MH = 16.32 g/kg
SH = 9.86 g/kg
Air mass
temperature =
15° C (59° F)
What is the
Relative humidity
& the approximate
Dew-point
temperature?
How do i set this problem up? I do not understand.
Thanks
To solve this problem, you can follow the steps below:
1. Convert the temperature from Celsius to Kelvin:
15°C + 273.15 = 288.15 K
2. Calculate the saturation vapor pressure (Ps) using the Magnus formula:
Ps = 6.112 * exp(17.67 * T / (T + 243.5))
where T is the temperature in Celsius (15°C in this case).
Ps = 6.112 * exp(17.67 * 15 / (15 + 243.5)) = 17.8967 hPa
3. Calculate the actual vapor pressure (Pa) using the formula:
Pa = MH * Ps / 1000
where MH is the mixing ratio of water vapor (16.32 g/kg in this case).
Pa = 16.32 * 17.8967 / 1000 = 0.2919 hPa
4. Calculate the relative humidity (RH) using the formula:
RH = 100 * Pa / SH
where SH is the saturation mixing ratio (9.86 g/kg in this case).
RH = 100 * 0.2919 / 9.86 = 2.96%
5. Calculate the approximate dew-point temperature (Td) using the Arden Buck equation:
Td = (237.7 * (log(Pa / 6.112))) / (7.5 - log(Pa / 6.112))
Td = (237.7 * (log(0.2919 / 6.112))) / (7.5 - log(0.2919 / 6.112)) ≈ 6.7°C
So, the relative humidity is approximately 2.96% and the dew-point temperature is approximately 6.7°C.