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EME 303 Fluid Mechanics 244!© 2012 Derek Elsworth
[8:1] Thermodynamics and Energy
Recap Outline
Transport Theorem:
DBsys
Dt= !!t cv" #bdV +
cs" #bV $ n̂dA for b = Bm
First Law of Thermodynamics: b = e and!!t cv" e#d V +
cs" e#V $ n̂dA = netin!Q + netin!W
pout
!+" oVout
2
2g+ zout + hL =
pin
!+" iVin
2
2g+ zin + hP
!m[("hout !
"hin)+ 1
2(vout
2!vin2)+ g(zout !zin)] = !Qnetin + !Wnetin
hP =
wshaftin
g; wshaftin =
shaftin!W!m
!
EME 303 Fluid Mechanics 299!© 2012 Derek Elsworth
[9:3] Dimensional Analysis
Recap Buckingham Pi &
Outline Relevance of dimensionless terms Use of models Similitude
Geometric Kinematic Dynamic
Re = !Vl
µ; Fr = V
gl; Eu = p
!V 2
Pipe Flow [10-11]
2 2
( )8 2
majorw L P
V l V Powerf h f h
D g Q!"
#= ; = ; =
2 2
1 1 2 21 22 2
major minorP L L
p v p vz h z h h
g g! !+ + + = + + + +" "
2
2122
minor minor LL L eq L
K DV ph K l K
g f V!"= ; = ; =
4
Non-circular: Laminar: [ ] Turbulent: [Use Moody; ( )]hh h
C Af D fP D
!"= ; = =Re
1 2 1 2Series: Parallel:
n nL L L L L L Lh h h … h h h … h= + + + ; = = =
1 2 24
1
2( )Flow meters:
(1 )p p DQ CA
D!
" !#= ; =#
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