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?