Tuesday, November 30, 2010 Introducing Fluids Hydrostatic Pressure

Fluids Fluids are substances that can flow, such as liquids and gases, and even a few solids. Fluids are substances that can flow, such as liquids and gases, and even a few solids. In Physics B, we will limit our discussion of fluids to substances that can easily flow, such as liquids and gases. In Physics B, we will limit our discussion of fluids to substances that can easily flow, such as liquids and gases.

Review: Density  = m/V  = m/V   : density (kg/m 3 )  m: mass (kg)  V: volume (m 3 ) Units: Units:  kg/m 3 You should remember how to do density calculations from chemistry!

Pressure P = F/A P = F/A  P : pressure (Pa)  F: force (N)  A: area (m 2 ) Pressure unit: Pascal ( 1 Pa = 1 N/m 2 ) Pressure unit: Pascal ( 1 Pa = 1 N/m 2 ) The force on a surface caused by pressure is always normal (or perpendicular) to the surface. This means that the pressure of a fluid is exerted in all directions, and is perpendicular to the surface at every location. The force on a surface caused by pressure is always normal (or perpendicular) to the surface. This means that the pressure of a fluid is exerted in all directions, and is perpendicular to the surface at every location. balloon

Atmospheric Pressure Atmospheric pressure is normally about 100,000 Pascals. Atmospheric pressure is normally about 100,000 Pascals. Differences in atmospheric pressure cause winds to blow. Differences in atmospheric pressure cause winds to blow. Low atmospheric pressure inside a hurricane’s eye contributes to the severe winds and the development of the storm surge.

Sample Problem Calculate the net force on an airplane window if cabin pressure is 90% of the pressure at sea level, and the external pressure is only 50% of that at sea level. Assume the window is 0.43 m tall and 0.30 m wide. Calculate the net force on an airplane window if cabin pressure is 90% of the pressure at sea level, and the external pressure is only 50% of that at sea level. Assume the window is 0.43 m tall and 0.30 m wide.

Hurricane Katrina’s Storm Surge Mississippi River Gulf Outlet New Orleans East/St. Bernard Parish

The Pressure of a Liquid P =  gh P =  gh  P: pressure (Pa)   : density (kg/m 3 )  g: acceleration constant (9.8 m/s 2 )  h: height of liquid column (m) This is often called hydrostatic pressure if the liquid is water. It excludes atmospheric pressure. This is often called hydrostatic pressure if the liquid is water. It excludes atmospheric pressure. It is also sometimes called gauge pressure, since a diver’s pressure gauge will read hydrostatic pressure. Gauge pressure readings never include atmospheric pressure, but only the pressure of the fluid. It is also sometimes called gauge pressure, since a diver’s pressure gauge will read hydrostatic pressure. Gauge pressure readings never include atmospheric pressure, but only the pressure of the fluid. Absolute pressure is obtained by adding the atmospheric pressure to the hydrostatic pressure Absolute pressure is obtained by adding the atmospheric pressure to the hydrostatic pressure  p abs = p atm +  gh

Sample Problem Calculate for the bottom of a 3 meter (approx 10 feet) deep swimming pool full of water: (a) hydrostatic pressure (a) hydrostatic pressure (b) absolute pressure (b) absolute pressure Which one of these represents the gauge pressure?

Hydrostatic Pressure in Dam Design The depth of Lake Mead at the Hoover Dam is 600ft. What is the hydrostatic pressure at the base of the dam?

Hydrostatic Pressure in Levee Design Hurricane Katrina, August 2005 A hurricane’s storm surge can overtop levees, but a bigger problem can be increasing the hydrostatic pressure at the base of the levee.

New Orleans Elevation Map New Orleans is largely below sea level, and relies upon a system of levees to keep the lake and the river at bay

Sample Problem Calculate the increase in hydrostatic pressure experienced by the levee base for an expected (SPH Design) storm surge. How does this compare to the increase that occurred during Hurricane Katrina, where the water rose to the top of the levee?

Wednesday, December 1, 2010 Buoyancy Force

Floating is a type of equilibrium An upward force counteracts the force of gravity for these objects. This upward force is called the buoyant force. An upward force counteracts the force of gravity for these objects. This upward force is called the buoyant force. F buoy mg

The Buoyant Force Archimedes’ Principle: a body immersed in a fluid is buoyed up by a force that is equal to the weight of the fluid displaced. Archimedes’ Principle: a body immersed in a fluid is buoyed up by a force that is equal to the weight of the fluid displaced. F buoy =  Vg F buoy =  Vg  F buoy : the buoyant force exerted on a submerged or partially submerged object.  V: the volume of displaced liquid.   : the density of the displaced liquid. When an object floats, the upward buoyant force equals the downward pull of gravity. When an object floats, the upward buoyant force equals the downward pull of gravity. The buoyant force can float very heavy objects, and acts upon objects in the water whether they are floating, submerged, or even sitting on the bottom. The buoyant force can float very heavy objects, and acts upon objects in the water whether they are floating, submerged, or even sitting on the bottom.

Buoyant force on submerged object mg F buoy =  Vg A sharks body is not neutrally buoyant, and so a shark must swim continuously or he will sink deeper.

Buoyant force on submerged object mg  Vg SCUBA divers use a buoyancy control system to maintain neutral buoyancy (equilibrium!).

Buoyant force on submerged object mg  Vg If the diver wants to rise, he inflates his vest, which increases the amount of water he displaces, and he accelerates upward.

Buoyant force on floating object mg  Vg If the object floats on the surface, we know for a fact F buoy = mg! The volume of displaced water equals the volume of the submerged portion of the ship.

Sample problem Assume a wooden raft has 80.0% of the density of water. The dimensions of the raft are 6.0 meters long by 3.0 meters wide by 0.10 meter tall. How much of the raft rises above the level of the water when it floats?

Sample problem You want to transport a man and a horse across a still lake on a wooden raft. The mass of the horse is 700 kg, and the mass of the man is 75.0 kg. What must be the minimum volume of the raft, assuming that the density of the wood is 80% of the density of the water. You want to transport a man and a horse across a still lake on a wooden raft. The mass of the horse is 700 kg, and the mass of the man is 75.0 kg. What must be the minimum volume of the raft, assuming that the density of the wood is 80% of the density of the water.

Parking in St. Bernard Parish after Hurricane Katrina

“Mobile” Homes in St. Bernard Parish after Hurricane Katrina

Estimation problem Estimate the mass of this house in kg.

Thursday, December 2, 2010 Buoyancy Force Lab

Buoyancy Lab Using the equipment provided, verify that the density of water is 1,000 kg/m 3. Using the equipment provided, verify that the density of water is 1,000 kg/m 3. Report must include: Report must include:  Free body diagrams.  All data.  Calculations. waterair Note: established value for the density of pure water is 1,000 kg/m 3.

Friday, December 3, 2010 Moving Fluids

Fluid Flow Continuity The volume per unit time of a liquid flowing in a pipe is constant throughout the pipe. The volume per unit time of a liquid flowing in a pipe is constant throughout the pipe. V = Avt V = Avt  V: volume of fluid (m 3 )  A: cross sectional areas at a point in the pipe (m 2 )  v: speed of fluid flow at a point in the pipe (m/s)  t: time (s) A 1 v 1 = A 2 v 2 A 1 v 1 = A 2 v 2  A 1, A 2 : cross sectional areas at points 1 and 2  v 1, v 2 : speed of fluid flow at points 1 and 2 oulli.html oulli.html oulli.html oulli.html

Sample problem A pipe of diameter 6.0 cm has fluid flowing through it at 1.6 m/s. How fast is the fluid flowing in an area of the pipe in which the diameter is 3.0 cm? How much water per second flows through the pipe? A pipe of diameter 6.0 cm has fluid flowing through it at 1.6 m/s. How fast is the fluid flowing in an area of the pipe in which the diameter is 3.0 cm? How much water per second flows through the pipe?

Natural Waterways Flash flooding can be explained by fluid flow continuity.

Sample problem The water in a canal flows 0.10 m/s where the canal is 12 meters deep and 10 meters across. If the depth of the canal is reduced to 6.5 meters at an area where the canal narrows to 5.0 meters, how fast will the water be moving through this narrower region? What will happen to the water if something prevents it from flowing faster in the narrower region?

Artificial Waterways Flooding from the Mississippi River Gulf Outlet was responsible for catastrophic flooding in eastern New Orleans and St. Bernard during Hurricane Katrina.

Fluid Flow Continuity in Waterways A hurricane’s storm surge can be “amplified” by waterways that become narrower or shallower as they move inland. Mississippi River Gulf Outlet levees are overtopped by Katrina’s storm surge.

Bernoulli’s Theorem The sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any one location in the fluid is equal to the sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any other location in the fluid for a non-viscous incompressible fluid in streamline flow. The sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any one location in the fluid is equal to the sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any other location in the fluid for a non-viscous incompressible fluid in streamline flow. All other considerations being equal, when fluid moves faster, the pressure drops. All other considerations being equal, when fluid moves faster, the pressure drops.

Bernoulli’s Theorem P +  g h + ½  v 2 = Constant P +  g h + ½  v 2 = Constant  P : pressure (Pa)   : density of fluid (kg/m 3 )  g: gravitational acceleration constant (9.8 m/s 2 )  h: height above lowest point (m)  v: speed of fluid flow at a point in the pipe (m/s)

Sample Problem Knowing what you know about Bernouilli’s principle, design an airplane wing that you think will keep an airplane aloft. Draw a cross section of the wing. Knowing what you know about Bernouilli’s principle, design an airplane wing that you think will keep an airplane aloft. Draw a cross section of the wing.

Bernoulli’s Principle and Hurricanes In a hurricane or tornado, the high winds traveling across the roof of a building can actually lift the roof off the building. In a hurricane or tornado, the high winds traveling across the roof of a building can actually lift the roof off the building. cid= &q=Hurri cane+Roof&hl=en cid= &q=Hurri cane+Roof&hl=en cid= &q=Hurri cane+Roof&hl=en cid= &q=Hurri cane+Roof&hl=en