Lecture 26
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Lecture 26. Goals:. U nderstand pressure in liquids Use Archimedes’ principle to understand buoyancy Understand the equation of continuity Use an ideal-fluid model to study fluid flow. Fluids. At ordinary temperatures, matter exists in one of three states

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Lecture 26

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Lecture 26

Lecture 26

Goals:

  • Understand pressure in liquids

    • Use Archimedes’ principle to understand buoyancy

    • Understand the equation of continuity

    • Use an ideal-fluid model to study fluid flow.


Fluids

Fluids

  • At ordinary temperatures, matter exists in one of three states

    • Solid: Has a shape and forms a surface

    • Liquid: Has no shape but forms a surface

    • Gas : No shape and does not form a surface

gas

liquid

solid

Increasing temperature


Fluids1

Fluids

  • Fluids: Liquids or Gases

    • Shape determined by container

    • Close contact at boundaries. No macroscopic gaps

    • Forces exerted by fluids are always normal to the surface.

    • Fluids can flow

  • Fluids:

    • They have mass

    • They have weight

    • They carry energy

    • They have velocity when flow

    • Newton’s Laws apply


Fluids2

Fluids

  • An intrinsic parameter of a fluid

    • Density

units :

kg/m3 = 10-3 g/cm3

r(water) = 1.000 x 103 kg/m3 = 1.000 g/cm3

r(ice) = 0.917 x 103 kg/m3 = 0.917 g/cm3

r(air) = 1.29 kg/m3 = 1.29 x 10-3 g/cm3

r(Hg) = 13.6 x103 kg/m3 = 13.6 g/cm3

r(W or Au) = 19.3 x103 kg/m3 = 19.3 g/cm3


Fluids3

A

Fluids

  • Another parameter: Pressure

    • A Fluid exerts force on the objects it contacts

    • Molecules constantly bounces off the surface with F =Σ(Δmv/Δt) (momentum transfer / time)

  • Any force exerted by a fluid is perpendicular to a surface of contact, and is proportional to the area of that surface.

    • Force (avector) in a fluid can be expressed in terms of pressure (a scalar) as:

Do not confuse pressure with momentum


Lecture 26

What is the SI unit of pressure?

  • Pascal

  • Atmosphere

  • Bernoulli

  • Young

  • p.s.i.

Units :

1 N/m2 = 1 Pa (Pascal)

1 bar = 105 Pa

1 mbar = 102 Pa

1 torr = 133.3 Pa

1 atm = 1.013 x105 Pa

= 1013 mbar

= 760 Torr

= 14.7 lb/ in2 (=PSI)


A bed of nails

A bed of nails

  • Distributing the force over a large area ….


Ping pong ball bazooka

Ping pong ball bazooka

  • What is the initial force on the ping pong ball?

  • Assuming this force is constant, how fast is the ping pong ball travelling when it leaves the tube?

F

This is a crude model….the speed of sound in air is 330 m/s


Pressure vs depth incompressible fluids liquids

P0

F1

y1

y2

P1

A

P2

mg

F2

Pressure vs. DepthIncompressible Fluids (liquids)

  • When the pressure is small, relative to the bulk modulus of the fluid, we can treat the density as constant independent of pressure:

    incompressible fluid

  • For an incompressible fluid, the density is the same everywhere, but the pressure is NOT!

  • P(y) = P0 - y g r

  • Gauge pressure (subtract P0)

  • PGauge = P(y) - P0

F2 = F1+ m g

= F1+ rVg

F2 /A = F1/A + rVg/A


Pressure vs depth in water

P0

F1

y1

y2

P1

A

P2

mg

F2

Pressure vs. Depth in water

Every 10 meters the pressure increases by 1 atm


Pascal s principle

Pascal’s Principle

  • For a uniform fluid in an open container pressure same at a given depthindependentof the container

  • Fluid level is the same everywhere in a connected container, assuming no surface forces


Exercise

Exercise

  • Does PA=PB?

B

A


Exercise pressure

(A)r1 < r2

(B)r1 = r2

(C)r1>r2

Exercise Pressure

  • What happens with two fluids??

  • Consider a U tube containing liquids of density r1 and r2 as shown:

    Compare the densities of the liquids:

dI

r2

r1


Pressure measurements barometer

Pressure Measurements: Barometer

  • Invented by Torricelli

  • A long closed tube is filled with mercury and inverted in a dish of mercury

    • The closed end is nearly a vacuum

    • PA=PB

  • Measures atmospheric pressure as

    1 atm = 0.760 m (of Hg)


Pascal s principle in action hydraulics a force amplifier

Pascal’s Principle in action: Hydraulics, a force amplifier

  • Consider the system shown:

    • A downward force F1 is applied to the piston of area A1.

    • This force is transmitted through the liquid to create an upward force F2.

    • Pascal’s Principle says that increased pressure from F1 (F1/A1) is transmitted throughout the liquid.

P2

P1

P1 = P2

F1 / A1 = F2 / A2

A2 / A1 = F2 / F1


Archimedes principle a eureka moment

W2?

W1

W1 > W2

W1 < W2

W1 = W2

Archimedes’ Principle: A Eureka Moment

  • Suppose we weigh an object in air (1) and in water (2).

    How do these weights compare?

  • Buoyant force = Weight of the fluid displaced


Sink or float

y

F

mg

B

Sink or Float?

  • The buoyant force is equalto the weight of the liquid that is displaced.

  • If the buoyant force is larger than the weight of the object, it will float; otherwise it will sink.

  • We can calculate how much of a floating object will be submerged in the liquid:

  • Object is in equilibrium


Bar trick

piece of rock

on top of ice

Bar Trick

What happens to the water level when the ice melts?

Expt. 1

Expt. 2

B. It stays the same

C. It drops

A. It rises


Exercise1

Exercise

V1 = V2 = V3 = V4 = V5

m1 < m2 < m3 < m4 < m5

What is the final position of each block?


Exercise2

Exercise

V1 = V2 = V3 = V4 = V5

m1 < m2 < m3 < m4 < m5

What is the final position of each block?

But this

Not this


For tuesday

For Tuesday

  • All of chapter 14


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