Physics

Physics 1408-002 Principles of Physics

Sung-Won Lee

[email protected]

Lecture 21

Chapter 13

April 2, 2009

Announcement I Lecture note is on the web

Handout (6 slides/page) http://highenergy.phys.ttu.edu/~slee/1408/

*** Class attendance is strongly encouraged and will be

taken randomly. Also it will be used for extra credits.

HW Assignment #8 will be placed on

MateringPHYSICS, and is due by

11:59pm on Wednesday, 4/**

Announcements II

3rd Exam

4/9 Thursday (Next week) 9: 30 am 10:50 am

Chapters 10, 11, 12, 13 Rotation motion, Angular momentum, Statics,

Fluids

Announcement III SI session by

Reginald Tuvilla

Thursday 4:00 - 5:30pm - Holden Hall 106

Next week, test review will be on Monday

04/06 in the BA room 55 from 4:30 - 7:30.

Chapter 13

Fluids

! Density and Specific Gravity

! Pressure in Fluids

! Atmospheric Pressure and Gauge Pressure & Measurement

! Pascals Principle

! Buoyancy and Archimedes Principle

!Fluids in Motion; Flow Rate and the Equation of Continuity

! Bernoullis Equation & its Applications!

13.3 Pressure

! The pressure P of the fluid at the level

to which the device has been submerged

is the ratio of the force to the area

! Pressure is a scalar quantity

! Because it is proportional to the magnitude of the force

! If the pressure P varies over an area A,

evaluate !F(=dF) on a surface of area !A(=dA)

as dF = P dA

! Unit of pressure: Pascal (Pa)

1 Pa = 1 N/m2

Pressure vs. Force

! Pressure is a scalar and force is a vector.

! The direction of the force producing a pressure is

perpendicular to the area of interest.

Measuring Pressure

! The spring is calibrated by a known force.

! The force due to the fluid presses on the top of the piston and compresses the spring.

! The pressure on the piston is then measured.

13-3 Pressure in Fluids

Example 13-2: Calculating pressure.

The two feet of a 60-kg person cover an

area of 500 cm2.

Determine the pressure exerted by the two

feet on the ground.


Pressure is the same in every direction in a

static (i.e. non-moving) fluid at a given depth;

if it were not true, the fluid would be flow in

motion.

If there were a component of force parallel to

the solid surface of the container, the liquid

would move in response to it.

For a liquid at rest,

there is no component of force parallel

(i.e. Fll = 0) surface of

container


The pressure at a depth h below the surface of the

liquid is due to the weight of the liquid above it.

We can quickly calculate the pressure at a depth h

in a liquid:

This relation is valid

for any liquid whose

density does not

change with depth.


F = Mg = "Ahg

13.3 Variation of P with Depth h ! Fluids have pressure that varies with depth.

! If a fluid is at rest in a container, all portions of the fluid must be

in static equilibrium.

! Examine the darker region, a sample of liquid within a cylinder

! It has a cross-sectional area A

! Extends from depth d to d + h below the surface

! Three external forces (F = PA) act on the region

! The liquid has a density !

! Assume the density is the same throughout the fluid

! The three forces are:

! Downward (- sign) force on the top, P0A

! Upward (+ sign) on the bottom, PA

! Gravity acting downward, Mg

! The mass can be found from the density:

! Since the net force must be zero (because the fluid is in static equilibrium)

! This chooses upward as positive

! Solving for the pressure gives

P = P0 + !gh ! The pressure P at a depth h below a point

in the liquid at which the pressure is P0

is greater by an amount !gh

! If the liquid is open to the atmosphere, and P0 is

the pressure at the surface of the liquid, then P0 is

atmospheric pressure

! P0 = 1.00 atm = 1.013 x 105 Pa (REMEMBER!!)

13.3 Variation of P with Depth h

= 0

Variation of pressure with depth

Feel it in your ears in a plane, in a pool!

Density = Mass/Volume

"!= M / V

Units = kg/m3


The surface of the water in a storage

tank is 30 m above a water faucet in

the kitchen of a house. Calculate the difference in water pressure between

the faucet and the surface of the

water in the tank.


Calculate the force due to water pressure exerted on

a 1.0 m x 3.0 m aquarium viewing window whose top

edge is 1.0 m below the water surface.

At sea level the atmospheric pressure is about 1.013 x

105 N/m2; this is called 1 atmosphere (atm).

Another unit of pressure is the bar:

1 bar = 1.00 x 105 N/m2.

Standard atmospheric pressure is just over 1 bar.

13-4 Atmospheric Pressure and

Gauge Pressure

Most pressure gauges measure the pressure

above the atmospheric pressure

this is called the gauge pressure.

The absolute pressure is the sum of the

atmospheric pressure and the gauge pressure.

13-4 Atmospheric Pressure and Gauge

Pressure

Absolute vs. Gauge Pressure

!P = P0 + "gh ! P: the absolute pressure !!

! P0: the atmospheric pressure!!

The gauge pressure: P P0 (= "gh)

This is what you measure

in your tires

13.5 Pascals Law

! The pressure in a fluid depends on depth & on the value of P0

! An increase in pressure at the surface must be transmitted to every

other point in the fluid

! This is the basis of Pascals law P = P0 + !gh ! Fig: A large output force can be

applied by means of a small input force

! The volume (A1*!x1) of liquid pushed down on the left must equal the volume pushed up on the right (A2*!x2)

! Since the volumes are equal

! Combining the equations,

! which means (using W = F!x), W1 = W2

!This is a consequence of Conservation of Energy

A2/A1 = "x1/"x2

13.6 Pressure Measurements: Barometer

! Invented by Torricelli to measure atmospheric

pressure.

! A long closed tube is filled with mercury and

inverted in a dish of mercury

! The closed end is nearly a vacuum

! He measures atmospheric pressure as

! !Hg = density of the mercury (see table)

! h = the height of the mercury column

! Let us determine the h for one atmosphere of

pressure, p0 = 1 atm = 1.013 x 105 Pa:

==> h = p0 / !Hg g = 0.706 m

13.6 Pressure Measurements: Manometer

! A device for measuring the pressure

of a gas contained in a vessel

! One end of the U-shaped tube is

open to the atmosphere

! The other end is connected to

the pressure to be measured

! Pressure @ B =

P0+!gh

Reminder: P = P0 + !gh

13-6 Measurement of Pressure; Gauges

and the Barometer

Pressure is measured in a variety of different

units. This table gives the conversion factors.

! The beach ball is in equilibrium, there must be an upward force to balance the downward force!

Q: Have you ever tried to push beach ball under water? !

A: Extremely difficult to do because of the large upward force exerted by the water on the ball. !

! The upward force, B, must equal (in magnitude) the downward gravitational force, Fg!

! The upward force is called the buoyant force!

13.7 Buoyant Force

This is an object submerged in a fluid. There is a

net force on the object because the pressures at

the top and bottom of it are different.

The buoyant force, FB, is

found to be the upward

force on the same volume

of water:

13-7 Buoyancy and Archimedes Principle 13-7 Buoyancy and Archimedes Principle

Archimedes principle:

The buoyant force on an object immersed in

a fluid is equal to the weight of the fluid

displaced by that object.

13-7 Buoyancy and Archimedes Principle

A 70-kg ancient statue lies at the

bottom of the sea. Its volume is 3.0

x 104 cm3. How much force is

needed to lift it?

Archimedes's Principle

! Before we proceed with a few examples, it is instructive for us to discuss about two common situations!

! A totally submerged object!

! A floating (partly submerged) object

Archimedes's Principle: "Totally Submerged Object

! When an object is totally submerged in a fluid of density!

the magnitude of upward buoyant force is !

! If the object has mass M and density, "obj , the downward gravitational force is !

! !

Fg = w = Mg =!

! So, the net force: B - Fg = !

volume of object!

! If the density of the object is less than the density of the fluid, (light object) the unsupported object accelerates upward!

! If the density of the object is more than the density of the fluid, (heavy object) the unsupported object sinks!

! The motion of an object in a fluid is determined by the densities of the fluid and the object!

Archimedes's Principle: "Totally Submerged Object

! Now consider an object of volume Vobj and density "obj < "fluid in static equilibrium - partially submerged (see Fig)!

! The upward buoyant force is balanced by the downward force of gravity: Fg = B!

! The following equation is tell us that the fraction of volume of a floating object is equal to the ratio of the density of the object to that of the fluid. !

Archimedes's Principle: "Floating Object

If an objects density is less than that of water,

there will be an upward net force on it, and it will

rise until it is partially out of the water.

13-7 Buoyancy and Archimedes Principle

(a) The fully submerged log accelerates upward because

FB > mg. It comes to equilibrium (b) when !F = 0, so FB =

mg = (1200kg)g. Thus 1200 kg, or 1.2 m3, of water is displaced.

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