K ¼ 92:5 þ C 1 þ β
ð
Þf U
ð Þ
ð5:5Þ
K ¼ 92:5 þ 0:468 þ 1:77
ð
Þ323:6 ¼ 816:5 kcal=m
2
Á d Á
C
Using the given solar radiation, H s ¼ 5750 kcal/m
2
Ád, the equilibrium temperature, E, can now be determined from Eq. (5.8):
E ¼ T d þ H s =K
ð
Þ
ð5:8Þ
E ¼ 23 þ 5, 750=816:5
ð
Þ¼23 þ 7:0 ¼ 30
C
The surface temperature is now determined using Eq. (5.3):
T s ¼ q=KA þ E
ð5:3Þ
T s ¼ 8 Â 10
9
= 816:5
ð
Þ 4 Â 10
6
À
Á
Â
Ã
È
É þ 30:0
T s ¼ 2:5 þ 30:0 ¼ 32:5
C versus the assumed value of 36
C
Repeating this procedure now using 33
C as T s , from Fig. 5.1, β ¼ 1.65 and
previously calculated value for f(U ) of 323.6 kcal/m
2 d, recalculated K and E
K ¼ 777:9 kcal=m
2
Á d Á
C and E ¼ 30:4
C
and
T s ¼ q=KA þ E
ð5:3Þ
T s ¼ 8 Â 10
9
= 777:9
ð
Þ 4 Â 10
6
À
Á
Â
Ã
È
É þ 30:4
T s ¼ 2:6 þ 30:4 ¼ 33:0
C
Because this calculated value for T s equals the assumed value, no additional
iterations are needed.
Design Chart
Figure 5.2 will assist in this type of cooling pond design calculation [3]. This figure
gives the values for heat transfer coefficient, K (in kcal/m
2
ÁdÁ
C), at the intersection
of the wind speed, U, in km/h and average temperature, T avg (in
C). The controlling
local weather conditions may be found in standard references [4].
5 Cooling and Reuse of Thermal Discharges
205