The term S b A h , representing direct solar radiation incident on the building, is
then the product of 872.67 Wm
−2 and 196.6 m
2 , giving 171.550 kW. This gives the
total direct solar radiation incident on the building.
For diffuse solar radiation, Eq. (7.18) is used with S dif representing the total
diffuse radiation incident on the surface facing the atmospheric semi-hemisphere:
S dif ¼ cos
2 a=2
ð
ÞS d þ cos
2 a=2
ð
ÞqS T
ð7:18Þ
where the albedo q, of the surface under consideration, is 0.25.
In the case of the building, this expression applies to two groups of surfaces with
different inclinations relative to the atmospheric half-hemisphere: the two surfaces
of the sloping roofs with 21.8º and the four walls with 90° inclination. In each case,
the overall diffuse light is the product of S dif and the areas of buildings exposed to
the atmospheric semi-hemisphere.
Applying Eq. (7.18) to the roofs gives
S dif ¼ cos
2
0:38=2
ð
Þx 87:08 x ((5/cos(0.38)) x 15 x 2)
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
rooftotal area
þ sin
2
ð0.38/2) x 959:75 x 0.25 x ((5/cos(0.38)) x 15 x 2) ¼ 14950 W
Similarly, applying Eq. (7.18) to the walls gives
S dif ¼ cos
2 90=2
ð
ÞÂ87.08 Â ð15 Â 8 Â 2 þ 10 Â 8 Â 2 þ ð10 Â 2=2Þ Â 2Þ
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
total wallarea
þ sin
2 90=2
ð
ÞÂ87.08 Â 0.25 Â ð15 Â 8 Â 2 þ 10 Â 8 Â 2 þ ð10 Â 2=2Þ Â 2Þ ¼ 68646W:
The total diffuse radiation (on the walls and roofs) will thus be 83.596 kW.
7.12 Example 11: Calculation of Kinetic Energy Budget
Components for a Flat Surface
From a height of 4 m from a flat surface, it was observed that the vertical variation
in the horizontal speed du/dz was 0.02 s
−1 , the average potential temperature was
20 ºC, the average of the product of the instantaneous fluctuations over a period of
half an hour w 0 T 0 was 0.25 K m/s, and the mean vertical moment of fluctuations
u 0 w 0 was −0.04 m
2 s
−2 .
Neglecting the terms for turbulent transport and by pressure correlation
(Eq. 3.89 in Chap. 3), calculate the TKE dissipation rate required to obtain a steady
state and the dimensionless TKE equation.
260
7 Examples of Applications
then the product of 872.67 Wm
−2 and 196.6 m
2 , giving 171.550 kW. This gives the
total direct solar radiation incident on the building.
For diffuse solar radiation, Eq. (7.18) is used with S dif representing the total
diffuse radiation incident on the surface facing the atmospheric semi-hemisphere:
S dif ¼ cos
2 a=2
ð
ÞS d þ cos
2 a=2
ð
ÞqS T
ð7:18Þ
where the albedo q, of the surface under consideration, is 0.25.
In the case of the building, this expression applies to two groups of surfaces with
different inclinations relative to the atmospheric half-hemisphere: the two surfaces
of the sloping roofs with 21.8º and the four walls with 90° inclination. In each case,
the overall diffuse light is the product of S dif and the areas of buildings exposed to
the atmospheric semi-hemisphere.
Applying Eq. (7.18) to the roofs gives
S dif ¼ cos
2
0:38=2
ð
Þx 87:08 x ((5/cos(0.38)) x 15 x 2)
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
rooftotal area
þ sin
2
ð0.38/2) x 959:75 x 0.25 x ((5/cos(0.38)) x 15 x 2) ¼ 14950 W
Similarly, applying Eq. (7.18) to the walls gives
S dif ¼ cos
2 90=2
ð
ÞÂ87.08 Â ð15 Â 8 Â 2 þ 10 Â 8 Â 2 þ ð10 Â 2=2Þ Â 2Þ
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
total wallarea
þ sin
2 90=2
ð
ÞÂ87.08 Â 0.25 Â ð15 Â 8 Â 2 þ 10 Â 8 Â 2 þ ð10 Â 2=2Þ Â 2Þ ¼ 68646W:
The total diffuse radiation (on the walls and roofs) will thus be 83.596 kW.
7.12 Example 11: Calculation of Kinetic Energy Budget
Components for a Flat Surface
From a height of 4 m from a flat surface, it was observed that the vertical variation
in the horizontal speed du/dz was 0.02 s
−1 , the average potential temperature was
20 ºC, the average of the product of the instantaneous fluctuations over a period of
half an hour w 0 T 0 was 0.25 K m/s, and the mean vertical moment of fluctuations
u 0 w 0 was −0.04 m
2 s
−2 .
Neglecting the terms for turbulent transport and by pressure correlation
(Eq. 3.89 in Chap. 3), calculate the TKE dissipation rate required to obtain a steady
state and the dimensionless TKE equation.
260
7 Examples of Applications