SME
Meteorology · Problem type
Saturation vapor pressure, humidity and mixing ratio
Use this for “Air at 25 °C has a dew point of 15 °C at 1,000 hPa. Find eₛ, e, the relative humidity and the mixing ratio.”
Diagram
eₛ
=
6.112
e
17.67T ÷ (T + 243.5)
=
31.67
hPa
at
25
°C;
at
the
dew
point
15
°C
it
is
e
=
17.04
hPa.
RH
=
100e
eₛ
=
100
×
17.04
31.67
=
53.8
%.
r
=
622e
p − e
=
622
×
17.04
1,000 − 17.04
r = 10.78 g/kg
This is an example. Type your own values to start a new problem.
T
Temperature
example · °C
Td
Dew point
example · °C
eₛ
Saturation vapor pressure
calculated · hPa
e
Vapor pressure
calculated · hPa
RH
Relative humidity
calculated · %
p
Pressure
example · hPa
r
Mixing ratio
calculated · g/kg
Formulas
eₛ
=
6.112
×
e
17.67 ×
T
÷ (
T
+ 243.5)
31.67
=
6.112
×
e
17.67 × 25 ÷ (25 + 243.5)
e
=
6.112
×
e
17.67 × Td ÷ (Td + 243.5)
17.04
=
6.112
×
e
17.67 × 15 ÷ (15 + 243.5)
RH
=
100
×
e
eₛ
53.7991
=
100
×
17.04
31.67
r
=
622
×
e
p
−
e
10.7829
=
622
×
17.04
1,000 − 17.04
Assumptions
•
Tetens’ formula gives the saturation vapor pressure over water: 6.112e17.67T ÷ (T + 243.5) hPa, T in °C.
•
The air’s vapor pressure e is the saturation value at its dew point; the dew point is never above T.
•
In r = 622e ÷ (p − e), 622 g/kg is 1,000 times 0.622, water’s molar mass over dry air’s.
Step-by-step
WE KNOW
T = 25 °C, Td = 15 °C, p = 1,000 hPa
FIND
saturation vapor pressure (eₛ), vapor pressure (e), relative humidity (RH), mixing ratio (r)
Step 1 · Find saturation vapor pressure (eₛ)
Use eₛ = 6.112 × e17.67 × T ÷ (T + 243.5)
Tetens’
formula:
the
most
vapor
the
air
can
hold
at
T
.
eₛ
=
6.112
×
e
17.67 × 25 ÷ (25 + 243.5)
17.67
×
25
25 + 243.5
=
1.645
e
1.645
=
5.182
6.112 × 5.182 = 31.67 hPa
eₛ = 31.67 hPa
Step 2 · Find vapor pressure (e)
Use e = 6.112 × e17.67 × Td ÷ (Td + 243.5)
The air’s vapor pressure is the saturation value at its dew point.
e
=
6.112
×
e
17.67 × 15 ÷ (15 + 243.5)
17.67
×
15
15 + 243.5
=
1.025
e
1.025
=
2.788
6.112 × 2.788 = 17.04 hPa
e
=
17.04
hPa
Step 3 · Find relative humidity (RH)
Use RH = 100 × e ÷ eₛ
The share of the most vapor the air could hold, in percent.
RH
=
100
×
17.04
31.67
RH
=
1,704
31.67
RH = 53.7991%
Step 4 · Find mixing ratio (r)
Use r = 622 × e ÷ (p − e)
Grams
of
vapor
per
kilogram
of
dry
air:
622
e
over
the
dry
air’s
pressure.
r
=
622
×
17.04
1,000 − 17.04
r
=
622
×
17.04
982.96
r
=
10,598.88
982.96
r
=
10.7829
g/kg
Check
Put the numbers back in. Both sides should match.
31.67
=
6.112
×
e
17.67 × 25 ÷ (25 + 243.5)
✓
17.04
=
6.112
×
e
17.67 × 15 ÷ (15 + 243.5)
✓
53.7991
=
100
×
17.04
31.67
✓
10.7829
=
622
×
17.04
1,000 − 17.04
✓
Topic check
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