TODAY - University of Crete ... FACTS about the CV 1) The CONTROL VOLUME (CV) IS DEFINED BY US 3)...

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Transcript of TODAY - University of Crete ... FACTS about the CV 1) The CONTROL VOLUME (CV) IS DEFINED BY US 3)...

  • TODAY

    THE REYNOLDS TRANSPORT THEOREM (RTT)

  • Image taken from: http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node19.html

  • Density Area

    Velocity

  • Μερικοί Ορισμοί SYSTEM: A Fixed number of fluidic particles (that move…)

    THE SYSTEM HAS PHYSICAL PARAMETERS: MASS, MOMENTUM, ENERGY

  • CONTROL VOLUME (CV): It is a volume in 3D Space

    CONTROL SURFACE (CS): The (outer) Surface of the Control Volume

  • FACTS about the CV

    1) The CONTROL VOLUME (CV) IS DEFINED BY US

    3) The CONTROL VOLUME COINCIDES WITH THE SYSTEM AT TIME t=0…

    2) The CONTROL VOLUME CAN BE: -FIXED in space -DEFORM in space -MOVE in space

  • The Big Picture

    CONTROL VOLUME

    THE REYNOLDS TRANSPORT THEOREM (RTT)

    SYSTEM

    Can you connect the above SYSTEM-VOLUME concept to the LOCAL-GLOBAL concept?

  • The RTT in Mathematical Terms

    CONTROL VOLUME

    SYSTEM

    If BSYS is a physical Property of the System and b = BSYS /(mass of the system)

    Volume Integral Surface Integral

  • RTT & the Conservation of Mass Let BSYS = MSYS (the mass of the system)  then b = 1

    For b = 1

  • Example 1: Steady Flow through a Pipe

    U0 is the initial uniform Velocity

  • Step 1: Define the Control Volume

    Step 2:

  • Example 2: Variation of Free Surface in a Tank

    Volumetric Flow Rate

    (coming in - known)

    Step 1: Define the Control Volume (deforming or non-deforming?)

  • Step 2:

    Could we have used the B.E.?

  • Example 3: Water Jet Hitting a flat, vertical plate

    V’ ?

  • Applications?

    https://en.wikipedia.org/wiki/Water_jet_cutter

    Water Jet cutting

  • Step 1: Define the Control Volume  You want V’ to appear in the Control Surface (CS)

    Step 2:

  • WHY RTT is SO POWERFUL?

    ANY WEAKNESSES?

    Can you combine RTT with Bernoulli?

    TODAY Slide Number 2 Slide Number 3 Μερικοί Ορισμοί Slide Number 5 FACTS about the CV The Big Picture The RTT in Mathematical Terms RTT & the Conservation of Mass Slide Number 10 Example 1: �Steady Flow through a Pipe Slide Number 12 Slide Number 13 Example 2:�Variation of Free Surface in a Tank Slide Number 15 Example 3:� Water Jet Hitting a flat, vertical plate Applications? Slide Number 18 Slide Number 19