!

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!

" !#= ; =#