OPERAÇÕES UNTÁRIAS CAULA 5 – Exercícios de fixação sobre torres de resfriamentoPROFESSOR: Nazareno Braga

1. Uma água quente gerada no resfriamento de uma planta de energia nuclear entra em uma torre de resfriamento a 40 ºC e 90 kg/s. A água é resfriada para 25 ºC na torre de resfriamento por um ar que entra na torre a 1 atm, 23 ºC e 60% de umidade relativa e deixa a torre saturado a 32 ºC. Determine: (a) o fluxo de massa do ar na entrada da torre e (b) taxa de escoamento da água de reposição requerida.

Assumptions 1 Steady operating conditions exist and thus mass flow rate of dry air remains constant during the entire process. 2 Dry air and water vapor are ideal gases. 3 The kinetic and potential energy changes are negligible. 4 The cooling tower is adiabatic.

Analysis (a) The mass flow rate of dry air through the tower remains constant ( )m m ma a a1 2 , but the mass flow rate of liquid water decreases by an amount equal to the amount of water that vaporizes in the tower during the cooling process. The water lost through evaporation must be made up later in the cycle to maintain steady operation. Applying the mass and energy balances yields

Dry Air Mass Balance:

Water Mass Balance:

Energy Balance:

334makeup312

33114422

outin

(steady) 0systemoutin

)()(0

0

0

0== since

0

hmhmmhhm

hmhmhmhm

hmhm

WQhmhm

EE

EEE

a

aa

iiee

eeii

Solving for ,

41212

433

)()(

)(

hhh

hhmma

From the psychometric chart (Figure A-33),

Systemboundary

1

2

4

32C100%

WATER

40C90 kg/s

1 atm23C60%

AIR

3

Makeup water

25C

and

From Table A-4,

Substituting,

Then the volume flow rate of air into the cooling tower becomes

(b) The mass flow rate of the required makeup water is determined from

2. Uma água quente proveniente de uma planta de resfriamento entre em uma torre de resfriamento a 43 ºC a uma velocidade de alimentação de 45 kg/s. A água é resfriada a 27 ºC por um ar que entra na torre a 1 atm, 24 ºC e 60% de umidade relativa e deixa

saturado a 35 ºC. Determine: (a) a vazão volumétrica do ar que entra na torre e (b) vazão mássica requerida para a água de reposição.

Assumptions 1 Steady operating conditions exist and thus mass flow rate of dry air remains constant during the entire process. 2 Dry air and water vapor are ideal gases. 3 The kinetic and potential energy changes are negligible. 4 The cooling tower is adiabatic.

Analysis (a) The mass flow rate of dry air through the tower remains constant , but the mass flow rate of liquid water decreases by an amount equal to

the amount of water that vaporizes in the tower during the cooling process. The water lost through evaporation must be made up later in the cycle to maintain steady operation. Applying the mass balance and the energy balance equations yields

Dry Air Mass Balance:

Water Mass Balance:

Energy Balance:

Solving for ,

From the psychometric chart (Figure A-33),

and

From Table A-4E,

Substituting,

Then the volume flow rate of air into the cooling tower becomes

Systemboundary

1

2

4

95F100%

WATER

110F100 lbm/s

1 atm76F60%

AIR

3

Makeup water

80F

(b) The mass flow rate of the required makeup water is determined from

3. Uma torre está resfriamento uma corrente de água quente de 40 ºC para 25 ºC onde a pressão atmosférica é 96 kPa. Ar entra na torre a 20 ºC e 70% de umidade e deixa saturado a 35 ºC. Determine: a vazão volumétrica do ar que entra na torre e (b) vazão mássica da água de reposição.

Assumptions 1 Steady operating conditions exist and thus mass flow rate of dry air remains constant during the entire process. 2 Dry air and water vapor are ideal gases. 3 The kinetic and potential energy changes are negligible. 4 The cooling tower is adiabatic.

Analysis (a) The mass flow rate of dry air through the tower remains constant ( )m m ma a a1 2 , but the mass flow rate of liquid water decreases by an amount equal to the amount of water that vaporizes in the tower during the cooling process. The water lost through evaporation must be made up later in the cycle to maintain steady operation. Applying the mass and energy balances yields

Dry Air Mass Balance:

Water Mass Balance:

Energy Balance:

Systemboundary

1

2

4

35C100%

WATER

40C50 kg/s

96 kPa20 ºC70%

AIR

3

Makeup water

25C

Solving for ma ,

The properties of air at the inlet and the exit of the tower are calculated to be

and

From Table A-4,

Substituting,

Then the volume flow rate of air into the cooling tower becomes

(b) The mass flow rate of the required makeup water is determined from