Chapter21 performanceoffluidflowequipment-150917142659-lva1-app6892

Chapter 21
Performance Curves for
Performance Curves for
Individual Unit Operations
(Fluid Flow Equipment)
Department of Chemical Engineering
West Virginia University
Copyright J. A. Shaeiwitz and R. Turton - 2012 1

Outline
Outline
• Flow in pipes
Flow in pipes
– laminar vs. turbulent
• NPSH
• NPSH
• Pump and system curves
– single vs. multiple pumps
– centrifugal vs. positive displacement
– compressors

Outline
Outline
• Flow in pipes
Flow in pipes
• NPSH
• NPSH
– compressors
Copyright J. A. Shaeiwitz and R. Turton
- 2012
3

Key Relationships
Key Relationships
2
• Turbulent flow
2
2
4
2
∝
Δ
⇒
=
Δ
m
m
v
P
D
fLv
P fr
fr
ρ
&
&
2
2
32
4
=
=
m
fL
D
m
A
m
v
ρπ
ρ
&
&
&
5
5
2
32 −
∝
Δ
⇒
=
Δ D
P
D
m
fL
P fr
fr
ρπ
&

Key Relationships
Key Relationships
• Laminar flow
L
L
L
D
P
v
D
v
Δ
=
=
128
32
128
4
4
2
μ
π
π
&
&
v
D
P
D
L
v
D
L
v
P fr
fr ∝
∝
Δ
⇒
=
=
Δ −
and
128
32 4
4
2
π
μ
μ &

Example 1
Example 1
• Increase velocity by 25% ‐ turbulent flow ‐
effect on ΔP
ld
1
2
25
.
1
old
1
new
2
2
=
=
=
v
v
2 2
2
1
∝
Δ
⇒
=
Δ v
P
D
fLv
P
v
fr
fr
ρ
5625
.
1
25
.
1 2
2
2
2
1
2
=
=
=
Δ
Δ
v
v
P
P
D
f
f
1
1
Δ v
P

Example 2
Example 2
• Double diameter – turbulent flow‐ effect on
ΔP
2
old
1
new
2
2
=
=
=
D
D
32 5
5
2
2
1
∝
Δ
⇒
=
Δ −
D
P
D
m
fL
P
D
fr
fr
ρπ
&
32
1
03125
.
0
5
.
0 5
5
5
1
1
2
=
=
=
=
Δ
Δ
D
D
P
P
D
ρπ
32
2
1
Δ D
P

Outline
Outline
• Flow in pipes
Flow in pipes
• NPSH
• NPSH
– compressors

NPSH
NPSH
NPSH N P i i S i H d
• NPSH = Net Positive Suction Head
• There is pressure drop upon entering pump,
p p p g p p,
before mechanism that increases pressure
• If fluid is too close to vapor pressure at pump
• If fluid is too close to vapor pressure at pump
inlet, it could flash upon entering pump
• Pumps are designed to handle liquids and do not
behave well with vapor

NPSH
NPSH
• NPSHA = Pinlet – P *
NPSHR
• NPSHA = NPSH “available”
NPSHR
• NPSHR = NPSH “required”
i f i li d b f
v
&
– information supplied by pump manufacturer

NPSH
NPSH
• Common situation
• Apply MEB
1
2
0
2
2
W
e
z
g
v
P
s
f −
→
Δ
=
−
+
Δ
+
Δ
+
Δ
ρ
2
0
2
2
2
1
2
fL
D
fLv
gh
P
P
=
+
−
−
ρ
ρ
*
2
*
2
2
2
1
2
P
fLv
gh
P
P
P
NPSH
D
fLv
gh
P
P
+
=
=
−
+
=
ρ
ρ
ρ
ρ
*
* 1
2 P
D
gh
P
P
P
NPSH A −
−
+
=
−
= ρ

NPSH
NPSH
5
2
2
1 *
32
P
D
v
fL
gh
P
NPSH A
π
ρ
ρ −
−
+
=
&
2
form
of
v
b
a
NPSH A −
= & NPSH
1
32
*
fL
b
P
gh
P
a
v
b
a
NPSH A
ρ
ρ −
+
=
NPSHA
5
2
32
D
fL
b
π
ρ
=
v
&
this is for turbulent flow
f l i fl t i ht li
for laminar flow – straight line
with negative slope

NPSH
NPSH
2
1
2
32
*
fL
P
gh
P
a
v
b
a
NPSH A
ρ −
+
=
−
= &
• How to increase NPSHA
• base case is line (1)
increase a line (2)
5
2
32
D
fL
b
π
ρ
=
– increase a – line (2)
• increase h
• increase P1
• decrease P*
– decrease T
– decrease b – line (3) NPSHA
• decrease L
• increase D
– suction line usually larger D
1
3
2
v
&

NPSH
NPSH
NPSHA > NPSHR
pump operates appropriately
R
NPSHA < NPSHR
pump will cavitate
inappropriate pump operation
but it will operate
NPSH
but it will operate
v
&
A
v
&

Outline
Outline
• Flow in pipes
Flow in pipes
• NPSH
• NPSH
– compressors

Pump and System Curves
• Pump curve (centrifugal pump shown)
• Pump curve (centrifugal pump shown)
• Supplied by manufacturer
• Can be measured in lab
• centrifugal is sometimes called “constant head” pump
ΔP in pressure units
or head developed
or head developed
v
&

• System curve
pump supplies pressure increase
)
(
)
( 3
2
3
1
2
1 Δ
−
+
Δ
−
+
Δ
=
Δ −
−
− P
P
P
P fr
to increase fluid pressure and to overcome all of these pressure losses
0)
(
h
)
0
or
0
be
could
(
)
0
usually
(
n
destinatio
to
source
in
-
out
3
1
Δ
<
>
Δ
+
>
Δ
=
Δ
=
Δ
−
P
z
g
P
P ρ
0)
(
valve
across
drop
pressure
frictional
0)
(
pipes
in
drop
pressure
frictional
0)
(
pump
across
change
pressure
3
2
2
1
<
=
Δ
<
=
Δ
>
=
Δ −
P
P
P
fr
0)
(
valve
across
drop
pressure
frictional
3
2 <
=
Δ −
P

• To plot system curve – look at source to
destination and frictional loss
3
1
3
1
)
0
or
0
be
could
(
)
0
usually
(
n
destinatio
to
source
in
-
out
)
(
z
g
P
P
P
P
P fr
sys
<
>
Δ
+
>
Δ
=
Δ
=
Δ
Δ
−
+
Δ
=
Δ −
ρ
5
2
2
3
1
2
3
1
3
1
so
32
2
)
o
be
cou d
(
)
usu y
(
des o
o
sou ce
D
v
fL
P
D
fLv
P
P
g
sys
&
+
Δ
=
+
Δ
=
Δ −
−
−
π
ρ
ρ
ρ
ΔPsys
( )
2
form
empirical
so
v
b
a
P
P
P
P
sys
valve
sys
pump
&
+
=
Δ
Δ
−
+
Δ
=
Δ
v
&
ΔPsys
v
&
this is for turbulent flow
for laminar flow – straight line

• Often expressed as head
sys
v
fL
h
fLv
h
h +
=
+
= −
−
32
2
5
2
2
3
1
2
3
1
&
sys
D
g
gD
−
−
so
5
2
3
1
3
1
π
valve
sys
pump h
h
h +
= hsys
v
&

ΔP
ΔPpump < ΔPsys
impossible operation
sys
ΔP
a = ΔPsource dest + ρgΔz if know this point
2
{
-ΔPvalve
ΔPpump
z
a ΔPsource-dest + ρgΔz
with
can find a and b
2
v
b
a
Psys &
+
=
Δ
operating
v
& v
&
pump
a
}-ΔPfr
z
ΔPpump > ΔPsys
excess pressure dissipated across partially closed valve
as open and close valve, flowrate changes
operating v
&
as open and close valve, flowrate changes
intersection point is fully open valve

Outline
Outline
• Flow in pipes
Flow in pipes
• NPSH
• NPSH
– compressors

Pumps in Series and Parallel
• Series
– Pump curve
two pumps
Pump curve
– 2X head at
same flowrate
ΔPpump
one pump
v
&

• Parallel
P
two pumps
– Pump curve
– 2X flowrate at
same head
ΔPpump
one pump
same head
v
&

• Which
configuration
two pumps
series
configuration
maximizes
flowrate?
ΔPpump z
flowrate?
– No general
result
one pump
two pumps
parallel
z
result
v
&

Outline
Outline
• Flow in pipes
Flow in pipes
• NPSH
• NPSH
– compressors

Centrifugal – variable speed
Centrifugal variable speed
ΔP
ΔPpump
rpm 5
rpm 3
rpm 2
rpm 4
v
&
rpm 1
rpm increases with number
more expensive pump
p p p
cost of “wasting” pressure across valve may be less than cost of pump

Positive Displacement
fl l /
flow regulation/pump curve
ΔP in pressure units
sometimes called “constant volume” pump
p
or head developed
v
&

Outline
Outline
• Flow in pipes
Flow in pipes
• NPSH
• NPSH
– compressors

Compressors
Compressors
locus of maxima = surge line
can also draw system
Pout /Pin
rpm 5
can also draw system
curves on this graph –
must change form of left-
hand side to ratio
rpm 3
rpm 2
rpm 4
v
&
rpm 1
rpm 2
usually worth using speed control here because of compression costs
usually worth using speed control here because of compression costs

Outline
Outline
• Flow in pipes
Flow in pipes
• NPSH
• NPSH
– compressors

Chapter21 performanceoffluidflowequipment-150917142659-lva1-app6892

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Chapter21 performanceoffluidflowequipment-150917142659-lva1-app6892