Warm-up
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Pick up the free response at the door and
begin working on it.
Do Now (10/24/13):
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What is Archimedes’ Principle?
What is Pascal’s Principle?
What is the buoyant force?
Objectives
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Define fluids.
Discuss and apply density principles.
Describe pressure and its measurement in
fluids.
Apply Pascal’s Principle.
Discuss buoyancy.
Describe and apply fluid flow continuity.
Discuss Bernoulli’s Equation.
Today’s Plan
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Discuss waves test
Discuss fluids
FR due tomorrow.
Test redo due Thursday 4/26.
Homework due Thursday 4/26.
Next Test Friday 4/27.
Fluids
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Characterized by ability to flow.
Gases and liquids.
Liquids: assumes shape of its container
but is not readily compressible
Gas: expands to fill container and is
compressible.
Density and Specific Gravity
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Density: mass per unit volume ()
Microscopically based on molecular size
and spacing between molecules.
Macroscopically based on solidity of
object.
Specific gravity: ratio of its density to that
of water at 4°C (1000 kg/m3)
Pressure
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Pressure = Force / Area
Measured in Pascals (Pa) = N/m2
Also reported in atmospheres, psi,
millibars
Fluids exert pressure in all directions.
P= gh
Practice Problem
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A vertical force of 30 N is applied uniformly to a
flat button with a radius of 1 cm that is lying on a
table. Which of the following is the best order of
magnitude estimate for the pressure applied to
the button?
(A) 10 Pa
(B) 102 Pa
(C) 103 Pa
(D) 104 Pa
(E) 105 Pa
Atmospheric Pressure
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Pressure due to the weight of air.
At sea level, 1.013 x 105 Pa.
Equates to 1.0 x 105 N per square meter
of surface area.
Differences in pressure are more
important than absolute pressure.
Practice Problem
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The surface of the water in a storage tank
is 30m above a water faucet in the kitchen
of a house. Calculate the water pressure
at the faucet.
Gauge Pressure
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Most gauges are calibrated so zero is
atmospheric pressure.
Add atmospheric pressure to gauge
pressure for absolute pressure readings.
Practice Problem
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If the gauge pressure of a device reads
2.026x105 N/m2, the absolute pressure it is
measuring is what?
Pascal’s Principle
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Pressure applied to an enclosed fluid is
transmitted undiminished to every part of
the fluid and to the walls of the container.
Hydraulic lifts—small force applied to
small area piston transformed to large
force at large-area piston.
Pascal’s Principle
Pascal’s Principle
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P1 = P2
F1/A1 = F2/A2
Though the force applied is less than the
force out, work is the same. (W=Fxd)
Measuring Pressure
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Manometers
Barometers
Maximum height of a column of water
Buoyancy and Archimedes
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Buoyancy force makes objects submerged
in a fluid appear to weigh less than they
do outside the fluid.
Buoyant force due to increase of pressure
in a fluid with depth. Upward pressure on
bottom surface is greater than downward
pressure on top.
Buoyancy and Archimedes
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Buoyant force equals weight of fluid
displaced by object.
 FB
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=( fluid)(Vdisplaced )g
Objects float when their density is less
than that of the fluid.
Practice
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A ball that can float on water has mass 5.00 kg
and volume 2.50 x 10-2 m3 . What is the
magnitude of the downward force that must be
applied to the ball to hold it motionless and
completely submerged in freshwater of density
1.00x103 kg/m3 ?
(A) 20.0 N
(B) 25.0 N
(C) 30.0 N
(D) 200 N
(E) 250 N
Do Now (10/25/13):
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Calculate the absolute pressure at an
ocean depth of 1000 m. Assume that the
density of water is 1x103 kg/m3.
Buoyancy and Archimedes
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A basketball floats in a tub of water. The
ball has mass of 0.5 kg and diameter of 22
cm. What is the buoyant force? What is
the volume of water displaced by the ball?
What is the average density of the
basketball?
Moving Fluids
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Laminar flow: steady velocity with
neighboring layers sliding by each other.
Turbulent flow: speed and or direction of
flow varies with erratic eddy currents
present.
Continuity Equation
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Mass flow rate in a tube of varying cross-section
remains constant in an incompressible fluid.
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(m/ t) =( V/ t) = A l/t = Av
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1A1v1 = 2A2v2
Continuity Equation
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Where cross-sectional area is large the
velocity is small; where area is small, the
velocity is large.
Fluid Flow Continuity
Straightstream flow
Curvestream flow
Practice Problem
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Water flows through the pipe shown
above. At the larger end, the pipe has
diameter D and the speed of the water is
v1 . What is the speed of the water at the
smaller end, where the pipe has diameter
d?
Making Fluids Flow
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Gravitational Potential Energy differences
Pressure differences
Bernoulli’s Equation relates pressure,
velocity, and height in a fluid.
Bernoulli’s Equation
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P1 + 1/2 v12 + gh1 = P2 + 1/2 v22 +
gh2
The difference in pressure does work to
change kinetic energy/potential energy of
the fluid.
Bernoulli’s Implications
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Where fluid velocity is high, pressure is
low.
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Curveballs
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Airplane wings