Environmental Engineering Reference
In-Depth Information
Q
l
= light-phase flow rate
A
= cross-sectional area
V
h
= heavy-phase velocity
V
l
= light-phase velocity
V
s
= slip velocity
The known quantities are normally
Q
t
,
A
,
V
s
, and
y
h
. The unknown quantities are
Q
h
and
Q
l
. With some minor algebraic manipulation an expression can be derived
for
Q
h
or
Q
l
as follows:
-
(
)
×× +
(
)
QQQQ yAVV
h
=
-
=
1
-
t
l
t
h
h
s
But,
VQyA
h
=
/
h
h
Thus,
(
)
××
(
)
QQ yAQyAV
h
=
--
1
/
+
t
h
h
h
s
hence
(
)
××
QyQy AV
h
=
ë
--
1
û
h
t
h
s
Once
Q
h
is determined,
Q
l
can be found from
QQQ
l
=
-
t
h
Practical Applications
In order to apply this equation to find the volumetric flow rates of the two phases,
consistency of units of measurement must be maintained. If flow rates are to be
expressed in barrels per day then the product
A. V
s
must also be in barrels per day.
However
A
, the cross-sectional area of the pipe available for flow, will normally be
quoted either in square inches or square centimeters, and
V
s
, the slip velocity, will
normally be quoted in feet per minute or centimeters per second. Therefore, a con-
version constant is required to convert the area
x
speed product into a flow rate in
B/D. Thus, in practical terms, the flow rate equation reduces to:
(
)
×××
QyQy AV
h
=
ë
-
1
-
1 781
.
û
h
t
h
s
where
A
is in sq in. and
V
s
is in ft/ min, or to
(
)
×××
QyQy AV
h
=
ë
-
1
-
0 5433
.
û
h
t
h
s
where
A
is in cm
2
and
V
s
is in cm/s.
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