Question

Wet material, containing 70% moisture on a wet basis, is to be dried at the rate of 0.15 kg/s in a counter-current dryer to give a product containing 5% moisture (both on a wet basis). The drying medium consists of air heated to 373 K and containing water vapor with a partial pressure of 1.0 kN/m². The air leaves the dryer at 313 K and 70% saturated Calculate how much air will be required to remove the moisture. The vapor pressure of water at 313 K may be taken as 7.4 kN/m2.

Answer 1

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.