For a sample of air having 22 degC DBT, relative humidity 30 % at barometric pressure of 760 mm of mercury, calculate the vapour pressure,humidity ratiio,dew point temperature,vapour density,and enthalpy
To calculate the various properties of air given the dry bulb temperature (DBT) and relative humidity, you will need to use various formulas and psychrometric charts. Let's break down each calculation one by one.
1. Vapour Pressure:
The vapour pressure can be calculated using the formula:
Vapour Pressure = (Relative Humidity / 100) * Saturation Vapour Pressure at DBT
First, we need to calculate the saturation vapour pressure at the given dry bulb temperature (DBT) of 22°C. You can find this value in the psychrometric chart or use the formula known as Magnus equation:
Saturation Vapour Pressure = 6.1078 * 10^((7.5 * DBT) / (237.3 + DBT))
Plug in the value of DBT = 22°C into the above equation to calculate the saturation vapour pressure.
Next, calculate the vapour pressure by multiplying the saturation vapour pressure with the relative humidity (RH) percentage divided by 100.
2. Humidity Ratio:
Humidity Ratio (W) represents the mass of water vapor per kilogram of dry air. You can calculate it using the formula:
Humidity Ratio = 0.622 * (Vapour Pressure / (Barometric Pressure - Vapour Pressure))
Here, we will use the calculated vapour pressure from step 1 and the given barometric pressure of 760 mmHg to find the humidity ratio.
3. Dew Point Temperature:
Dew Point Temperature is the temperature at which air becomes saturated, and condensation begins to form. To calculate the dew point temperature, you can use the Magnus equation mentioned earlier. Rearrange the formula to solve for the dew point temperature:
Dew Point Temperature = (237.3 * log((Vapour Pressure / 6.1078))) / (7.5 - log((Vapour Pressure / 6.1078)))
Use the calculated vapour pressure from step 1 to find the dew point temperature.
4. Vapour Density:
Vapour Density is the density of the water vapor in the air. It can be calculated using the ideal gas law:
Vapour Density = (Vapour Pressure / Rv) * (Mv / P)
Where:
- Rv is the specific gas constant for water vapor (461.51 J/(kg·K))
- Mv is the molecular weight of water, which is 18.01528 g/mol
- P is the atmospheric pressure in Pascals (Pa)
Convert the provided barometric pressure from mmHg to Pa before using the values in the equation.
5. Enthalpy:
Enthalpy (H) represents the total heat content of the air. To calculate it, you can use the formula:
Enthalpy = CP * DBT + W * hfg
Where:
- CP is the specific heat of dry air at constant pressure (approximately 1.006 kJ/(kg·K))
- DBT is the given dry bulb temperature
- W is the humidity ratio (calculated in step 2)
- hfg is the specific enthalpy of vaporization of water at the given dry bulb temperature. You can find this value in the steam tables.
These calculations should provide you with the desired properties of air based on the given conditions.