Solutions to Chapter 3

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Solutions to Chapter 3

• Assignment 3 CE/AE/EnvSci 4/524

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3.7 The wind has a velocity of 10 m/h at 10 m
in a rural area. When lapse rate is 0.2C/100,
what is the velocity at an elevation of 100 m in
miles per hour? u/u1 (z/z1)p Table 3-2, ?T/?Z
0.2C/100, Stability Class E U u1 (z/z1)p
10 mph (100m/10m)0.35 22.4 mph
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3.9 Consider that the wind speed u is 2 m/s at
a height of 10 m. Estimate wind speed at a) 200
m and b) 300 m for the 6 stability classes in
Table 3-3 for rural conditions. U u1 (z/z1)p
2 m/s (200/10)P A U 2 (200/10)0.07 2.47
m/s B U 2 (200/10)0.07 2.47 m/s C U 2
(200/10)0.10 2.70 m/s D U 2 (200/10)0.15
3.13 m/s E U 2 (200/10)0.35 5.71 m/s F U
2 (200/10)0.55 10.39 m/s U u1 (z/z1)p 2
m/s (300/10)P A U 2 (300/10)0.07 2.54
m/s B U 2 (300/10)0.07 2.54 m/s C U 2
(300/10)0.10 2.81 m/s D U 2 (300/10)0.15
3.33 m/s E U 2 (300/10)0.35 6.58 m/s F U
2 (300/10)0.55 12.9 m/s
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3.14 In a given situation the ground-level air
temperature is 15 C, while the normal maximum
surface temperature for that month is a) 26C and
b) 24C. At an elevation of 300 m, the
temperature is found to be 21C. What is the
maximum mixing depth in meters for the two
cases? Air parcel will rise until its
temperature T local atmospheric temperature,
neutral equilibrium. Temperature profile
DT/dz, solid line Dry adiabatic is dashed
MMD
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3.14 In a given situation the ground-level air
temperature is 15 C, while the normal maximum
surface temperature for that month is a) 26C and
b) 24C. At an elevation of 300 m, the
temperature is found to be 21C. What is the
maximum mixing depth in meters for the two
cases? Air parcel will rises until intersection
of lines. Slope for existing condition is (21
15) 0.02C/m
300m Adiabatic lapse rate (slope) is -0.0098C/m
(equation 3-5) MMD is point where slopes
intersect (Z)
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3.14 for condition A existing condition is
0.02C/m Adiabatic
lapse rate (slope) is -0.0098C/m (equation
3-5) MMD is point where slopes intersect (Z) 15
Z (0.02C/m) 26 Z(-0.0098C/m) Z
_______26C - 15C_____ 369.13 m
(0.02C/m 0.0098C/m)
MMD
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3.14 for condition B existing condition is
0.02C/m Adiabatic
lapse rate (slope) is -0.0098C/m (equation
3-5) MMD is point where slopes intersect (Z) 15
Z (0.02C/m) 24 Z(-0.0098C/m) Z
_______24C - 15C_____ 302 m (0.02C/m
0.0098C/m)
MMD