Fluid Mechanics and Energy Transport BIEN 301 Lecture 4 Pressure Distribution, Hydrostatic Forces, and Pressure Measurement

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Fluid Mechanics and Energy TransportBIEN
301Lecture 4 Pressure Distribution,
Hydrostatic Forces, and Pressure Measurement

• Juan M. Lopez, E.I.T.
• Research Consultant
• LeTourneau University
• Adjunct Lecturer
• Louisiana Tech University

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Pressure

• Definition (White 2.1)
• A force applied over a surface area.
• In fluid statics, the forces exerted by the
  pressures on each of the faces of the fluid
  element must sum to zero.

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Pressure

• From this formula, we can see that a few
  principal facts fall out
• Hydrostatic pressure is a function of height of
  the fluid column
• The pressure in any plane normal to the
  gravitational field is identical.
• For hydrostatic conditions, the forces generated
  by the fluid must come from the
  gravitationally-induced weight component only.

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Pressure

• What about if the fluid is moving?
• Strain rates will exist, and they will be out of
  balance.
• Viscous stresses will exist

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Pressure

• Forces from Pressure
• From our definition, pressure is a force over a
  surface area.
• What happens when we get pressure variations?
• What causes pressure variations?
• Because pressure variations can come from many
  different sources, we need a more generalized
  expression for expressing these forces.

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Pressure

• Surface and Body Forces
• Two types of forces that can act on our fluid
  element
• Can you think of examples of surface vs. body
  forces?
• Principal body force well deal with here
• GRAVITY
• Integrating the force from gravitational effects
  over our element volume

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Pressure

• Were missing one principal force
• Surface forces due to viscous effects

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Pressure

• We can now combine all of our defined terms to
  generate a more general expression for the
  balance of forces on a fluid element.
• This is a form of the differential momentum
  equation from Chapter 4.

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Pressure

• For now, we assume that we know the velocity and
  acceleration acting on our fluid. If we have an
  acceleration vector, a, we can then re-express
  our equation as follows

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Pressure

• With the knowns (V, a), we can solve for the
  pressure field via direct integration.

• This form will be very useful. To illustrate
  this, well take a few examples

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Pressure

• Flow under balanced forces (SF0)
• Hydrostatic
• Steady motion

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Pressure

• Rigid Body Motion, drops out the viscous term
• Rotation
• Translation
• Examples? Why does the viscous term disappear?

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Pressure

• Irrotational Motion
• Different than rigid body flowwhy?

• Does not have to behave like a rigid body
• There simply are no rotational terms.

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Pressure Measurement

• Absolute, Vacuum, and Gauge pressure
• Can anyone tell me what the most commonly used
  pressure reporting method is?
• Is there a better scientific way of reporting the
  pressure?
• Why?

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Pressure Measurement

• Hydrostatic condition
• As we mentioned before, the hydrostatic (no
  motion, or balanced forces) condition reduces to

• For a fluid at rest, the horizontal components
  drop out.

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Pressure Measurement

• We can also express this in terms of an integral

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Pressure Measurement

• For liquids, incompressibility is a good
  assumption

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Pressure Measurement

• It is this simple relationship which is exploited
  in many pressure measurement devices and/or
  calculations.
• For example, calculating the rise of mercury in a
  tube (a mercury barometer)

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Pressure Measurement

• What if the medium is a gas (compressible)?
• How about introducing the ideal gas law?
• A sufficiently accurate assumption for most cases.

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Pressure Measurement

• Pressure is not something we can measure
  directly, but rather derive it from some other
  measurement.
• What forms of measurement of pressure are used,
  and how do we have to derive the signal from
  these?

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Pressure Measurement

• Common pressure measurement instrument
  designations
• Gravity-based
• barometer, manometer, dead weight piston
• Elastic deformation
• bourdon tube, diaphragm, bellows, strain gauge,
  displaced optical beams
• Gas behavior
• Gas compression, thermal conductance, molecular
  impact, ionization, thermal conductivity.
• Electric output
• Resistance, diffused strain gauge, piezoelectric,
  potentiometric, magnetic inductance, linear
  variable differential transformer, resonant
  frequency.
• Luminescent coatings
• Surface Pressures

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Pressure Measurement

• Common pressure measurement instrument
  designations
• Electric output
• Resistance, diffused strain gauge, piezoelectric,
  potentiometric, magnetic inductance, linear
  variable differential transformer, resonant
  frequency.
• Luminescent coatings
• Surface Pressures
• Examples of where we might choose different
  pressure measurement devices in biomedical
  applications?

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Pressure Measurement

• Lets apply what weve learned to some flow
  examples
• Ex. 2.4
• Ex. 2.7
• P2.23

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Assignment

• HW 4 has been posted on blackboard
• Exam 1
• Reviews have been posted
• In-class exam materials allowed
• 1 Calculator
• Writing Implements
• Chapter Reviews from course documents, NO NOTES.
• Lecture slides, 6 to a page, NO NOTES.
• Fluid Mechanics, fifth edition, by White (class
  textbook), NO NOTES.
• If I find handwritten notes in these sections,
  your materials will be removed. Any additional
  cheating will result in failing the test, and
  maybe the course.
• Take-Home Option
• Sign-Up E-mail due by Wednesday, 1159 pm.

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Questions?