tuesday, november 30, 2010 introducing fluids hydrostatic pressure

Tuesday, November 30, 2010Tuesday, November 30, 2010

Introducing FluidsIntroducing Fluids

Hydrostatic PressureHydrostatic Pressure

FluidsFluids

Fluids are substances that can Fluids are substances that can flowflow, such as liquids and gases, , such as liquids and gases, and even a few solids.and even a few solids.

In Physics B, we will limit our In Physics B, we will limit our discussion of fluids to substances discussion of fluids to substances that can easily flow, such as liquids that can easily flow, such as liquids and gases.and gases.

Review: DensityReview: Density

= m/V= m/V: density (kg/m: density (kg/m33))m: mass (kg)m: mass (kg)V: volume (mV: volume (m33))

Units:Units:kg/mkg/m33

You should remember how to do density calculations from chemistry!

PressurePressure P = F/AP = F/A

P : pressure (Pa)P : pressure (Pa)F: force (N)F: force (N)A: area (mA: area (m22))

Pressure unit: Pressure unit: PascalPascal ( 1 Pa = 1 N/m ( 1 Pa = 1 N/m22)) The force on a surface caused by The force on a surface caused by

pressure is always normal (or pressure is always normal (or perpendicular) to the surface. This perpendicular) to the surface. This means that the pressure of a fluid is means that the pressure of a fluid is exerted in all directions, and is exerted in all directions, and is perpendicular to the surface at every perpendicular to the surface at every location.location.

balloon

Atmospheric PressureAtmospheric Pressure

Atmospheric pressure is Atmospheric pressure is normally about normally about 100,000 100,000 PascalsPascals..

Differences in Differences in atmospheric pressure atmospheric pressure cause winds to blow.cause winds to blow.

Low atmospheric pressure Low atmospheric pressure inside a hurricane’s eye inside a hurricane’s eye contributes to the severe contributes to the severe winds and the development of winds and the development of the the storm surgestorm surge..

Sample ProblemSample Problem Calculate the net force on an airplane window if cabin Calculate the net force on an airplane window if cabin

pressure is 90% of the pressure at sea level, and the pressure is 90% of the pressure at sea level, and the external pressure is only 50% of that at sea level. external pressure is only 50% of that at sea level. Assume the window is 0.43 m tall and 0.30 m wide.Assume the window is 0.43 m tall and 0.30 m wide.

Hurricane Katrina’s Storm SurgeHurricane Katrina’s Storm Surge

Mississippi River Gulf OutletMississippi River Gulf OutletNew Orleans East/St. Bernard ParishNew Orleans East/St. Bernard Parish

The Pressure of a LiquidThe Pressure of a Liquid P = P = gh gh

P: pressure (Pa)P: pressure (Pa) : density (kg/m: density (kg/m33)) g: acceleration constant (9.8 m/sg: acceleration constant (9.8 m/s22)) h: height of liquid column (m)h: height of liquid column (m)

This is often called This is often called hydrostatic pressurehydrostatic pressure if the if the liquid is water. It excludes atmospheric pressure.liquid is water. It excludes atmospheric pressure.

It is also sometimes called It is also sometimes called gauge pressuregauge pressure, since , since a diver’s pressure gauge will read hydrostatic a diver’s pressure gauge will read hydrostatic pressure. Gauge pressure readings never include pressure. Gauge pressure readings never include atmospheric pressure, but only the pressure of atmospheric pressure, but only the pressure of the fluid.the fluid.

Absolute pressureAbsolute pressure is obtained by adding the is obtained by adding the atmospheric pressure to the hydrostatic pressureatmospheric pressure to the hydrostatic pressure ppabsabs = p = patmatm + + ghgh

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

Hydrostatic Pressure Hydrostatic Pressure in Dam Designin 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 Hydrostatic Pressure in Levee Pressure in Levee

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

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

Wednesday, December 1, Wednesday, December 1, 20102010

Buoyancy ForceBuoyancy Force

Floating is a type of Floating is a type of equilibriumequilibrium

An upward force An upward force counteracts the force of counteracts the force of gravity for these objects. gravity for these objects. This upward force is This upward force is called the called the buoyant forcebuoyant force..

Fbuoy

mg

The Buoyant ForceThe Buoyant Force Archimedes’ Principle: a body immersed in a Archimedes’ Principle: a body immersed in a

fluid is fluid is buoyedbuoyed up by a up by a forceforce that is equal to the that is equal to the weight of the fluid displaced.weight of the fluid displaced.

FFbuoybuoy = = VgVg FFbuoybuoy: the buoyant force exerted on a submerged or : the buoyant force exerted on a submerged or

partially submerged object.partially submerged object. V: the volume of displaced liquid.V: the volume of displaced liquid. : the density of the displaced liquid.: the density of the displaced liquid.

When an object floats, the upward buoyant When an object floats, the upward buoyant force equals the downward pull of gravity.force equals the downward pull of gravity.

The buoyant force can float very heavy objects, The buoyant force can float very heavy objects, and acts upon objects in the water whether and acts upon objects in the water whether they are floating, submerged, or even sitting on they are floating, submerged, or even sitting on the bottom.the bottom.

Buoyant force on Buoyant force on submerged objectsubmerged object

mg

Fbuoy = Vg

A sharks body is not neutrally buoyant, and so a shark must swim continuously or he will sink deeper.


mg

VgSCUBA divers use a buoyancy control system to maintain neutral buoyancy (equilibrium!).


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 Buoyant force on floating objectobject

mg

Vg

If the object floats on the surface, we know for a fact Fbuoy = mg! The volume of displaced water equals the volume of the submerged portion of the ship.

Sample problemSample problemAssume a wooden raft has 80.0% of the density of water. The 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 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 0.10 meter tall. How much of the raft rises above the level of the water when it floats?water when it floats?

Sample problemSample problem You want to transport a man and a horse across a still lake on a wooden 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 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 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.density of the wood is 80% of the density of the water.

Parking in St. Bernard Parish Parking in St. Bernard Parish after Hurricane Katrinaafter Hurricane Katrina

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

Hurricane KatrinaHurricane Katrina

Estimation problemEstimation problem

Estimate the mass of this house in kg.Estimate the mass of this house in kg.

Thursday, December 2, Thursday, December 2, 20102010

Buoyancy Force LabBuoyancy Force Lab

Buoyancy Buoyancy LabLab

Using the Using the equipment equipment provided, verify provided, verify that the density that the density of water is of water is 1,000 kg/m1,000 kg/m33. .

Report must Report must include:include: Free body Free body

diagrams.diagrams. All data.All data. Calculations.Calculations.

waterair

Note: established value for the density of pure water is 1,000 kg/m3.

Friday, December 3, 2010Friday, December 3, 2010

Moving FluidsMoving Fluids

Fluid Flow ContinuityFluid Flow Continuity

The volume per unit time of a liquid flowing The volume per unit time of a liquid flowing in a pipe is constant throughout the pipe.in a pipe is constant throughout the pipe.

V = AvtV = Avt V: volume of fluid (mV: volume of fluid (m33)) A: cross sectional areas at a point in the pipe (mA: cross sectional areas at a point in the pipe (m22)) v: speed of fluid flow at a point in the pipe (m/s)v: speed of fluid flow at a point in the pipe (m/s) t: time (s)t: time (s)

AA11vv11 = A = A22vv22 AA11, A, A22: cross sectional areas at points 1 and 2: cross sectional areas at points 1 and 2 vv11, v, v22: speed of fluid flow at points 1 and 2: speed of fluid flow at points 1 and 2

http://library.thinkquest.org/27948/bernoulli.html

Sample problemSample problem A pipe of diameter 6.0 cm has fluid flowing through it at 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 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 in which the diameter is 3.0 cm? How much water per second flows through the pipe?second flows through the pipe?

Natural WaterwaysNatural Waterways

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

Sample problemSample problemThe water in a canal flows 0.10 m/s where the canal is 12 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 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 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 to 5.0 meters, how fast will the water be moving through this narrower region? What will happen to the water if something narrower region? What will happen to the water if something prevents it from flowing faster in the narrower region?prevents it from flowing faster in the narrower region?

Artificial WaterwaysArtificial 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 Fluid Flow Continuity in Continuity in WaterwaysWaterways

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 TheoremBernoulli’s Theorem

The sum of the pressure, the potential The sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume, and the kinetic energy per unit volume at any one location energy per unit volume at any one location in the fluid is equal to the sum of the in the fluid is equal to the sum of the pressure, the potential energy per unit pressure, the potential energy per unit volume, and the kinetic energy per unit volume, and the kinetic energy per unit volume at any other location in the fluid for a volume at any other location in the fluid for a non-viscous incompressible fluid in non-viscous incompressible fluid in streamline flow.streamline flow.

All other considerations being equal, when All other considerations being equal, when fluid moves faster, the pressure drops.fluid moves faster, the pressure drops.

Bernoulli’s TheoremBernoulli’s Theorem

P + P + g h + ½ g h + ½ vv22 = Constant = ConstantP : pressure (Pa)P : pressure (Pa) : density of fluid (kg/m: density of fluid (kg/m33))g: gravitational acceleration constant g: gravitational acceleration constant

(9.8 m/s(9.8 m/s22))h: height above lowest point (m)h: height above lowest point (m)v: speed of fluid flow at a point in the v: speed of fluid flow at a point in the

pipe (m/s)pipe (m/s)

Sample ProblemSample Problem Knowing what you know about Bernouilli’s principle, Knowing what you know about Bernouilli’s principle,

design an airplane wing that you think will keep an design an airplane wing that you think will keep an airplane aloft. Draw a cross section of the wing.airplane aloft. Draw a cross section of the wing.

Bernoulli’s Principle and Bernoulli’s Principle and HurricanesHurricanes

In a hurricane or tornado, the high In a hurricane or tornado, the high winds traveling across the roof of a winds traveling across the roof of a building can actually lift the roof building can actually lift the roof off the building.off the building.

http://video.google.com/videoplay?docid=6649024923387081294&q=Hurricane+Roof&hl=en

tuesday, november 30, 2010 introducing fluids hydrostatic pressure

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