SME
Grade 12 Science · Problem type
The height of a cloud’s base
Use this for “The air is 24 °C with a dew point of 12 °C. How high is the cloud base?”
Diagram
The
parcel
cools
10
°C
per
km
and
its
dew
point
falls
2
°C
per
km,
so
they
close
8
°C
per
km:
h
=
24 − 12
8
=
1.5
km.
There the air is 9 °C, saturated, and a cloud forms; above it the parcel cools about 6 °C per km.
This is an example. Type your own values to start a new problem.
h (km)
=
(
T (°C)
−
Td (°C)
)
÷
8
Formulas
h
=
T
− Td
8
1.5
=
24 − 12
8
Assumptions
•
Rising air expands and cools about 10 °C per km until it is saturated.
•
Its dew point falls only about 2 °C per km, so the two close 8 °C per km.
•
Where they meet, water vapor condenses: the flat base of a cumulus cloud.
Step-by-step
WE KNOW
T = 24 °C, Td = 12 °C
FIND
height of the cloud base (h)
Step 1 · Find height of the cloud base (h)
Use h = (T − Td) ÷ 8
The gap closes 10 − 2 = 8 °C for each km the parcel rises.
h
=
24 − 12
8
h
=
12
8
h
=
1.5
km
Check
Put the numbers back in. Both sides should match.
1.5
=
24 − 12
8
✓
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