This paper contains SIX questions. Full marks can be obtained by the correct solutions to FIVE
questions. All questions carry the same marks.
... [Show More]
Electronic Calculators:
Only approved calculators as announced by the Examinations Secretary can be used in this
examination. It is the candidates’ responsibility to ensure that the calculator operates satisfactorily,
and candidates must record the name and type of the calculator used on the front page of the
examination script.
5. Given an adiabatic process of dry air parcel
d d C T v p p (5a)
in hydrostatic pressure
d
d
p
g
z
(5b)
where Cp (= 1,005 J kg-1 K-1) is the specific heat capacity at constant pressure, g (= 9.81 m
sec-2) the gravitational acceleration, p the pressure, T the air temperature, v the specific
volume of air, z the height and the air density.
(a) Prove that:
(i) Potential temperature
0
R Cp
p
T
p
(5c)
and (3 marks)
(ii) Altimeter calibration
0
0
1
R g
T p
z
p
(5d)
under the condition that temperature T decreases uniformly with height z at a constant lapse
rate . (5 marks)
Here, p0 (= 1,000 mbar) is the standard pressure at mean sea leave, T0 the sea-level
temperature at z = 0 and R (= 287 J kg-1 K-1) the gas constant of dry air. Assume ideal gas law
pv RT . (5e)
(b) Given the data on Table Q5(a), calculate the potential temperatures at points B, C and D.
Hence, determine the potential temperature gradient /z and the atmospheric stability of
the layers AB, BC and CD. (4 marks)
(c) Compare, using also sketches wherever applicable, the near-field transport characteristics
of pollutants being emitted from (two) chimneys of height 0.05 km and 0.3 km. The pollutant
plume is hot and the discharge velocity is non-negligible. (8 marks)
Table Q5(a). Atmospheric data recorded on a certain day.
Height
z (km)
Pressure
p (mbar)
Air
temperature
T (K)
Potential
temperature
(K)
Potential
temperature
gradient
/z (K km-1)
Atmospheric
stability
A 0 1,000 303 303 --- ---
B 0.1 988 301.5 ______ ______ ______
C 0.25 970.895 300 ______ ______ ______
D 0.5 943 298.5
6. A passive and chemically inert pollutant is emitted from a chimney of height h (= 120 m) and
diameter d (= 0.8 m) into the atmosphere of ambient temperature Ta (= 298 K). The pollutant
emission rate, discharge velocity and temperature are Q (= 2,000 kg hr-1), v (= 10 m sec-1) and
T0 (= 398 K), respectively. The wind speed at 10-m elevation is u10 (= 1.8 m sec-1) and the
incoming solar radiation is strong. The surrounding land type is rural.
(a) Calculate:
(i) The wind speed at the chimney height u(z = h); (2 marks)
(ii) The plume rise h; and (3 marks)
(iii) The maximum ground-level pollutant concentrations (4 marks)
(b) Sketch the ground-level, centreline concentrations C(x, y = 0, z = 0) for 10-1 km ≤ x ≤ 1
km. (8 marks)
(c) Briefly explain why increasing wind speed leads to less unstable and less stable,
respectively, in the daytime and nighttime atmosphere as listed in Table Q6(a). (3 marks) [Show Less]