Pumping Station Desing - Second Edition by Robert L. Sanks, George Tchobahoglous, Garr M. Jones
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For a
prismatic channel
of any
shape,
as in
Figure
3-5b,
dA
=
bdy. Substituting
b
dy
for dA,
canceling
dy/dy,
and
collecting terms yields
n
2
A
3
*-
=
4-
(3-21)
8
b
at
critical depth. Substituting
v
c
= QIA
gives
21
=
T
b
(3
'
22)
at
critical depth. Note that
b is the
width
of the
water
surface
—
not
the
average width.
One
illustration
of the
usefulness
of
Equations
3-
21
and
3-22
is the
application
to
open-channel Venturi
flumes
(Figure 3-6)
for
measuring discharge.
Any
obstruction
in the
channel that produces
a
short length
of
uniform
flow
with straight, level streamlines
at
crit-
ical depth
can be a
Venturi
flume. One
example
is the
Palmer-Bowlus
meter (see Chapter 20).
The
Parshall
is
another popular measuring
flume, but it
does
not
have
straight, level streamlines
at the
critical section
and
is not
really
a
Venturi
flume. In the
Venturi
flume
of
Figure 3-6,
flow
over
the
step meets
the
previous
criteria. Strange though
it may
seem,
the
water
surface
drops between sections
b-b
and
c-c,
then
rises
again
from
sections
c-c
to
e-e
so
that
j
e
nearly equals
j
a
.
If
either
(1) the
step,
(2) a
reduced throat width,
or (3) a
combination
of (1) and (2)
produces
critical
depth
for
a
suitably wide range
of flow, the
Venturi
flume can be
used
to
meter
the
discharge with
a
basic uncertainty
of
only
about
±3%
[24].
Metering
is
easily accomplished
because
a
wide range
of
dimensional changes between
channel
and
throat
—
even
a
change
in
shape
—
can
be
used.
For
example,
Palmer-Bowlus
meters with trape-
zoidal throats
are
commonly installed
in
circular
sewers.
Figure 3-5. Energy
in
open
channel
flow,
(a)
Specific
energy
for
constant
discharge;
(b)
channel
cross
section.
Figure 3-6.
Longitudinal
section
through
a
Venturi
flume
in an
open
channel.
Discharge
can be
calculated
by
measuring
y
c
,
using
it to find A and
/?,
and
substituting into Equation
3-21.
It
is
customary, however,
to
measure
y
a
(upstream)
because
it is
greater than
y
c
and, hence,
the
accuracy
is
better. Methods
for
obtaining rating curves
for
v
a
are
given
in
Example 3-4.
Example
3-4
Venturi
Flume
in a
Channel
Problem:
A
smooth, rectangular
concrete
channel
is 610 mm (2 ft)
wide
and
carries
a flow of
0.170
m
3
/s
(6
ft
3
/s)
at a
slope
of
0.00124
m/m.
A
rectangular Venturi
flume
with
a
throat width
of
457 mm
(1.5
ft) is
installed with
its
step
76 mm (3
in.) above
the
channel invert. Calculate
(1)
the
depth
of flow in the
throat
and (2) the
depth
in the
channel
in
front
of
(upstream
from)
the
flume,
(3)
compare that depth with
the
depth
far
upstream,
and (4) find
whether critical depth
truly
occurs
in the
measuring
flume.
Solution:
(1)
Assume critical depth occurs
in the
throat
and find the
critical depth
from
Equa-
tion
3-21.
Sl
Units U.S. Customary Units
0.170
2
A
3
,
ftlin
2
6
2
A
3
A
.
10ft
2
TST
=
0457'^
=
°-
110m
3l2
=
L5'
A
=
L19ft
A
0.110
no/11
A
1.119
n
™
a
*
y
*
=
b
=
0457
=
a241m
*
=
5
=
TT
=
°'
793ft
From Equation
3-1,
the
throat velocity
is
v
c
= QIA =
0.170/0.110
=
1.55
m/s
v
c
= QIA =
6/1.19
=
5.04
ft/s
(2)
To find
conditions
in
front
of the
measuring
flume, use
Bernoulli's equation
(Equation
3-4)
and
assume
h
f
is
zero (which
is
practically true).
2 2
z
a
+
?
a
+^
=
z
c
+
?c
+
J+°
(3-4)
Note that
the
velocity
in the
channel
is
QIA
=
Q/by
=
(0.170/0.61)j
a
=
0.279/j
a
QIA =
Q/by
=
(6/2)y
a
=
3/y
a
so
Bernoulli's equation becomes
»-.^™
.,,.,<*£.
3^
5
JgI
.-^L.
2x9.81
By
trial,
y
a
=
0.416m
y
a
=
1.36ft
So the
water surface
falls
^a
-0>
c
+
ste
P)
=
y
a
-(}>
c
+
step)
=
0.416-(0.241
+0.76)
=
0.099
m
1.36-(0.793+
0.25)
=
0.317
ft
(3)
Use
Equation 3-16 (Manning)
to find the
depth
far
upstream
(or
downstream). Choose
n =
0.011
for
smooth concrete.
Field
Determination
of
Critical Flow
The
very uniqueness
of
critical
flow
makes
it
easy
to
determine
if the
metering
flume is
registering properly.
A
drowned meter
usually
has a
nearly level
surface
from
inlet
to
outlet.
If a
hydraulic jump occurs
at the
down-
stream
end,
the flow in the
throat
is
certain
to be
critical.
But
a
jump does
not
always occur,
so
another criterion
is
to
compare
the
depths
of flow
upstream
(at
section
a-a in
Figure 3-6)
and
downstream
(at
section
e-e).
If the
downstream
depth
is no
more than
85% of the
upstream
depth,
the flow in the
throat
is
critical
[25].
In
Example
3-4,
the
upstream depth
is
0.416
m and the
downstream
depth
is
0.305
m or 73% of the
upstream
depth
—
another
demonstration that critical
flow
does occur.
Ar
red
i
Diagram
Trial solutions
are
unsatisfactory
for
more than
one or
two
points (unless programmed
on a
computer).
To
make
a
rating curve
of
head
vs.
discharge,
an
Arredi
dia-
gram [26]
is
preferable. Select several values
of
dis-
charge
(Q
19
Q
2
,
etc.) covering
an
appropriate range
from
small
to
large
values.
For
each
<2,
plot
a
curve
of
throat
area versus
v
2
/2g
as
shown
in the
upper half
of
Figure 3-7. These curves
are the
same
for all
Venturi
flumes
regardless
of
size
or
shape.
Now
plot
a
curve
of
V
2
J
2g
versus throat area (curve
OA)
from
Equation
3-21
in
the
upper half
of
Figure
3-7.
This curve
is
specific
for
a
particular throat.
The
points
of
intersections with
the Q
curves give velocity head energy
for
each value
of Q.
In
the
lower half
of the figure,
plot
(to the
same
scale) depth,
d,
versus area
for the
channel (curve
OB)
and
plot depth versus throat area referred
to the
chan-
nel
invert (curve CD). Note that
OC is the
height
of
the
step,
s,
so
throat depth
is d - s =
y
c
.
Consider point
e in
Figure 3-7.
The
total energy
in
the
throat
is eh,
because
ef is
v
2
/2g,
fg is
s,
and gh is
y
c
.
Set a
pair
of
dividers
to
length
eh and
follow
the
curve
of
Q
2
to the right
until
the
dividers intersect
Sl
Units
U.S. Customary
Units
v
=
1
-R
2I3
S
112
v =
l^R^S
1
'
2
n n
v
= QIA =
(0.170/0.610)
y =
0.219/y
v =
Q/A
=
6/2
y = 3y
R
= AIP =
0.6lOy/(2y
+
0.610)
R = A/P =
2y/(2y
+
2)
0.279
=
1
(
0.610);
\
2/3
3
=
1.486f
2y
\
2/3
y
0.011
{2y
+
0.6IQJ
y
0.011
\2y
+
2J
x
(0.00124)
1/2
x
(0.00124)
172
y
=
0.305
m
by
trial
y =
1.00
by
trial
So
the
measuring
flume
acts
as a
choke
to
raise
the
water surface
from
0.305
m to
0.416
m
(1.00
to
1.36 ft).
The
"backwater"
created
by the
choke extends
far
upstream.
(4)
If the
total energy
in the
throat
is
greater (say,
5%
greater
to
allow
for
friction
losses)
than
the
energy
in the
channel without
the
choke, critical depth must theoretically occur
in the
throat. With-
out
the
choke,
the
total energy (referenced
to the
channel bottom) would
be,
from
Equation 3-2,
2 2
E
= z
+
y
+
^
E = z
+
y
+
^-
E
=
0
+
a3M
+
[0.170/(a610x0.305)]
2
£
=
O
+
I
+
^
E
=
0.348
m
E=
1.140
ft
With
the
choke,
the
total energy
in the
throat (again referenced
to the
invert
of the
channel)
is
E
=
0.076
+
0.241
+
iifg
E
=
0.25
+
0.793
+
&jt
E
=
0.438
m
E=
1.44
ft
which
is 26%
greater than
the
energy without
the
choke,
so
critical depth does occur.
curve
OB so
that
jm
equals
eh. The
depth
indicated
by
km
is the
upstream channel depth,
v
a
,
for
Q
1
.
To
develop
a
rating curve, repeat this procedure
for
several
values
of Q and
construct
a
graph
of
y
a
(as the
ordinate) versus
Q (as the
abscissa).
For
shapes such
as
trapezoidal throats
in
semicircular
flumes,
lines
OA,
OB, and CD are
curved.
The
difference
between these theoretical rating
curves
and
discharges measured
in the
laboratory
is
less
than about
4% of the
maximum
flow. In the field,
the
uncertainty
of
measurement would
not
exceed
4 or
5%
if the flume is
installed with reasonable care.
3-8.
Unbalanced
Hydraulic
Forces
Adequate
pipe support
is
important
to
protect
flanges,
bolts,
and the
pipe itself
from
destructive forces
due to
the
weight
of
pipe
and
water
or due to a
change
in
fluid
velocity. (Earthquake, vibration,
and
water ham-
mer may
also
be
destructive.) Valve bodies
and
pump
casings
are
especially vulnerable,
and
undue strain
can
cause binding long before breakage occurs.
Straight pipe needs support
in the
vertical plane
(to
resist gravity)
and in the
horizontal plane
(to
resist
earthquake). Hangers
or
piers should
be
spaced
to
minimize vibration (see Chapter 22). Bends,
tees,
and
wyes
produce unbalanced thrusts
in the
plane
of the
fitting
and, hence, require substantial anchors that
must
often
resist large horizontal forces without
appreciable deformation.
The
purpose
of the
following example
is to
show
how
to
compute
the
unbalanced forces. Review
the
fundamentals
of
momentum
in
Section
3-1,
if
neces-
sary.
Figure
3-7. Arredi diagram.
Example
3-5
Unbalanced
Forces
on a Wye
Problem:
Compute
the
forces
due to
water velocity, static pressure,
and
water hammer
on the
horizontal
steel
wye
shown
in
Figure
3-8 and
determine whether
an
anchor
is
required.
Solution:
Force
due to
velocity
and
pressure.
In the
force system
of
Figure 3-8, positive vec-
tors
act
right
or up. The net
forces
(R
x
or
R
y
)
to
produce
the
accelerations
are
assumed
to be
Figure
3-8.
Flow
in a
wye.
positive (and, therefore,
act up or
right),
so a
negative answer indicates
a
force acting
opposite
(down
or
left).
The x
component
of
Equation
3-7 is
F
1
A^P
2
A
2
COsSO
0
-F
3
A
3
+
R
x
=
PQ
3
V
3
-P(Q
1
V
1
-Q
2
v
2
cos30°)
The y
component
is
O
+
P
2
A
2
SmSO
0
+0
+
R
y
= O -
pG
2
v
2
sin30°
+ O
Calculations
for
these terms
are as
follows.
Sl
Units
P
1
A
1
:
379 x
0.
165
=
62.5
kN
P
2
A
2
:
372 x
0.0512
=
19.0
kN
P
3
A
3
:
352 x
0.
164
= 58.
IkN
PQ
1
V
1
:
1000
x
0.165
x
1.00
=
0.165
kN
Pg
2
V
2
:
1000
x
0.0906
x
1.77
=
0.160
kN
PG
3
V
3
:
1000
x
0.256
x
1.55
=
0.397
kN
The
jc
component
is
62.5
+
19.0cos30°-58.1
+R
x
=
0.397-
(0.165
+
0.160cos30°)
R
x
=
-20.8
kN =
20.8
kN
(acting
left)
The y
component
is
0+19.0sin30°
+ 0 + Ry =
0-0.160
sin
30°
R
y
=
-9.58
kN =
9.58
kN
(acting
down)
U.S.
Customary
Units
55.0x1.78x144=14,10015
53.9
x
0.553
x 144 =
4290
Ib
51.0
x
1.78
x 144
=13,100
Ib
1.94
x
5.82
x
3.28
=
37.0
Ib
1.94
x
3.20
x
5.81 =36.1
Ib
1.94
x
9.02
x
5.07
=
88.7
Ib
14.100
+
4290cos30°
-
13,000
+
R
x
=
88.7
-
(37.0-
36.1
cos30°)
R
x
=
-4630
Ib
=
4630
Ib
(acting
left)
0 +
4290sin30°+0
+
R
y
=
O
-36.1
sin
30°
+
O
R
y
=
-2160
Ib
=
2160
Ib
(acting
down)
Force
due to
water hammer.
As
shown
in
Chapter
6,
water hammer pressure
for the
instanta-
neous (worst-case) closure
of a
downstream valve
is
A#
=
J***
(6-2)
8
3-9.
Field
Measurement
of
Friction
Coefficient
Obstructions
such
as
trash, valves partially closed
through
carelessness, reduction
in
pipe diameter
due
to
mineral deposits,
and the
increase
of
roughness
due
to
tuberculation
or
unevenness
of
mineral deposits
are
all
manifested
by an
apparent
decrease
in the
Hazen-
Williams
coefficient,
C (or by an
increase
in the
Darcy-Weisbach
coefficient,
/). The flow
decreases
markedly
and the
discharge pressure increases some-
what.
Pumps
run
longer
and
consume more power
unnecessarily
—
often
at
significant
cost.
Field
measurements
to
determine pipe roughness
are
needed whenever
• a new
pump
is to be
used with
an
existing pipeline;
• the
pumping station
is to be
remodeled;
where
AH is
pressure rise
in
meters (feet),
a is
wave velocity
in the
pipeline
in
meters
per
sec-
ond
(feet
per
second),
g is the
acceleration
due to
gravity (9.81
m/s
2
[32.2
ft/s
2
]),
and v is the
change
in
velocity
in
meters
per
second
(feet
per
second), which
is
1.55
m/s
(5.07 ft/s)
in
this
problem. Assuming some
air is
present
in the
steel pipe (see Equation
6-4 and
Table 6-2),
a is
about
981
m/s
(3220
ft/s),
so
Sl
Units
U.S.
Customary
Units
A//
=
981
X
L55
=
155 m
A//
=
3220x^5.07
=
^
ft
and
the
pressure
from
Appendix Table
A-Il
is
A/?
=
155x9.79
=
1520
kPa
A/?
=
507x0.433
= 220
Ib
This
pressure
increment
can be
assumed
uniform
throughout
the
wye,
so the
forces
are
P
1
A
1
:
(379
+
1520)0.165
= 313 kN
(55.0
+
220)1.78
x 144
=
70,500
Ib
P
2
A
2
:
(372
+
1520)0.0512
=
96.8
kN
(53.9
+
220)0.553
x 144 =
21,800
Ib
P
3
A
3
:
(352
+
1520)0.165
= 309 kN
(51.0
+
220)1.78
x 144 =
69,500
Ib
Assume
that
the
pQv
terms remain essentially unchanged because
the
water
may
still
be
moving
when
the
shock wave arrives. Reinforcement
by
reflected waves could possibly occur
in
a
complex situation,
but the
assumptions here
are
reasonable
for
most applications.
313
+
96.8
cos
30°
-309
+
R
x
=
0.397-
(0.165
+
0.160cos30°)
R
x
=
-87.7
kN =
87.7
kN
(acting
left)
0 +
96.8sin30°
+ 0 +
R
y
=
0-0.160sin30°
+ 0
R
y
=
-48.5
kN =
48.5
kN
(acting down)
70,500
+
2
1,800
cos
30°
-69
,500
+
R
x
=
88.7
-
(37.0-
36.1
cos30°)
R
x
=
-19,800
Ib
=
19,800
Ib
(acting
left)
0 +
21
,800
sin
30°
+
0
+
Ry
=
0-36.1sin30°
+ 0
R
y
=
-10,900
Ib
=
10,900
Ib
(acting down)
and
the
forces acting
on the
anchor bolts
are
equal
and
opposite, i.e., same
as
force
on
water
and
opposite
to
forces
on
pipe.
The wye
need
not be
anchored
if the
piping
is
able
to
resist
the final
resultant, which
is
R =
V(87.7)
2
+
(485)
2
=
100 kN R =
7(19,80O)
2
+
(10,90O)
2
=
22,600
Ib
at
a
reasonable deflection (which should
be
calculated).
Do not
allow this resultant force
to be
transferred
into valve bodies
or
pump casings, because they
are not
designed
to
resist such
forces
and are
likely
to
bind
or
break. Anchorage
for
unbalanced forces
is
always required
at
flexible
couplings.
• any
expensive change
is
contemplated that involves
existing pipe;
and
• the
capacity
of the
pump
has
declined without
excessive impeller wear.
Other reasons
for
determining roughness include
•
timing
for
cleaning
and
relining;
•
calibration
of a
network model;
and
•
plans
to
increase
the flowrate.
Using
old
plans
and
specifications
as
data
for a
new
design without
a
confirming
field
survey
is
dan-
gerous. According
to
some experienced consultants,
the
majority
of
record
(or
"as
-built")
drawings con-
tain serious errors, such
as
wrong dimensions, alter-
ations never recorded, significant mistakes
in the
static head,
and an
inability
to
achieve
the
design
flow.
Without
a
survey, trusting
the
plans
is
thus likely
to
lead
to
more blunders, embarrassment
to
both engi-
neer
and
client,
and an
added, unnecessary cost
for
rectification.
The
most dramatic result
of a field
survey
is to find
excessive roughness (low
C
value), which usually indi-
cates
a
force
main partially plugged with debris
or
heavily
coated with grease, mineral deposits,
or
tuber-
culation.
Mineral deposits over
50 mm (2
in.)
in
thick-
ness were developed
in one
transmission main within
two
months
[27].
Valves
have been
found
partially
closed,
and
improper repairs
or
additions long
forgot-
ten
have collected sticks
and
rags. Camera inspection
or
forcing
"pigs"
through
the
line
can
disclose gross
problems
—
once
the
need
for
such methods
has
been
established
by a field
survey
of
pipe roughness.
(A
self-
destructing
pig
that need
not be
recovered
can be a
loaf
of
hard bread,
a
block
of
ice,
or a bag of ice
cubes.)
Roughness
is
determined
by
measuring
the
friction
headloss between
two
points separated
by a
known
length
of
pipe
of
known internal diameter
at a
known
rate
of flow.
Several runs
(at
least three) should
be
made,
preferably
at
different
flowrates, to
obtain
an
average roughness
coefficient.
It is
wise
to
demand
two
independent determinations
of the
roughness
coefficient
because either blunders
or
excessive errors
can
be so
costly.
Pressure Gauging
Headloss
can be
measured with (usually)
sufficient
accuracy
by
installing
a
suitable pressure gauge down-
stream
from
the
pump
to
determine
the
pressure drop
to a
free
surface.
The
static head
can be
determined
from
a field
survey
or by
halting
the flow and
reading
the
pressure gauge.
To
measure
the
friction head loss
with
enough accuracy,
a
"suitable"
pressure gauge
should have
at
least
a
150-mm
(6-in.)
face,
be
accurate
to
0.25%,
and
have
a
maximum pressure reading
of
not
much more than
150%
of the
expected pressure;
it
should
also
have been calibrated recently.
Pressure gauges
can be
installed (without inter-
rupting
flow) by
attaching them
to
corporation cocks,
which
in
turn
can be
installed under pressure
by the
water
utility
for a
nominal cost
if the
pipe
is
exposed.
A
short piece
of flared
copper tubing leading
to
pipe
threads
to
match
the
gauge completes
the
installation.
Some corporation cocks
can be
obtained with stan-
dard pipe threads
or
with standard pipe thread adapt-
ers
(see Figure 20-6
for a
good gauge assembly).
To
obtain
a
static pressure reading, stop
the flow in
the
force main
and
read
the
static gauge pressure,
p
s
.
(It can
also
be
calculated
if the
difference
in
elevation
between
the
gauge
and the
free
water
surface
is
known.)
After
the flow is
resumed,
the
gauge pressure
is
p
t
and the
pressure loss
due
only
to
friction
head
loss
is
Ap
=
p,-
Pt
(3-23)
Convert
differential
pressure,
A/7,
to
differential
head,
Ah,
by
using Table
A-Il,
then calculate
friction
loss,
/z
f
,
in the
usual units, meters
per
1000
meters
(or
feet
per
1000
feet),
as
h
f
=
1000
A/i/L
(3-24)
where
L is the
length
of
pipe between gauge
and
free
water
surface
in
meters
(feet).
If
the
transmission main branches
or the
diameter
changes
or if
there
is no
free
water surface, pressure
must
be
obtained
at a
second point.
If two
pressure
gauges
are
used,
one at
point
A and
another
at
point
B,
Equation 3-23
is
modified
to
&P
A
-B
=
(A-PS)A-(A-PS)B
(
3
~
25
)
Exposing buried pipe
for the
attachment
of
pres-
sure gauges
is
very expensive,
so
connect
the
second
gauge
to a fire
hydrant
or a
service line,
if
possible.
Unless
the two
pressure gauges
are far
apart,
the
error (even with gauges accurate
to
0.25%)
can
become unacceptable.
An
alternative
is to
connect
hoses
or
tubing
at
points
A and B and
lead them
to a
differential
gauge
or an air
manometer such
as
that
shown
in
Figure 3-4.
The
hoses must
be
purged,
and a
snubber
may be
needed
to
prevent rapid
fluctuations.
Differential
Pressure
Differential
pressures must
be
measured when pitot
tubes, Venturi meters,
or
orifice
meters
are
used
to
determine
flow.
Usually,
differential
pressures range
from
2 to 500 mm
(0.1
to 20
in.)
of
water column.
Pressure
in the
pipe
may be 200 to
10,000
times
greater,
so it is
futile
to
measure
the
differential
pres-
sure
by
trying
to
subtract gauge readings
at the two
pressure taps.
Differential
gauges
are
both expensive
and
delicate. Manometers that
use
mercury, carbon
tetrachloride,
or oil
are, according
to
Murphy's Law,
almost certain
to
blow
out
sooner
or
later
and
contam-
inate
the
pipeline
—
a
serious
disaster
in a
public water
supply.
An
inexpensive substitute
is the
air-filled,
upside-
down
manometer
in
Figure 3-4.
If the air
blows
out it
can
easily
be
replaced
by a
tire pump
or a
pressure
tank,
so a
tire valve should
be
installed
at the
top. Pet-
cocks
to
bleed
air
from
the
tubing leading
to the
manometer
are
also
needed.
Glass tubing
is
fragile,
but
plastic tubing
is
rugged.
A
satisfactory homemade
device equipped with
(1)
6-mm
(V
4
-Ui.)
valves
or
pet-
cocks,
(2) a
method
for
attaching
it to the
copper
tub-
ing
from
the
meter (such
as
6-mm
[V
4
-Ui-]
heavy rub-
ber
tubing with hose clamps),
and (3) a
meter stick
can
be
made
for a few
dollars
from
materials available
at
hardware stores
or
laboratories. Commercial mod-
els are
available.
Differential
pressure measurement
is
discussed thoroughly
by
Walski [28,
29].
Pipe
Diameter
The
internal pipe diameter (ID) must
be
known with
any
of
these methods,
and the
true
ID
must
be
known
with
reasonable accuracy
to use a
pitot tube, strap-on
meter,
or any
device that measures only velocity
in the
pipe.
Wall
thicknesses
of
pipe
are
increased
by
decreasing
the ID, so OD
does
not
indicate
ID
with
accuracy.
Furthermore, coatings (with unreliable
thicknesses)
and
mineral deposits reduce
the ID.
Hence,
do not
trust
the
plans
or
specifications.
The
most
reliable means
is to
remove
a
section
of
pipe
and
measure
the ID. If the
pipe cannot
be
taken
out of
ser-
vice,
a
"feeler"
rod
inserted through
a
packing gland
fitted
to
a
corporation cock gives
the
thickness,
but
only
at one
point
and at a
cost that
is
exorbitant
for the
purpose
unless
the
cock
is
also needed
for a
pitot tube.
(Note
that
mineral deposits
may not be
uniform.)
Other nondestructive ways
of
measuring pipe thick-
ness
may
exist
or be
developed,
but
thickness trans-
ducers
(at the
time
of
this writing)
are
inaccurate
for
pipe
with
a
mortar lining
or
mineral deposits.
Calculation
of
Average
Pipe
Diameter
Equation
3-1
can be
used
to find the
average pipe
diameter
if
both average velocity
and flowrate are
known.
A
tracer
can be
used
to find the
average veloc-
ity
as
follows:
•
Introduce
the
tracer
as a
slug
at one
point.
•
Measure
the
average time
for the
tracer
to
pass
a
downstream point (actually,
the
time
for
half
of the
tracer
to
pass
the
point).
•
Measure
the
length
of
pipe
between
the two
points
and
calculate
the
velocity.
Tracers
can
also
be
used
to find the
discharge inde-
pendently
of the
velocity
as
discussed
at the end of
this
section.
(Other methods
discussed
in the
follow-
ing
subsection could also
be
used.) With very
careful
work,
the
average
ID of a
pipe
can be
found
to
about
the
nearest
2% of the
pipe diameter.
Flowrate
Measurement
Flowrate,
in
conjunction with
friction
headloss,
is
use-
ful
for
constructing
the
existing system curve
as
well
as the
coefficient
of
friction. Flowrate
can be
mea-
sured
in a
variety
of
ways, generally dictated
by the
specific
situations encountered.
•
Obtain volumetric measurements using
a
stopwatch
and
the wet
well, clear well,
or the
reservoir.
Always
make every
effort
to
measure
flow
volumet-
rically
by
using
any
practical means available.
• Use the
existing
flowmeter in the
station,
but be
suspicious
if the
calibration
is not
recent. Check
the
read-out system
by
manual readings,
if
possible,
or
by
comparison with volumetric measurements.
As a
rule, errors
in
most
flowmeter
readings exceed 10%,
and
50 to
200% errors
are not
uncommon
[27].
•
Temporarily install
a
Palmer-Bowlus
flume in a
manhole (preferably downstream) where there
is
open channel
flow.
• Use the
manufacturer's pump curves
as a
convenient
check
to
confirm
any of the
other methods. When
carefully
done,
the
uncertainty
of flowrate
measure-
ment
can be
kept
to
±7%,
if
there
is
reasonable
surety that
(1)
no
wear
has
occurred,
(2) the
impel-
ler has not
been replaced with
a
significantly
differ-
ent
one,
and (3) the
pump curves were developed
from
good data under conditions that
can be
repro-
duced
in the field.
Some consultants
do not
trust
pump
curves,
but
others have
found
them
reliable.
•
Install
a
temporary
flowmeter
(preferably
in a
long,
straight
section
of
pipeline), such
as a
multiport
pitot tube
or
magnetic
flow
rod,
or use a
strap-on
Doppler
or
ultrasonic meter.
A
traverse with
a
sin-
gle
port pitot tube
is a
useful
substitute,
but
travers-
ing is
tedious,
and
within, say,
15
pipe
diameters
downstream
from
a
discontinuity (e.g.,
an
elbow),
accuracy
suffers
because
of
unsteady
flow
lines.
• Use
tracers.
The use of
tracers provides
the
highest
accuracy
and
reliability,
but it
requires either expen-
sive
equipment
or a
consulting specialist.
Errors
in
repeatability can, with care,
be
kept within less than
2%
of the
particular
flowrate
being tested.
All
of
these techniques require resourceful, knowl-
edgeable personnel
who are
either experienced
or
aggressive enough
to
learn
how to
make
the
selected
tests with accuracy.
If
needed, pump consultants,
some consulting engineers,
or
university
staff
mem-
bers
in
environmental, civil, mechanical,
or
chemical
engineering
may be
able
to
assist.
Volumetric
Measurement
Volumetric
measurement,
the
method
of
choice,
is
often
the
most convenient
and
reliable
because
many,
perhaps most, pumping stations have associated
wet
wells, clear wells,
or
storage tanks. Volume computed
from
careful
measurements
can be
used
in
conjunc-
tion
with timed drawdown
to
determine
flowrate
with
precision. Again, beware
of
trusting
the
construction
drawings
for
calculating volumes; always make
at
least
two
confirming
field
measurements
of the
basin
size. Under
field
conditions,
it is
difficult
to
time
an
event
to the
nearest second,
so the
running time
should
be at
least
2
min;
5
min
is
better.
If
the
influent
flow
into
a wet
well
or
clear well
cannot
be
halted
for the
duration
of a
run,
a
reasonable
approximation
of
volume pumped
can be
made
by
first
measuring
inflow
with
the
pumps
off and
then
accounting
for
inflow
while
the
pumps run. Because
sewage
inflow
varies, several runs
are
necessary
to get
a
reasonable, average result. Because
the
volume
of a
sewer
pipe
is not
only very large
but
also indetermi-
nate,
be
sure
to
keep
the
upper
wet
well level below
the
influent
sewer pipe.
One
method
for
timing
wet
well drawdown
is to tie
two
short objects
to a
string
at a
convenient, measured
distance apart. Attach
a
weight
(a
rock
or
brick will
do) to the end of the
string
and
suspend
it in the wet
well.
As the
water
rises (or
falls)
the
meniscus
at the
objects
can
usually
be
clearly seen
by
using
a flash-
light
[3O].
If
visibility
is
poor,
a
pair
of
electrical
con-
tacts
and a
battery
to
operate low-voltage lights
can be
used.
Permanent
Flowmeters
When
present,
a flowmeter may be the
most conve-
nient
way to
measure discharge,
but
care must
be
taken
to
ensure that
the
meter itself
is not a
source
of
error.
Manufacturers' claims
of
accuracy
are
rarely
realized
in the field, and a
surprising number
of
instal-
lations have shown excessive
errors
—
usually
more
than
10%,
often
more than 20%,
and
occasionally
as
much
as
200%
[31].
(For example,
the
influent
flow-
meter
at a
water treatment plant
in
Montana
was
about
100%
in
error
for
nearly
a
year
[32].)
Reasons
for
poor accuracy include improper installation, clogged
pressure taps, improper adjustment
of the
read-out
system
(mechanical
or
electrical), nonideal hydraulic
conditions,
incorrect
flow
coefficients, incorrect
flow-
meter gearing,
and
corrosion
or
moisture
in
electrical
circuits.
The
electronic
read-out system
of any
differential
pressure device, such
as a
Venturi
or
orifice,
can
sometimes
be
checked
by
temporarily installing
a
dif-
ferential
head device (differential pressure gauge
or
air
manometer) that
can be
read manually. Unfortu-
nately, only
the
differential pressure device
is
checked, whereas
the
meter itself
may be at
fault.
Temporary
Meters
in
Open
Channels
Sewage force mains
and
some water pumping stations
take
fluid
from
(or
discharge into) open channels.
Palmer-Bowlus
flumes can be
placed
in
sewer pipes
at
manholes. Weirs
and
Parshall
or
Venturi
flumes can
be
installed
in
ditches.
The
water level
can be
read
with
a
point gauge (equipped
for
convenience with
a
battery-operated electric contacter)
in the
upstream
channel. Floats, battery-powered
"dipper"
needles,
and
sonic meters
are
also available.
Pump
Curves
The use of
pump curves
is a
convenient check
on
other methods. Pressure gauges
are
needed
on
both
the
suction
and the
discharge spools (but
not in the
pump
casing). Worn
impellers
must
not be
used.
(Of
course,
it is
even better
if the
pump
has
been recently
tested
and
certified test curves
are
available.)
The
accuracy
of flowrate
determination depends
on
know-
ing
the
conditions used
by the
manufacturer
to
derive
the
pump curves
and
avoiding operation where
the
pump curve
is too flat.
Begin
by
operating
the
pump against
a
closed dis-
charge valve
and
adjust
(by
calculation)
the
manufac-
turer's impeller head-discharge (H-Q) curve
up or
down
to
correspond
to the
differential
pressure gauge
reading across
the
pump
at
shutoff.
If
possible,
oper-
ate the
system
at a
point where
the
pump
H-Q
curve
is
reasonably steep
by
running only
one of a
bank
of
pumps. Calculate
the flow
from
the
adjusted pump
curve
at the
proper
differential
pressure across
the
pump.
This
technique
and the
probable errors associated
with
each component
of the
measurement
are
thor-
oughly
discussed
in DIN
[33].
With care,
the
uncer-
tainty
of flowrate
measurement
can be
kept within
±7%
and,
frequently,
to
within
5%
[34].
Temporary
Flowmeters
in
Pipelines
The
recommendations
for
installing temporary
flow-
meters
are the
same
as
those
for
permanent ones.
The
manufacturer's
advice must
be
followed, especially
with
regard
to the
required lengths
of
straight pipe
before
and
after
the
meter.
If
there
is
insufficient
length
of
straight pipe (which
is
often
true
in the
cramped
quarters
of
pumping stations), consider
a
meter
installation
in the
yard piping.
Assuming
a
satisfactory
location
for a
meter, sev-
eral available types
are
compared
in
Table
3-1
(see
also
Chapter 20).
Tracers
The
purpose
of
this subsection
is to
introduce
a
little-
known,
little-understood,
but
versatile
and
accurate
method
for
measuring
flowrate and for
calibrating
flowmeters
in
place. Errors
of
less than
5% of the
measured
flowrate are
easily achievable,
and
with
care,
the
errors
can be
reduced
to
less than
2%.
There
are few
places where
the use of
tracers would
be
inap-
propriate (e.g.,
a
closed
or
recirculating system).
The
method
is
useful
for
measuring
flows in
manufactur-
ing
plants, open channels,
and
pipelines
of any
size
or
of
varying size. Engineers
who
have some background
in
wet
chemistry
can
learn
to use
tracers
in a
couple
of
days.
Tracers
can be
used
in
three ways:
•
Tracer velocity
or
time-of-
travel,
•
Slug addition,
and
•
Constant rate injection.
In
the first
method,
a
concentrated dose
of
tracer
is
dumped
into
an
upstream point,
and the
time required
Table
3-1.
Temporary
Flowmeters
Type
Advantages Disadvantages
Flow nozzle Locate anywhere along pipe; only
one
Expensive
to
dismantle pipe.
pressure gauge required
if at end of
pipe.
Pitot tube, single port Insert through corporation
cock.
Can
Unsuitable
for raw
sewage. Must take
install under pressure, inexpensive
in
many readings
to find
average
flow
exposed
pipe,
one
pitot tube
can
[35],
flow
must
be
steady while
serve
all
stations. survey
is in
progress, expensive
for
buried
pipe.
Pitot tube,
multiport
(integrating) Single reading gives average
flow; can
Suitable
for
only
a
single
ID.
Unsuitable
follow
changing
flow,
good
as a for raw
sewage.
permanent meter.
Strap-on meters
Can
apply
to
outside
of
pipe. Meter itself
is
expensive. Readings
Installation
is
inexpensive,
can be
suspect without independent check,
used permanently. should calibrate meter
on
pipe.
Magnetic
For raw
sewage
or
clean
water.
Time
of flight
Accurate
for
clean water
but
only
if Not for raw
sewage
or
dirty water.
installed
far
enough
(2
blocks)
downstream
from
the
pump
so
that
minute
vapor bubbles
are
dissipated.
Doppler
For raw
sewage
and
dirty water.
Not for
clean water.
Magnetic tube type Same
as
multiport pitot tube. Expensive. Requires corporation cock.
Orifice
plate Same
as for flow
nozzle;
for
grit-laden Unsuitable
for
rags
and
stringy material.
water,
use
segmental orifice plate
to
provide smooth invert.
Elbow
meter Inexpensive;
can
construct
in the field
Must calibrate
in
place;
low
differential
using
any
elbow,
fair
accuracy
but
pressure (use
air
manometer) (see
good precision (repeatability), stable Miller
[36]).
operation, unobstructed
flow.