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.

Understand the Problem

The question is asking us to calculate the weight of the bone-dry product and the amount of water evaporated from two tonnes of paddy that has a moisture content of 22%. We need to find out the final weight of the paddy once it is dried to a moisture content of 13%. This involves understanding moisture content on both a wet basis (wb) and a dry basis (db) and performing calculations accordingly.

Answer

The weight of the bone-dry product is approximately 1.56 tonnes, and the amount of water evaporated is approximately 0.21 tonnes.
Answer for screen readers

The weight of the bone-dry product is approximately 1.56 tonnes, and the amount of water evaporated is approximately 0.21 tonnes.

Steps to Solve

  1. Calculate the initial weight of the moisture in the paddy

First, we determine the weight of the moisture in the paddy. The moisture content is given as 22%, so for 2 tonnes of paddy, we calculate the moisture weight as follows:

[ \text{Moisture weight} = \text{Total weight} \times \text{Moisture content} = 2 \text{ tonnes} \times 0.22 = 0.44 \text{ tonnes} ]

  1. Determine the weight of the bone-dry product

Next, we find the weight of the dry matter in the paddy. This is the total weight minus the moisture weight:

[ \text{Dry weight} = \text{Total weight} - \text{Moisture weight} = 2 \text{ tonnes} - 0.44 \text{ tonnes} = 1.56 \text{ tonnes} ]

  1. Calculate the target moisture weight when dried to 13%

Now, we need to find out what the total weight will be when the moisture content is reduced to 13%. Let ( W_d ) be the final weight:

We're given that the final moisture content is 13%, which means that 87% of the final weight will be the bone-dry product. We can set up the following equation:

[ W_d \times 0.87 = \text{Dry weight} ]

Substituting the dry weight:

[ W_d \times 0.87 = 1.56 ]

Solving for ( W_d ):

[ W_d = \frac{1.56}{0.87} \approx 1.79 \text{ tonnes} ]

  1. Calculate the amount of water evaporated

To find out the amount of water that has evaporated, we subtract the final weight from the initial total weight:

[ \text{Water evaporated} = \text{Initial weight} - \text{Final weight} = 2 \text{ tonnes} - 1.79 \text{ tonnes} \approx 0.21 \text{ tonnes} ]

The weight of the bone-dry product is approximately 1.56 tonnes, and the amount of water evaporated is approximately 0.21 tonnes.

More Information

This problem illustrates the concept of moisture content in agriculture, which is crucial for understanding how much water is in crops. The difference between wet basis and dry basis measurements is essential for those dealing with agricultural products, storage, and processing.

Tips

  • One common mistake is confusing the wet basis and dry basis moisture content. Ensure to clarify which type is being used.
  • Another mistake is not converting units or not keeping consistent units throughout the calculation. Always check that all weights are in the same measurement system.

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