Physics 201: Lecture 26, Pg 1

Lecture 26Goals: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.

Physics 201: Lecture 26, Pg 2

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

Increasing temperature

solid liquid gas

Physics 201: Lecture 26, Pg 3

Fluids

Fluids: Liquids or GasesShape 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

Physics 201: Lecture 26, Pg 4

Fluids

An intrinsic parameter of a fluid Density

V

m units :

kg/m3 = 10-3 g/cm3

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

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

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

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

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

Physics 201: Lecture 26, Pg 5

Fluids

nF ˆAP

Any force exerted by a fluid is perpendicular to a surface of contact, and is proportional to the area of that surface. Force (a vector) in a fluid can be expressed in terms

of pressure (a scalar) as:

A F

P 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)

A

n̂

Do not confuse pressure with momentum

Physics 201: Lecture 26, Pg 6

What is the SI unit of pressure?

A. PascalB. AtmosphereC. BernoulliD. YoungE. p.s.i.

Units : 1 N/m2 = 1 Pa (Pascal)1 bar = 105 Pa1 mbar = 102 Pa1 torr = 133.3 Pa

1 atm = 1.013 x105 Pa = 1013 mbar

= 760 Torr = 14.7 lb/ in2 (=PSI)

Physics 201: Lecture 26, Pg 7

A bed of nails

Distributing the force over a large area ….

Physics 201: Lecture 26, Pg 8

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

N )020.0(10atm1 252 rPAF

N 130F

J 260m 2 N 130 FdW

J 260221 mvW m/s 404v

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

Physics 201: Lecture 26, Pg 9

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 Gauge pressure (subtract P0) PGauge = P(y) - P0

Pressure vs. DepthIncompressible Fluids (liquids)

F2 = F1+ m g = F1+ VgF2 /A = F1/A + Vg/A

gy 12 PP

F2mg

P2

A

y2

y1

P1

F1

P0

Physics 201: Lecture 26, Pg 10

Pressure vs. Depth in water

Every 10 meters the pressure increases by 1 atm

gy 12 PP333

water kg/m 10gm/cm 0.1 2m/s 10g

2512 N/m 10PP

m 10y F2mg

P2

A

y2

y1

P1

F1

P0

Physics 201: Lecture 26, Pg 11

Pascal’s Principle

For a uniform fluid in an open container pressure same at a given depth independent of the container

p(y)

y

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

Physics 201: Lecture 26, Pg 12

Exercise

Does PA=PB?

A B

Physics 201: Lecture 26, Pg 13

Exercise Pressure

What happens with two fluids??

Consider a U tube containing liquids of density 1 and 2

as shown:

Compare the densities of the liquids:

(A) 1 < 2 (B) 1 = 2 (C) 1 > 2

1

2

dI

Physics 201: Lecture 26, Pg 14

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)

Physics 201: Lecture 26, Pg 15

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.

P1 = P2

F1 / A1 = F2 / A2

A2 / A1 = F2 / F1

F F

1

2

d

2d

1

A A21

P1

P2

1

212 AA

FF

Physics 201: Lecture 26, Pg 17

Archimedes’ Principle: A Eureka Moment

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

How do these weights compare?

W2?W1

W1 < W2 W1 = W2W1 > W2

Buoyant force = Weight of the fluid displaced

Physics 201: Lecture 26, Pg 19

Sink or Float?

The buoyant force is equal to 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.

F mgB

y

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

Object is in equilibrium mgFB

objectobjectliquidliquid VgVg

liquid

object

object

liquid

V

V

Physics 201: Lecture 26, Pg 20

Bar Trick

piece of rockon top of ice

What happens to the water level when the ice melts?

A. It rises B. It stays the same C. It drops

Expt. 1 Expt. 2

Physics 201: Lecture 26, Pg 21

Exercise

V1 = V2 = V3 = V4 = V5

m1 < m2 < m3 < m4 < m5

What is the final position of each block?

Physics 201: Lecture 26, Pg 22

Exercise

V1 = V2 = V3 = V4 = V5

m1 < m2 < m3 < m4 < m5

What is the final position of each block?

Not this But this

Physics 201: Lecture 26, Pg 28

For Tuesday

All of chapter 14