CHEMICAL ENGINEERING

24 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

Noting that: RADRB

AtsDa: usAD 0 usBD 0

On the centre plane: AtsD 0

usADusB

AD

P

(^) Al
a^2
2

C

RA

(^) A
a

BD

P

(^) Bl
a^2
2

C

RB

(^) B
a
Thus: usAD

P

(^2) Al
fa^2 s^2 g

RA

(^) A
as
and: usBD

P

(^2) Bl
fa^2 s^2 gC

RA

(^) B
as sinceRADRB
Centre line velocity, uACLD
Pa^2
(^2) Al

C

RAa

(^) A
and: uBCLD
Pa^2
(^2) Bl

C

RAa

(^) B
Equating:
P^2 a
2 l

{

1

(^) A



1

(^) B

}

DaRA

{

1

(^) A

C

1

(^) B

}

∴ RAD

Pa

2 l

{

(^) B (^) A
(^) BC (^) A

}

Substituting:

usAD

P

(^2) Al
a^2 s^2 
Pa
(^2) Al
as
(^) B (^) A
(^) BC (^) A
D

P

(^2) Al

{

a^2 s^2 C

(^) A (^) B
(^) AC (^) B
aas

}

Totalflowrate ofADQAis given by:

QAD

∫a

0

busdsD

Pb

(^2) Al
{∫a
0

[

a^2 s^2 C

(

(^) A (^) B
(^) AC (^) B

)

a^2 as

]

ds

}

D

Pb

(^2) Al

[(

a^2 s

s^3

3

)

C

[

(^) A (^) B
(^) AC (^) B

](

a^2 sa

s^2

2

)]a

0

D

Pb

(^2) Al

[

2 a^3

3

C

[

(^) A (^) B
(^) AC (^) B

]

a^3

2

]

D

Pba^3

(^2) Al

[

2

3

C

(^) A (^) B
2 AC (^) B

]