Two tonnes of paddy with 22% moisture content (wb) are to be dried to 13% moisture content (db). Calculate the weight of bone-dry product and water evaporated during the drying.

Steps to Solve

1. Calculate Initial Bone-Dry Weight

To find the initial weight of the bone-dry product from the total weight, we use the formula for dry basis moisture content:

$$ X_{db} = \frac{W_{w}}{W_{d} + W_{w}} $$

Where:

• $X_{db}$ is the dry basis moisture content (0.22 for 22% moisture content)
• $W_{w}$ is the weight of water
• $W_{d}$ is the weight of bone-dry product

Rearranging gives us:

$$ W_{d} = \frac{W_{total}}{1 + X_{db}} $$

Substituting $W_{total} = 2000$ kg (2 tonnes) and $X_{db} = 0.22$:

$$ W_{d} = \frac{2000}{1 + 0.22} \approx 1639.34 \text{ kg} $$

2. Calculate Initial Water Weight

Now find the weight of water at the initial moisture content:

$$ W_{w, initial} = W_{total} - W_{d} = 2000 - 1639.34 \approx 360.66 \text{ kg} $$

3. Calculate Final Bone-Dry Weight

The weight of the bone-dry product remains the same after drying, which we already calculated as $W_{d} \approx 1639.34$ kg.

4. Calculate Final Water Weight

Now calculate final water weight using the final moisture content (13%):

$$ W_{w, final} = W_{d} \times \frac{X_{final}}{1 - X_{final}} = 1639.34 \times \frac{0.13}{1 - 0.13} \approx 246.67 \text{ kg} $$

5. Calculate Water Evaporated

To find the amount of water that evaporated during drying:

$$ W_{evaporated} = W_{w, initial} - W_{w, final} = 360.66 - 246.67 \approx 113.99 \text{ kg} $$