For a sample of air having 22 degC DBT, relative humidity 30 % at barometric pressure of 760 mm of mercury, calculate the vapour pressure
To calculate the vapor pressure, we need to know the Relative Humidity (RH) and the saturation vapor pressure at the given temperature.
The saturation vapor pressure is the maximum amount of water vapor that air can hold at a specific temperature. It increases with higher temperatures and vice versa.
There are several empirical formulas to calculate the saturation vapor pressure, but one commonly used formula is the Magnus-Tetens formula:
e = 6.112 * exp((17.67 * T) / (T + 243.5))
where e is the saturation vapor pressure in hPa (hectopascals) and T is the temperature in degrees Celsius.
Plugging in the given temperature of 22 degrees Celsius into the formula, we get:
e = 6.112 * exp((17.67 * 22) / (22 + 243.5))
e = 6.112 * exp(391.74 / 265.5)
e ≈ 23.474 hPa
Now that we have the saturation vapor pressure, we can calculate the actual vapor pressure. The vapor pressure is a fraction of the saturation vapor pressure determined by the relative humidity (RH).
Vapor Pressure = (Relative Humidity / 100) * Saturation Vapor Pressure
Given the relative humidity of 30%, we can calculate the vapor pressure:
Vapor Pressure = (30 / 100) * 23.474
Vapor Pressure ≈ 7.042 hPa
Therefore, the vapor pressure for the given conditions is approximately 7.042 hPa.