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EGR 334 Thermodynamics

Chapter 4: Section 1-3

Lecture 12:

Control Volumes and

Conseration o! "ass#ui$ Today%

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Today&s main concepts:

'e a(le to e)plain *hat a control olume is 'e a(le to *rite mass (alance and mass rate (alance e+uations

!or a control olume,

'e a(le to e)plain the continuity o! mass !lo* e+uation,

E)plain the di!!erence (et*een mass !lo* rate and olumetric!lo* rate,

'e a(le to set up pro(lems inolin mass (alance

Readin .ssinment:

/ome*or0 .ssinment:

Read Chap 4: Sections 4-

rom Chap 4: 1 11 22

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So !ar *e hae loo0ed at closed systems

5nly Qand Wpass the (oundary

Enery 'alance

3Sec 4,1: Conseration o! "ass

6o* moe to open system

mass can also pass the (oundary,

add the mass (alance,

E *ithin

the system

net #

input

net 7

output8 9 8 9;

8 9

rom Chapter 2: Enery 'alance

m *ithin

the system

net m

input

net m

output8 98 9;8 9

"ass 'alance

# and 7

"ass

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4Sec 4,1: Conseration o! "ass

m *ithin

the system

net m

input

net m

output

8 9

8 9;

8 9

"ass 'alance

CV control olume

i inlet e e)it

General !orm !or multiple inlets

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Sec 4,1,2: "ass lo* Rate

"ass lu)

*here = density

Vn normal elocity component

. cross sectional area V olume

Continuity >rinciple:

mass !lo* is steady and continuous

"ass !lo* rate:

!or constant .rea

!or aria(le .rea

(V )nm

V tA = =

Vn

A

m dA= &

Vn=

Vn

dmm A

dt= =&

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Sec 4,2 "ass Rate 'alance

5ne-?imensional lo* @Continuity E+uationA

lo* is normal to the (oundary

The !luid is homoeneous @intensie propertiesare uni!orm *ith positionA,

where: = mass flow rate = density

= volumetric flow rate V = velocity

v= specific volume A = area

General !orm !or multiple inlets

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B

E)ample: @4,1A .mmonia enters a control olume operatin at steady state at

p. 14 (ar T. 2oC *ith a mass !lo* rate o! D, 0

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Sec 4,3 : .pplications o! the "ass Rate 'alance

p. 14 (ar

T. 2oC

m.D, 0

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ISec 4,3 : .pplications o! the "ass Rate 'alance

Saturated

li+uid

state Inlet A Exit B Exit C

> @(arA 14 4 4

T @CA 2 -1,ID -1,ID

@m3

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1DSec 4,3 : .pplications o! the "ass Rate 'alance

Saturated

li+uid

state Inlet A Exit B Exit C

> @(arA 14 4 4

T @CA 2 -1,ID -1,ID

@m3

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11Sec 4,3 : .pplications o! the "ass Rate 'alance

Saturated

li+uid

state Inlet A Exit B Exit C

> @(arA 14 4 4

T @CA 2 -1,ID -1,ID

@m3

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state Inlet A Exit B Exit C

V 8!t

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13Sec 4,3 : .pplications o! the "ass Rate 'alance

state Inlet A Exit B Exit C

V 8!t

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14Sec 4,3 : .pplications o! the "ass Rate 'alance

state Inlet A Exit B Exit C

V 8!t

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1

inally the olumetric !lo* rate o! the inlet may (e !ound:

Sec 4,3 : .pplications o! the "ass Rate 'alance

state Inlet A Exit B Exit C

V 8!t

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End o! slides !or Lecture 12

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