To calculate the amount of air required to remove the moisture from the wet material, we need to determine the mass flow rate of the drying air.
Given:
- Initial moisture content of the wet material = 70%
- Final moisture content required in the product = 5%
- Mass flow rate of the wet material to be dried = 0.15 kg/s
We can use the following equation to calculate the mass flow rate of the drying air:
m_air = (m_water_removed) / (x_water_in_air - x_water_in_product)
where:
m_air = mass flow rate of drying air
m_water_removed = mass flow rate of water to be removed from the wet material
x_water_in_air = humidity ratio of the drying air
x_water_in_product = humidity ratio of the product
To calculate the humidity ratio of the drying air (x_water_in_air), we can use the vapor pressure of water in the drying air and the temperature of the air. Similarly, the humidity ratio of the product (x_water_in_product) can be calculated using the vapor pressure of water in the product and the temperature of the product.
Let's calculate the mass flow rate of the drying air:
Step 1: Calculate the humidity ratio of the drying air (x_water_in_air):
Using the vapor pressure of water in the drying air (1.0 kN/m²) and the temperature of the air (373 K), we can find the humidity ratio using a psychrometric chart or equations. For simplicity, let's assume the air is nearly saturated, so the humidity ratio is close to the saturation humidity ratio.
Assuming the air is saturated:
x_water_in_air = x_saturated(313 K)
Step 2: Calculate the humidity ratio of the product (x_water_in_product):
Using the vapor pressure of water in the product (7.4 kN/m²) and the temperature of the product (313 K), we can find the humidity ratio using the same approach as in Step 1.
x_water_in_product = x_saturated(313 K)
Step 3: Calculate the mass flow rate of the drying air (m_air):
m_water_removed = m_wet_material * (initial moisture content - final moisture content)
m_air = m_water_removed / (x_water_in_air - x_water_in_product)
By substituting the values into the equations and performing the calculations, you can find the mass flow rate of the drying air.