CIEG 305 REYNOLDS TRANSPORT THEOREM

1
CIEG 305 REYNOLDS TRANSPORT THEOREM
Time t
b
a
1
2
3
Time tdt
Control Volume
b
a
1
2
3
dVinAaVadt
dVoutAbVbdt
2
Think of the system as fluid parcels.
Denote B as any property of interest (mass,
momentum, energy).
Let
The amount of B per unit mass (called the
intensive value)
Total B in control volume is thus
Need to relate rate of change of BcV to rate of
change of B in system 2 that coincides with the
control volume at t
3
Whats there now
What came out
What went in
What was there
Rate of change of B in system 2 the instant it
occupies control volume
4
THUS
Rate of change of B in CV
Flux of B passing out of CV
Flux of B passing into CV
If steady state conditions, then the first term
on RHS drops out. Normally the case for our
problems.