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When to calculate the tower capability by the method
of tower performance curves, it is required to convert
the test water flow rate to the water flow rate at the
design conditions.
The equation is necessary
to predict the amount of water that the tower can cool,
at test temperatures, if the fan drives were loaded
to design power, and is based on the following assumptions:
- The GPM capacity of a
cooling tower is directly proportional to the air
flow.
- The air flow is proportional
to the cube root of the power delivered to the fans.
Actually the GPM capacity
of a cooling tower deviates from the straight line relationship
with air flow, due to changes in drop size, interfacial
area, and distribution, but the error is small for small
changes in air flows. Also, air flow deviates from the
cube root relationship with power, due to the fact that
a change in water loading is involved, and to the fact
that fan efficiency does not remain exactly constant
as air and water flows, and hence static pressure, are
changed. For these reasons it is desirable that water
circulation rate and fan power beheld reasonably close
to design during test.
In summary, the closer water
circulation rate and fan power are to design, the less
will be the error due to the adjustment of test water
circulation rate by means of equations below.
The determination of predicted
GPM from the performance curves is accomplished in the
following manner:
- Outlet water temperatures
at the test wet bulb temperature are read from the
performance curve. These values are shown on a table
titled "Cold Water Temp. @ Test WBT".
- The data from table are
then plotted to obtain the curves shown in "Cold
Water Temp. vs Ranges".
- The cold water temperatures
at the test range are then read from the curves. These
are shown in table titled "Cold Water Temp. @
Test WBT & Range".
- The data in table are
plotted to produce the curve shown in "Water
Flow Rate vs Cold Water Temp.". The predicted
GPM is found from this curve.
- Compute the adjusted test
GPM.
- Compute the performance
from the ratio of adjusted test GPM to predicted GPM.
There are three methods in
converting the test water flow rate to the water flow
of the design conditions. They vary on the assumption
as follows;
- Constant Fan BHP (BHP
off = BHP dsn)
- Constant Fan Pitch (VOL
off = VOL dsn)
- Constant Air Mass Flow
Rate (GAS off = GAS dsn)
1) Adjusted Test Water
Flow Rate @ Constant Fan BHP
| The
relation of L/G off at the constant fan bhp to
L/G dsn was already discussed and is given to
Eq. 16-6. This equation could be expressed to
the relation of L/G test and L/G dsn. |
| L/G
test |
=
L/G dsn x (L test / L dsn) x (DEN test / DEN test)1/3
x (SV test / SV dsn) |
Eq.
22-1 |
| L/G
test |
=
L test / G test
= L test / (Vol test / SV test)
= L test x SV test / Vol test |
Eq.
22-2 |
| BHP
test |
=
VOL test3 x DEN test VOL test |
|
| VOL
test |
=
BHP test1/3 / DEN test1/3 |
Eq.
22-3 |
|
Substitute VOL test
of right side in Eq. 22-2 by Eq. 22-3. |
| L/G
test |
=
L test x SV test / (BHP test1/3 / DEN
test1/3) |
Eq.
22-4 |
| L/G
dsn |
=
L dsn / G dsn
= L dsn / (Vol dsn / SV dsn)
= L dsn x SV dsn / Vol dsn |
Eq.
22-5 |
| BHP
dsn |
=
VOL dsn3 x DEN dsn VOL dsn = BHP dsn1/3
/ DEN dsn1/3 |
Eq.
22-6 |
|
Substitute VOL dsn
of right side in Eq. 22-5 by Eq. 22-6. |
| L/G
dsn |
=
L dsn x SV dsn / (BHP dsn1/3 / DEN
dsn1/3) |
Eq.
22-7 |
|
Substitute L/G test
and L/G dsn in Eq. 22-1 by Eq. 22-4 and Eq. 22-7. |
|
L test x SV test /
(BHP test1/3 / DEN test1/3)
= L dsn x SV dsn / (BHP dsn1/3 / DEN
dsn1/3) x (L test / L dsn) x (DEN test
/ DEN test)1/3 x (SV test / SV dsn)
1 = (BHP test / BHP
dsn)1/3 |
Eq.
22-8 |
|
Therefore, Eq. 22-8
can be rewritten to Eq. 22-9. |
|
| L
adj |
=
L test x (BHP dsn / BHP test)1/3 |
Eq.
22-9 |
2) Adjusted Test Water
Flow Rate @ Constant Fan Pitch
| The
relation of L/G off at the constant fan pitch
to L/G dsn was discussed and is given to Eq. 16-14.
Also, this equation could be expressed to the
relation of L/G test and L/G dsn. |
| L/G
test |
L/G
dsn x (L test / L dsn) x (SV test / SV dsn) |
Eq.22-10 |
|
Substitute L/G test
and L/G dsn in Eq. 22-10 by Eq. 22-4 and Eq. 22-7
which were derived previously. |
|
L test x SV test /
(BHP test1/3 / DEN test1/3)
= L dsn x SV dsn / (BHP dsn1/3 / DEN
dsn1/3) x (L test / L dsn) x (SV test
/ SV dsn)
1 = (BHP test / BHP
dsn)1/3 x (DEN dsn / DEN test)1/3 |
Eq.
22-11 |
|
Therefore, Eq. 22-11
can be rewritten to Eq. 22-12. |
| L
adj |
=
L test x (BHP dsn / BHP test)1/3 x
(DEN test / DEN dsn)1/3 |
|
3) Adjusted Test Water
Flow Rate @ Constant Gas
| The
relation of L/G off at the constant gas to L/G
dsn was discussed and is given to Eq. 16-22. Also,
this equation could be expressed to the relation
of L/G test and L/G dsn. |
| L/G
test |
=
L/G dsn x (L test / L dsn) |
Eq.
22-12 |
|
Substitute L/G test
and L/G dsn in Eq. 64-12 by Eq. 64-4 and Eq. 64-7
which were derived previously. |
|
L test x SV test /
(BHP test1/3 / DEN test1/3)
= L dsn x SV dsn / (BHP dsn1/3 / DEN
dsn1/3) x (L test / L dsn)
1 = (BHP test / BHP
dsn)1/3 x (DEN dsn / DEN test)1/3
x (SV dsn / SV test) |
Eq.
22-13 |
|
Therefore, Eq. 22-13
can be rewritten to Eq. 22-14. |
| L
adj |
L
test x (BHP dsn / BHP test)1/3 x (DEN
test / DEN dsn)1/3 x (SV test / SV
dsn) |
Eq.
22-14 |
Example 22-1:
Determine the capability of cooling tower on the basis
of Constant Fan Pitch by the analysis method of performance
curve using the same design and test conditions as example
21-1.
(Solution)
Sorry. Will add the solution later.
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