ChemE 260 Conservation of Mass & Energy, Steady-State Processes April 15, 2005 Dr. William Baratuci...

ChemE 260 Conservation of Mass & Energy,

Steady-State Processes

April 15, 2005

Dr. William BaratuciSenior Lecturer

Chemical Engineering Department

University of Washington

TCD 5: A - CCB 4: 3 & 4

Conservation of Mass• Mass is neither created nor destroyed

• Integral Mass Balance on an Open System

• Differential Mass Balance on an Open System

BaratuciChemE 260April 15, 2005

#feeds #effluents

in,i out , jsysi 1 j 1

dm m m

dt

#feeds #effluents

sys in,i out , ji 1 j 1

m m m

min,1

min,2

min,3

mout,1

mout,2

.

.

.

.

.

Flow Rates and Velocity

• Specific Volume: or:

– Therefore:

• Volumetric Flow Rate:– Where: <v> = average fluid velocity

Across = cross-sectional area for

flow

• Conclusion:

VV

m VV

m

Vm

V

R

cross0

V v dA 2 v dr v A

crossv AVm

ˆ ˆV V


1st Law, Open Systems• SISO = Single Inlet, Single Outlet

• At Steady-State nothing changes with respect to time

mout

min

.

.

outE

inE

in outsys in kin,in pot,in out kin,out pot,out

d ˆ ˆ ˆ ˆ ˆ ˆE Q W m U E E m U E Edt

kin potˆ ˆ ˆQ W m U E E

in outsys

dm m m

dt

sys

dm 0

dt

sys

dE 0

dt

in outm m m


Flow Work• Three main types of work in this course:

– Wb is boundary work

– Ws is shaft work

• Associated with the rotating shafts in fluid processing equipment

– Wflow is flow work or inection work

• Work done to force fluid to flow into and out of the system

• Evaluating Net Flow Work

• 1st Law :

s flow bW W W W

Pin

Pout

flow flow,in flow,out in in in out out outW W W P A v P A v

flowout in

out in

ˆ ˆ ˆW PV PV m PV PV m PV

s kin potˆ ˆ ˆ ˆQ W m PV m U E E

s kin potˆ ˆ ˆQ W m H E E

flowW PV P vA


MIMO Processes• MIMO = Multiple Inlet, Multiple Outlet• 1st Law :

• 1st Law, SS :

min,1

.

min,2

.

min,3

.

mout,1

.

mout,2

.

in,1E

in,2E

in,3E

out,1E

out,2E

# inlets #outlets

in,i out, jsys in kin,in pot,in out kin,out pot,out ji 1 j 1i

d ˆ ˆ ˆ ˆ ˆ ˆE Q W m U E E m U E Edt

#outlets # inlets

out, j in,iout kin,out pot,out in kin,in pot,injj 1 i 1 i

ˆ ˆ ˆ ˆ ˆ ˆQ W m U E E m U E E

#outlets # inlets

out, j in,iS out kin,out pot,out in kin,in pot,injj 1 i 1 i

ˆ ˆ ˆ ˆ ˆ ˆQ W m H E E m H E E


Steady-State Processes• In the real world, the goal is usually to operate flow

processes at steady-state.• Common steady-state flow processes:

– Nozzles & Diffusers

– Turbines

– Pumps and Compressors

– Throttling Devices

– Heat Exchangers

– Mixing Chambers

– Pipes


Nozzles & Diffusers

• Common Assumptions:

• 1st Law :

Nozzle Diffuser

potE 0

Q 0

2

C

vH 0

2g

SW 0


Turbines

Turbine

potE 0

kinE 0

Q 0

sˆW m H

• A turbine is a device which converts the energy of a flowing fluid into shaft work.


• 1st Law :


• Pumps cause liquids to flow by raising the pressure• Compressors cause gases to flow by raising the

pressure• Common Assumptions:

• 1st Law :

Pumps & Compressors

PumpCompressor

potE 0 kinE 0

Q 0

sˆW m H


Throttling Devices• A common throttling device is a partially closed valve

• Other throttling devices include capillary tubes and porous plugs.

• Common Assumptions :

• 1st law :

Valve

potE 0 kinE 0

Q 0

H 0

SW 0


Heat Exchangers


• 1st law

– Hot Side:

– Cold Side:

– Overall:

potE 0 kinE 0

overallQ 0

SW 0

Process HEX Utility HEX

hot hotˆQ m H

cold coldˆQ m H

cold hotcold hotˆ ˆm H m H


Mixers, Splitters

• Mixers and Splitters are tees in a pipe where streams join and mix or split, depending on the direction of flow into and out of the tee.


• 1st Law:

• Conservation of Mass:

Mix

potE 0 Q 0

SW 0

Split

# inlets #outlets

in,i out, jin kin,in out kin,out ji 1 j 1i

ˆ ˆ ˆ ˆm H E m H E

# inlets #outlets

in,i out, ji 1 j 1

m m


Pipe Flow: Bernoulli Equation• Assumptions:

– Incompressible fluid:

– No friction:

• 1st Law:

• BernoulliEquation :

overallQ 0

SW 0

V 0

U 0

s kin potˆ ˆ ˆQ W m H E E

kin potˆ ˆ ˆ ˆ ˆ0 m U V P P V E E

2

C C

P v gz 0

2g g


Next Class …• Prepare for Test #1

– TCD Chapters 1 – 4

– CB Chapters 1 – 3 , 4.1 & 4.2, Supplements

• Transient Mass Balances

– Ordinary differential equations

– Not too difficult.

• Transient Energy Balances

– Ordinary differential equations

– WAY too difficult !

– Simplifying assumptions let us solve some special problems

– General case requires numerical solution by a computer

• We won’t do these in this course ! BaratuciChemE 260April 15, 2005

ChemE 260 Conservation of Mass & Energy, Steady-State Processes April 15, 2005 Dr. William Baratuci...

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