Chapter 14FluidsPart 1

What is a fluid• A substance that can flow

• Liquids (difficult to compress)• Gases (easy to compress)

• Basic properties:• Fluids take the form of the container.• When shear stress is applied they flow.• The molecules in fluids are in constant random

motion (Brownian motion).• The field of science that describes the

fluid motion is called “Fluid Mechanics”

Density

• Mass per unit volume.• Unit kg/m3.• The density can be different at each

point of the fluid.• An object is uniform if the density is

constant at any point of the body• A fluid is incompressible if the density

does not change as a result of an appliedpressure.

!

" =#m

#V

Some examples

• Interstellar space 10-20 kg/m3

• Laboratory vacuum 10-17 kg/m3

• Air (1 atm 20C) 1.21 kg/m3

• Ice 0.917x103 kg/m3

• Water 0.998x103 kg/m3

• Seawater 1.024x103 kg/m3

• Earth 5.5x103 kg/m3

• Neutron star 1018 kg/m3

Pressure

• Force per unit area (the force is perpendicular tothe surface)

• Scalar: the pressure has the same value in alldirections!

• Units: 1Pa=1N/1m2.• Other popular units 1 atm = 1 bar = 1.01x105 Pa = 760 torr = 14.7 lb/in2

!

p ="F

"A

Some Examples

• Sea level atm. pressure 105 Pa• Bottom of the ocean 1.1x108 Pa• Center of the Earth 4x1011 Pa• Center of the Sun 2x1016 Pa

Fluids at rest• Static equilibrium

!

F2

= F1+ mg

!

F1

= p1A F

2= p

2A

!

p2A = p

2A + "Vg

!

V = A(y1" y

2)

!

p2

= p1

+ "g(y1# y

2)

!

p = p0

+ "gh Hydrostatic pressure

Gauge pressure

• Absolute pressure = total pressure• Gauge pressure = total - atmospheric• The atmospheric pressure on the free surface

of a liquid is often neglected.

!

pgauge = "gh

Measuring pressure

• Mercury barometer:measures theatmospheric pressure.

• Open tube manometer:measures the gaugepressure of a gas.

!

pg = p " p0

= #gh

!

p0

= "gh

Sample problem

• What gauge pressure must a machine produceto suck mud of density 1800 kg/m3 up a tubeby a height of 1.5 m?

mud

p

h pa

!

pg = p " pa

pa = p + #gh

pg = "#gh = "2.6 $104Pa

HITT question

• The figure shows four containers of oliveoil. For which container the pressure atdepth h is greatest?

1) A 2) B 3) C 4) D 5) it is the same for all cases

Pascal’s Principle

• A change in the pressure appliedto an enclosed incompressiblefluid is transmitted undiminishedto every portion of the fluid andto the walls of the container.

!

"p = "pext

Hydraulic Lever• An input force applied over a

distance is transformed intobigger force over a shorterdistance

• The work done by the input forceand the output force is the same!!

"p =Fi

Ai

=Fo

Ao

!

Fo

= Fi

Ao

Ai

> Fi

!

V = Aidi= A

odo

!

W = Fodo

= doFi

Ao

Ai

= doFi

di

do

= Fidi