Survey $150 !!!

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Survey 150 !!!

• The Faculty of Science is conducting an online
  survey to help us better
• understand your educational and career goals, and
  your views on how well
• your undergraduate program is helping you reach
  those goals. Faculty of
• Science students will find the survey at
• http//iserv.mcmaster.ca/science/survey.htm
• and it will be available until April 23rd.
• The survey will take about 5 minutes to complete,
  and the department
• will be awarding 150 Titles gift certificates to
  two students who complete
• the survey. Your input as a Science student will
  help us ensure that the
• quality of undergraduate education in the Faculty
  of Science is as high as
• we can make it.

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Fluid Mechanics

• Pressure
• Pascals Law
• Pressure and Gravity
• Buoyancy

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Fluids

• Includes liquids and gases. No resistance to
  shear (changes in shape), in equilibrium.
• To describe mechanics of a continous fluid
  (instead of a discrete object), we use density,
  pressure instead of mass and force.
• Dynamics is approached from an energy perspective
  (Bernoullis equationnext lecture) .

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Density
Density, r (rho), is mass per unit volume
(kg/m3). Specific Gravity (SG) is the ratio
(density of substance)/(density of
water), which is a pure number (no units).
Substance r SG water 1000 kg/m3
1 mercury 13600 kg/m3 13.6
air 1.29 kg/m3 0.00129
helium 0.18 kg/m3 0.00018
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Pressure
P ? force per unit area unit 1 N/m2
1 pascal (Pa) Also, 1 atmosphere (atm)
101.3 kPa
Pressure is a scalar property of the fluid the
force is always exerted perpendicular to the
surface in contact with the fluid.
Forces exerted by the fluid
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Pascals Law Pressure in an enclosed fluid in
equilibrium is the same everywhere, except for
differences due to gravity. Or, pressure changes
are transmitted throughout a fluid in equilibrium
without loss there is no static friction in
fluids.
push here
Pressure increases here as well
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Example How hard do you need to push to lift a
cement truck (weight w 200 kN)?
w
piston, radius 100mm
F1 ?
piston, radius 5mm
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Pressure variation with depth
Pressure increases with depth, by an amount P2
P1 r gh (if r and g are uniform).
P1
h
Proof Consider forces on a cylinder of fluid
P2
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Gauge Pressure pressure difference between a
fluid and the surrounding atmosphere. It is
equal to P2P1. Example a tire gauge measures
gauge pressure, and reads zero when the air
inside the tire is at atmospheric pressure.
Absolute Pressure is the pressure compared to
vacuum. Zero absolute pressure means a vacuum.
Example the pressure on the surface of the
earth.
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ExampleAt what depth in water is the pressure 1
atm higher than the pressure on the surface?
That is, where is P2atms ?
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ExampleWhat is the difference in air pressure
between the floor and the ceiling?
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ExampleWhat is the total mass of air directly
above a 1-metre square, from ground level all the
way to outer space? Approximately how
thick is the atmosphere, assuming (incorrectly)
that the air density is uniform?