today - university of crete...facts about the cv 1) the control volume (cv) is defined by us 3) the...
TRANSCRIPT
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?