Fluid MechanicsFluid Mechanics

Chapter 8Chapter 8

Fluid StateFluid State

Flow and have no definite shape Flow and have no definite shape – Liquids and gasses are fluidsLiquids and gasses are fluids

Pressure is the force on a surface Pressure is the force on a surface divided by the area of the surface divided by the area of the surface

P = F/AP = F/A

– The force (F) on the surface is assumed to The force (F) on the surface is assumed to be perpendicular to the surface area (A)be perpendicular to the surface area (A)

When you stand on ice, the ice exerts When you stand on ice, the ice exerts on your body an upward normal force on your body an upward normal force that has the same magnitude as your that has the same magnitude as your weightweight

The upward force is spread over the The upward force is spread over the area of your body that touches the ice, area of your body that touches the ice, which is the soles of your feet. which is the soles of your feet.

If you lay on the ice there is a larger If you lay on the ice there is a larger area for the force to be spread out overarea for the force to be spread out over

PressurePressure

Pressure (P) is a scalar quantityPressure (P) is a scalar quantity

Unit is the pascal (Pa) = to 1N/mUnit is the pascal (Pa) = to 1N/m22

Atmospheric pressure- On every Atmospheric pressure- On every square centimeter of the Earth’s square centimeter of the Earth’s surface at sea level, the atmosphere surface at sea level, the atmosphere exerts a force of approximately 10 N.exerts a force of approximately 10 N.– Balanced on your body, notice when Balanced on your body, notice when

ears popears pop

Fluids at restFluids at rest

Ideal fluid- has no internal friction Ideal fluid- has no internal friction among its particlesamong its particles– Used as a model for fluidsUsed as a model for fluids

Examples of FluidsExamples of Fluids

Water, honey, oil, tar, and airWater, honey, oil, tar, and air

Pascal’s PrinciplePascal’s PrincipleBlaise Pascal (1623-1662), a French Blaise Pascal (1623-1662), a French physician, noted that the shape of a physician, noted that the shape of a container has no effect on the pressure of container has no effect on the pressure of the fluid it contains at any given depththe fluid it contains at any given depth

Pascal’s principle- any change in pressure Pascal’s principle- any change in pressure applied at any point on a confined fluid is applied at any point on a confined fluid is transmitted undiminished throughout the transmitted undiminished throughout the fluidfluid– Squeeze a tube of toothpasteSqueeze a tube of toothpaste

Pressure exerted at bottom is transmitted through Pressure exerted at bottom is transmitted through the tube, forcing the paste out the topthe tube, forcing the paste out the top

Hydraulic pressureHydraulic pressure

When fluids are used in machines When fluids are used in machines (hydraulic lifts) to multiply forces, (hydraulic lifts) to multiply forces, Pascal’s principle is being appliedPascal’s principle is being applied

In a hydraulic system a fluid is In a hydraulic system a fluid is confined to two connecting chambers confined to two connecting chambers with a piston that is free to move. with a piston that is free to move.

Force exerted by a hydraulic liftForce exerted by a hydraulic lift– FF22 = F = F11AA22 / A / A11

Gas PressureGas Pressure

Gases are made up of small Gases are made up of small particles, widely separated, in particles, widely separated, in constant, random motion at high constant, random motion at high speeds, making elastic collisions with speeds, making elastic collisions with each other and surfaces.each other and surfaces.

The forces exerted by these The forces exerted by these collisions result in gas pressure on collisions result in gas pressure on the surfacethe surface

Pressure of Water on a BodyPressure of Water on a Body

P = FP = Fgg/A = /A = ppAhg/A = Ahg/A = DDhghg

The pressure of the water on a body The pressure of the water on a body depends on the density of the fluid, depends on the density of the fluid, its depth, and g.its depth, and g.

BuoyancyBuoyancyThe increase of pressure with depth The increase of pressure with depth creates an upward force on all creates an upward force on all objectsobjectsCalled the buoyant forceCalled the buoyant force

Buoyant force is FBuoyant force is Fbuoyant buoyant = = ppVgVg

The volume of the object is equal to The volume of the object is equal to the volume of the fluid that was the volume of the fluid that was displaceddisplaced

Archimedes’ PrincipleArchimedes’ Principle

The relationship that the buoyant The relationship that the buoyant force (force (ppVg) is equal to the weight of Vg) is equal to the weight of the fluid displaced was discovered by the fluid displaced was discovered by Archimedes in 212 B.C.Archimedes in 212 B.C.

All objects in a liquid have an All objects in a liquid have an apparent weight that is less than apparent weight that is less than when the object is in airwhen the object is in air

FFapparent apparent = F= Fgg - F - Fbuoyantbuoyant

Uses of Archimedes’ principleUses of Archimedes’ principleAs a result of the buoyant force ships As a result of the buoyant force ships can be made of steel and still float as can be made of steel and still float as long as the hull is hollow and large long as the hull is hollow and large enough so that the density of the enough so that the density of the ship is less than the density of watership is less than the density of water

Submarines take advantage of Submarines take advantage of Archimedes’ principle as water is Archimedes’ principle as water is pumped into or out of chambers to pumped into or out of chambers to change the net vertical forcechange the net vertical force

Fluids in MotionFluids in Motion

The relationship between the velocity The relationship between the velocity and pressure exerted by a moving and pressure exerted by a moving fluid is described by Bernoulli’s fluid is described by Bernoulli’s principleprinciple

As the velocity of a fluid increases, As the velocity of a fluid increases, the pressure exerted by that fluid the pressure exerted by that fluid decreasesdecreases

Uses of Bernoulli’s PrincipleUses of Bernoulli’s Principle

Most aircraft get part of their lift from Most aircraft get part of their lift from this principlethis principle

As the wings travels through the air, As the wings travels through the air, the air moving over the top surface the air moving over the top surface travels farther, and therefore must travels farther, and therefore must go faster than the air moving past go faster than the air moving past the bottom surfacethe bottom surface

Forces within LiquidsForces within LiquidsIn real liquids particles exert In real liquids particles exert electromagnetic forces of attraction electromagnetic forces of attraction on each other – called cohesive on each other – called cohesive forcesforces

Surface tension- a result of the Surface tension- a result of the cohesive forces among the particles cohesive forces among the particles of a liquid. It is the tendency of the of a liquid. It is the tendency of the surface of a liquid to contract to the surface of a liquid to contract to the smallest possible areasmallest possible area

Capillary ActionCapillary ActionAdhesion is the attraction force that acts Adhesion is the attraction force that acts between particles of different substancesbetween particles of different substances

If a piece of glass tubing with a small inner If a piece of glass tubing with a small inner diameter is placed in water, the water diameter is placed in water, the water rises inside the tube.rises inside the tube.

The adhesive force between the glass and The adhesive force between the glass and water is stronger than the cohesive force water is stronger than the cohesive force of the water molecules- called the capillary of the water molecules- called the capillary actionaction

Examples of capillary actionExamples of capillary action

Molten wax rises the wick of a candleMolten wax rises the wick of a candle

Paint moves up through the bristles Paint moves up through the bristles of a brushof a brush

Water moving through the soil and Water moving through the soil and up the roots of a plantup the roots of a plant

Evaporation & CondensationEvaporation & Condensation

The escape of particles from a liquid The escape of particles from a liquid is evaporationis evaporation– Cooling effectCooling effect

Evaporated particles can return to Evaporated particles can return to the liquid phase if the Ke or temp the liquid phase if the Ke or temp decreases. Called condensationdecreases. Called condensation– fogfog

Solid StateSolid State

Close fitting particlesClose fitting particles

More dense than liquidsMore dense than liquids

Water is an exception- solid water is Water is an exception- solid water is less dense than liquid waterless dense than liquid water

Thermal expansionThermal expansionWhen heated all forms of matter When heated all forms of matter become less dense and expand to fill become less dense and expand to fill more spacemore space

Hot air expands and rises – Cold air Hot air expands and rises – Cold air contracts, becomes more dense, and contracts, becomes more dense, and sinkssinks

Coefficient of Linear ExpansionCoefficient of Linear Expansion– αα = = ΔΔL /LL /L11 ΔΔTT