outline - los rios community college districtalmarazr/s19-ps300/ppts/fluid_mecha_v1.pdftimes as much...

2/20/2019

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Conceptual

Physical

Science6th Edition

Chapter 5:

FLUID MECHANICS

Outline

• Density• Pressure• Buoyancy in a Liquid• Archimedes’ Principle• Pressure in a Gas• Atmospheric Pressure• Pascal’s Principle• Bernoulli’s Principle

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Fluid Mechanics

Blood pump

Ventricular assist device

Air pollution

River hydraulics

SubmarinesSurface ships

Density

Density

• Important property of materials (solids, liquids, gases)

• Measure of compactness of how much mass an object occupies

• “lightness” or “heaviness” of materials of the same size

• Equation :– Units of:

• mass in grams or kilograms

• volume in cm3 or m3

• density in kg/m3 or g/cm3

Example: The density of mercury is 13.6 g/cm3, so mercury has 13.6 times as much mass as an equal volume of water (density 1 g/cm3).

density = massvolume

D V

m

Density

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Pressure

• force per unit area that one object exerts on another

• equation:

•

• depends on area over which force is distributed

• units in lb/ft2, N/m2, or Pa (Pascals)

• Other units: atm, Torr, mmHg

P A

F

Pressure

Pressure =𝐹𝑜𝑟𝑐𝑒 (𝑁)

𝐴𝑟𝑒𝑎 (𝑚2)

Gases::: Physical variables

Physical Characteristics Typical Units

Volume, V liters (L)

Pressure, P

atmosphere

(1 atm = 760 torr =1.015x105 N/m2Pa

(Pascals) )

Temperature, T Kelvin (K)

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Pressure in a Liquid

• Independent of shape of container

whatever the shape of a container, pressure at any particular depth is the same

• Equation:

liquid pressure = weight density depth

Water Tower

• Force of gravity acting on the water in a tall tower produces pressure in pipes below that supply many homes with reliable water pressure.

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Archimedes’ Principle


discovered by Greek scientist Archimedes

relates buoyancy to displaced liquid

states that an immersed body (completely or partially) is buoyed up by a force equal to the weight of the fluid it displaces applies to gases and liquids.

Archimedes of Syracuse287 BCGreek mathematician, physicist, engineer, inventor, and astronomer.


• Displacement rule: A completely submerged object always displaces a volume of liquid equal to its own volume.

Example: Place a stone in a container that is brim-full of water, and the amount of water overflow equals the volume of the stone

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ml6

5

4

3

2

1

3 ml

Archimedes Principle

Displacement rule:

A completely submerged object always displaces a

volume of liquid equal to its own volume.

3 ml

6 mlm

l6

5

4

3

2

1

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Buoyancy in a Liquid

F F F

F F F

F F

𝐹𝑛𝑒𝑡 = 𝐵𝑜𝑢𝑦𝑎𝑛𝑐𝑦 𝑓𝑜𝑟𝑐𝑒

• An immersed object is buoyed up by force equal to the weight of the fluid it displaced.

Buoyancy in a Liquid

Buoyancy • apparent loss of weight of a submerged object

• amount equals the weight of water displaced

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Apparent weight of a submerged object• weight out of water – buoyant force

Example: if a 3-kg block submerged in water apparently “weighs” 1 kg, then the buoyant force or weight of water displaced is 2 kg

(BF = wt out of water – apparent wt = 3 kg – 1 kg = 2 kg)

Archimedes’ Principle-Flotation

Flotation• Principle of flotation

– A floating object displaces a weight of fluid equal to its own weightExample: A solid iron 1-ton block may displace 1/8 ton of water

and sink. The same 1 ton of iron in a bowl shape displaces a greater volume of water—the greater buoyant force allows it to float

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Buoyancy in a Gas

• Archimedes’ principle applies to fluids—liquids and gases alike.

• Force of air on bottom of balloon is greater than force on top.

• Net horizontal forces cancel, but not vertical ones, which supplies the buoyant force.

• And this buoyant force equals the weight of displaced air!

Is there a buoyant force acting on your classmates at this moment? Defend your answer.

A. No. If there were, they would float upward.

B. Yes, but it is insignificant compared with their weights.

C. Only in water, but not in air.

D. None of these.

Buoyant Force

CHECK YOUR NEIGHBOR

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The reason a person finds it easier to float in salt water, compared with fresh water, is that in salt water

A. the buoyant force is greater.

B. a person feels less heavy.

C. a smaller volume of water is displaced.

D. None of the above.


CHECK YOUR NEIGHBOR


CHECK YOUR ANSWER

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❖ Pressure and volume are inversely related at constant temperature.

❖ PV = K

❖ As one goes up, the other goes down.

❖ P1V1 = P2V2

Boyle’s Law

Robert BoyleChemist & Natural Philosopher

Listmore, Ireland

January 25, 1627 – December 30, 1690

Pressure in a Gas

• Gas pressure is a measure of the amount of force per area that a gas exerts against containing walls.

• Here the force is exerted by the motion of molecules bouncing around.

• Temperature is a measure of the KE per molecules of the gas.

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Boyle’s Law: Robert Boyle (1627–1691)

• Robert Boyle and Robert Hooke used a J-tube to measure the volume of a sample of gas at different pressures.

• They trapped a sample of air in the J-tube and added mercury to increase the pressure on the gas.

✓He observed an inverse relationship between volume

and pressure.

✓Hence, an increase in one causes a decrease in

the other.

A Sample of Boyle’s Observations

Moles and temperature of gas are constant

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• We can also rearrange it to PV = k.

P1V1 = k

P1V1 = P2V2

Boyle’s Law

y = mx + b.

V vs P V vs 1/P

Graphs of Boyle’s Observations

V∝ 1 .P

↑V ↓P V = k 1 .P

+ 0 .

P2V2 = k

Molecular Interpretation of Boyle’s Law

As the volume of a gas sample is decreased, gas molecules collide

with surrounding surfaces more frequently, resulting in greater

pressure.

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Boyle’s Law Problem

• A 3.50 L sample of methane gas exerts a pressure of 1550 mm Hg. What is the final pressure if the volume changes to 7.00 L?

P1V1 = P2V2

When you squeeze a party balloon to 0.8 its volume, the pressure in the balloon

A. is 0.8 its former pressure.

B. remains the same if you squeeze it slowly.

C. is 1.25 times greater.

D. is 8 times greater.

Pressure in a Gas

CHECK YOUR NEIGHBOR

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Atmospheric Pressure

Atmospheric pressure• Caused by weight of air• Varies from one locality to

another• Not uniform• Measurements are used to

predict weather conditions

Atmospheric Pressure• Pressure exerted against bodies immersed in the

atmosphere result from the weight of air pressing from above

• At sea level is 101 kilopascals(101 kPa)

• Weight of air pressing down on 1 m2 at sea level ~ 100,000 N, so atmospheric pressure is ~ 105 N/m2

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• Pressure at the bottom of a column of air reaching to the top of the atmosphere is the same as the pressure at the bottom of a column of water 10.3 m high.

• Consequence: the highest the atmosphere can push water up into a vacuum pump is 10.3 m

• Mechanical pumps that don’t depend on atmospheric pressure don’t have the 10.3-m limit

Two people are drinking soda using straws. Do they suck the soda up? Could they drink a soda this way on the Moon?


CHECK YOUR NEIGHBOR

A. Yes and yes.B. No, they suck the air out and the

atmospheric pressure pushes the soda up. Yes, they could do the same thing on the Moon.

C. No, they reduce air pressure in the straw and the atmospheric pressure pushes the soda up. No, they could not do the same thing on the Moon.

D. Yes. No, they could not do the same thing on the Moon.

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• Pascal’s Principle states that a change in pressure at any point in an enclosed fluid at rest is transmitted undiminished toall points in the fluid

•Applies to all fluids—gasesand liquids

Pascal’s Principle

Blaise Pascal Scientist and theologian

in the 17th century


• Application in hydraulic press

Example:– Pressure applied to the left piston is transmitted to

the right piston

– A 10-kg load on small piston (left) lifts a load of 500 kg on large piston (right)

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A 10-kg load on the left piston will support a 500-kg load on the right piston. How does the pressure of fluid against the lower part of the left piston compare with the pressure against the lower right piston?

A. More pressure on the left piston.

B. More pressure on the right piston.

C. Same pressure on each.

D. Same force on each.


CHECK YOUR NEIGHBOR


• Application for gases and liquids– seen in everyday hydraulic devices used in

construction– in auto lifts in service stations

• increased air pressure produced by an air compressor is transmitted through the air to thesurface of oil in anunderground reservoir.The oil transmits thepressure to the piston,which lifts the auto.

(Here surface area of reservoir is irrelevant.)

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Fluid FlowContinuous flow• Volume of fluid that flows past any cross-

section of a pipe in a given time is the same as that flowing past any other section of the pipe even if the pipe widens or narrows.

• Fluid speeds up when it flows from a wide to narrow pipe

• Motion of fluid follows imaginary streamlines

❖ In fluid dynamics,

Bernoulli's principle states that

an increase in the speed of a

fluid occurs simultaneously

with a decrease in pressure or a

decrease in the fluid's potential

energy.

Bernoulli’s Principle

Daniel BernoulliMathematician, Physicist, Inventor

Swiss

8 Feb, 1700 – March 17, 1782

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Streamlines• Thin lines representing fluid motion

• Closer together, flow speed is greater and pressure within the fluid is less (note the larger bubbles!)

• Wider, flow speed is less and pressure within the fluid is greater (greater pressure squeezes bubbles smaller)

What happens to the internal water pressure in a narrowing pipe of moving water?

A. Pressure is higher.

B. Pressure remains unchanged.

C. Pressure is less.

D. None of these.


CHECK YOUR NEIGHBOR

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Applications of Bernoulli• Moving air gains speed

above the roof of a house. This change in air velocity means reduced pressure on the roof.

• Therefore, air pressure inside the house is greater, which can raise the roof.

The pressure in a stream of water is reduced as the stream speeds up. How then can a stream of water from a fire hose actually knock a person off his or her feet?

A. It can’t, as Bernoulli’s principle illustrates.

B. The pressure due to water’s change in momentum can be much greater than the water’s internal pressure.

C. Bernoulli’s principle works only for laminar flow, which the stream is not.

D. None of the above.

Bernoulli Application

CHECK YOUR NEIGHBOR

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Airplane wing• The vertical vector

represents the net upward force (lift) that results from more air pressure below the wing than above the wing.

• The horizontal vector represents the air drag force.

Air speeds up as it is blown across the top of the vertical tube. How does this affect the air pressure in the vertical tube, and what then occurs?

A. The air jet pulls liquid up the tube.

B. Liquid mysteriously rises in the tube.

C. Reduced air pressure in the tube (due to Bernoulli) lets atmospheric pressure on the liquid surface push liquid up into the tube where it joins the jet of air in a mist.

D. Liquid in the vessel somehow turns to mist.

Bernoulli Application

CHECK YOUR NEIGHBOR

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Bernoulli Boats

• When the speed of water increases between boats, Bernoulli must be compensated for or else the boats collide!

Bernoulli Umbrella

• Why does Nellie Newton blame Bernoulli for her predicament?

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• Displacement rule:

A completely submerged object always displaces a volume of liquid equal to its own volume.

• Buoyant force:Apparent weight of a submerged objectweight out of water = buoyant force

P A

F

Pressureunits in lb/ft2, N/m2, or Pa (Pascals) Other units: atm, Torr, mmHg

Summary

Pressure =𝐹𝑜𝑟𝑐𝑒 (𝑁)

𝐴𝑟𝑒𝑎 (𝑚2)

Boyle’s Law P1V1 = P2V2 = constant

❖ Pressure and volume are inversely related at constant temperature.


• Pascal’s Principle states that a change in pressure at any point in an enclosed fluid at rest is transmitted undiminished toall points in the fluid

•Applies to all fluids—gases and liquids

1P

2

2

A

F

1

1

A

F

2P𝑃1 = 𝑃2

𝐹1

𝐴1=

𝐹2

𝐴2= constant

Bernoulli’s Principle❖ In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.

v vP P

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outline - los rios community college districtalmarazr/s19-ps300/ppts/fluid_mecha_v1.pdftimes as much...

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