Physics 1408-002
Principles of Physics
Lecture 24
– Chapter 13 –
October 27, 2008
Sung-Won Lee
Sungwon.Lee@ttu.edu
Chapter 13
Fluids
Announcements
Lecture notes
http://highenergy.phys.ttu.edu/~slee/1408/
SI Session (Mitchell Lowery)
No SI Session on Tue.
Thu. 4:30 – 6:00 pm @ Holden Hall 226
HW Assignment #6 (Ch11/12) is placed on
MateringPHYSICS, and is due by 11:59 PM
on Tuesday, 10/28
13-1 Phases of Matter
The three common phases of matter are solid,
liquid, and gas.
•!A solid has a definite shape and size.
•!Density and Specific Gravity
•!A liquid has a fixed volume but can be any shape
•!Pressure in Fluids
•!Atmospheric Pressure and Gauge Pressure & Measurement
•!A gas can be any shape and also can be easily
compressed.
•!Pascal’s Principle
Liquids and gases both flow, and are called fluids.
•!Buoyancy and Archimedes’ Principle
•!Fluids in Motion; Flow Rate and the Equation of Continuity
•!Bernoulli’s Equation & its Applications!
Fluids
•! A fluid is a collection of molecules that are randomly arranged and
held together by weak forces and by forces exerted by the walls of
a container.
•! Both liquids and gases are fluids.
Statics & Dynamics with Fluids
•! Fluid Statics
–! Describes fluids at rest.
•! Fluid Dynamics
–! Describes fluids in motion.
•! The same physical principles that have applied to statics and
dynamics will also apply to fluids.
13-2 Density and Specific Gravity
Example 13-1: Mass, given volume and
density.
13-2 Density & Specific Gravity
The density ! of a substance is its
mass per unit volume:
The SI unit for density: kg/m3.
Density is also sometimes given
in g/cm3; to convert g/cm3 to kg/m3,
multiply by 1000.
Water at 4°C has a density of
1 g/cm3 = 1000 kg/m3.
The specific gravity of a substance is
the ratio of its density to that of water.
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
What is the mass of a solid iron wrecking
ball of radius 18 cm?
•! Pressure is a scalar quantity
–! Because it is proportional to the magnitude of the force
•! If the pressure varies over an area,
evaluate dF on a surface of area(dA)
as dF = P dA
•! Unit of pressure: Pascal (Pa)
2
1 Pa = 1 N/m
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.
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.
•! 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
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 flow (i.e in
motion).
13-3 Pressure in Fluids
For a fluid at rest, there is also no component
of force parallel (i.e. Fll = 0) to any solid
surface of container—once again, if there
were, the fluid would flow.
13-3 Pressure in Fluids
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:
This relation is valid
for any liquid whose
density does not
change with depth.
Pressure and Depth
•! Since the net force must be zero (because the fluid is in static equilibrium)
13.3 Variation of P with Depth
•! 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 force on the top, P0A
–! Upward on the bottom, PA
–! Gravity acting downward, Mg
•! The mass can be found from the density:
Variation of pressure with depth
Density = Mass/Volume
!!= M / V
Units = kg/m3
–! 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
Feel it in your ears in a plane, in a pool!
13-3 Pressure in Fluids
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.
13-4 Atmospheric Pressure and
Gauge Pressure
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.
13-3 Pressure in Fluids
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.
13-4 Atmospheric Pressure and
Gauge Pressure
Most pressure gauges measure the pressure
above the atmospheric pressure —
this is called the gauge pressure.
Standard atmospheric pressure is just over 1 bar.
This pressure does not crush us, as our cells
maintain an internal pressure that balances it.
The absolute pressure is the sum of the
atmospheric pressure and the gauge pressure.
13.5 Pascal’s 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 Pascal’s law
0
P = P + !gh
•! Fig: A large output force can be
applied by means of a small input
force
•! The volume (A*"x) of liquid
pushed down on the left must
equal the volume pushed up
on the right
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
•! Since the volumes are equal
•! !Hg = density of the mercury (see table)
•! h = the height of the mercury column
A2/A1 = "x1/"x2
•! Combining the equations,
–!
which means (using W = F"x) W1 = W2
–! This is a consequence of Conservation of Energy
•! 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
Here are two more devices
for measuring pressure:
the aneroid gauge and the
tire pressure gauge.
Absolute vs. Gauge Pressure
•!P = P0 + !gh!
•! P: the absolute pressure !!!
The gauge pressure: P – P0 (= !gh)!
!!
!
This is what you measure !
! !
!
!
in your tires