manometer Many different devices used to measure pressureManometer – consists of a U-shaped tube filled with a liquid of known density. It is open in one end and the other end is connected to a container filled with gas whose pressure to be measured.
15Pressure Gauges - Manometer Bottom of tube has same pressureGauge pressure is proportional to height difference
16Pressure Gauges - Barometer Mercury barometer – consists of filled tube of mercury closed on one end and the other end is inverted into a dish of mercury.Pressure in the closed end of the tube can be approximated to be zero.
17Pressure Gauges - Barometer mmHg or Torr, is another common unit of measure of pressure. But it is affected by temperature (density of Hg changes) as well as gravity.
18Buoyancy Bodies immersed in water will weigh less Bouyant Force is exerting an upward forceAssume a submerged object with uniform cross section area A
20BouyancyArchimedes’ Principle- When a body is immersed in a fluid, the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body.
21ExampleArchimedes was supposedly tasked to determine if the crown of the king was pure gold. He solved this by first weighing the crown in air, and then weighing the crown when submerged in water. Suppose the scale read 7.84N in air and 6.84N in water, what is the crown made of?
27ExampleA water hose of 2.50cm diameter is used by a gardener to fill a 30.0L bucket. The gardener notes that it takes 1.00min to fill the bucket. A nozzle with an opening of cross-sectional area 0.500cm2 is attached and held so water is projected horizontally from a point 1.00m above ground. Over what horizontal distance can the water be projected?
32ExampleWater enters a house through a pipe with an inside diameter of 2.0 cm at an absolute pressure of 4.0x105 Pa. A 1.0cm diameter pipe leads to the second floor bathroom 5.0 m above. When the flow speed at the inlet pipe is 1.5 m/s, find the flow speed, pressure and volume flow in the bathroom.
35ProblemsGiancoli 10-20In working out Pascal’s principle, Pascal showed dramatically how force can be multiplied with fluid pressure. He placed a long thin tube of radius r=0.30cm, vertically into a wine barrel of radius R=21cm. He found that when the barrel was filled with water and the tube filled to a height of 12m, the barrel burst. Calculate (a) the mass of water in the tube? (b) the net force exerted on the barrel lid just before rupture.
36Serway 14-20A U tube of uniform cross-secitonal area, open to the athmosphere, is partially filled with mercury. Water is then poured into both arms. If the equilibrium configuration fo the tube is as shown with h2=1.00cm, find h1.
37Young and Friedman 14.31A cubical block of wood, 10 cm on a side, floats in the interface of oil and water with its lower surface, 1.50cm below the interface. The density of oil is 790kg/m3. (a) what is the gauge pressure at the upper face of the block? (b) What is the gauge pressure at the lower face of the block? (c) What are the mass and density of the block?
38Young and Friedman 14.46A golf course sprinkler system discharges water from a horizontal pipe at the rate of 7200cm3/s. At one point in the pipe, where the radius is 4.00cm, the absolute pressure is 2.40x105 Pa. At a second point in the pipe, the water passes through a connection where the radius is 2.00cm. What is the absolute pressure as it flows through the constriction?