Two tonnes of wheat grains are to be dried from 20% (wb) moisture content to 12% moisture content (wb) in 2 hrs using a mechanical dryer. How much air and heat will be required to... Two tonnes of wheat grains are to be dried from 20% (wb) moisture content to 12% moisture content (wb) in 2 hrs using a mechanical dryer. How much air and heat will be required to dry the grains?
Understand the Problem
The question is asking how much air and heat are needed to dry two tonnes of wheat grains, reducing their moisture content from 20% to 12% within 2 hours using a mechanical dryer. This involves calculations regarding moisture loss and the heat energy required for drying.
Answer
Moisture removed: \(160 \, \text{kg}\), Heat required: \(361600 \, \text{kJ}\), Heat per hour: \(180800 \, \text{kJ/hour}\), Air needed: \(80 \, \text{m³}\).
Answer for screen readers
- Total moisture removed: (160 , \text{kg})
- Heat required: (361600 , \text{kJ})
- Heat per hour: (180800 , \text{kJ/hour})
- Air required: (80 , \text{m³})
Steps to Solve
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Calculate the initial moisture content
The initial moisture content can be calculated as:
[ \text{Initial moisture content (kg)} = \text{Total weight} \times \text{Moisture content} ] For 2 tonnes (2000 kg) at 20% moisture: [ \text{Initial moisture content} = 2000 , \text{kg} \times 0.20 = 400 , \text{kg} ]
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Calculate the final moisture content
The final moisture content at 12% can be calculated as:
[ \text{Final moisture content (kg)} = \text{Total weight} \times \text{Moisture content} ] For 2000 kg at 12% moisture: [ \text{Final moisture content} = 2000 , \text{kg} \times 0.12 = 240 , \text{kg} ]
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Determine the moisture loss
The moisture loss is the difference between the initial and final moisture content:
[ \text{Moisture loss (kg)} = \text{Initial moisture} - \text{Final moisture} ] [ \text{Moisture loss} = 400 , \text{kg} - 240 , \text{kg} = 160 , \text{kg} ]
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Calculating the heat required for drying
To calculate the heat required, we need to know the latent heat of vaporization for water, which is approximately 2260 kJ/kg:
[ Q = \text{Moisture loss} \times \text{Latent heat} ] [ Q = 160 , \text{kg} \times 2260 , \text{kJ/kg} = 361600 , \text{kJ} ]
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Calculate the heat per hour
Since we are drying the grains in 2 hours, the heat energy required per hour is:
[ Q_{\text{hour}} = \frac{Q}{\text{Time}} ] [ Q_{\text{hour}} = \frac{361600 , \text{kJ}}{2 , \text{hours}} = 180800 , \text{kJ/hour} ]
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Air required for drying
To compute the air needed, we use the concept of specific humidity, but this requires specific values that depend on the drying conditions. For simplicity, let's assume a basic airflow model that requires about 0.5 m³ of air per kg of moisture removed:
[ \text{Air required (m³)} = \text{Moisture loss} \times 0.5 ] [ \text{Air required} = 160 , \text{kg} \times 0.5 = 80 , \text{m³} ]
- Total moisture removed: (160 , \text{kg})
- Heat required: (361600 , \text{kJ})
- Heat per hour: (180800 , \text{kJ/hour})
- Air required: (80 , \text{m³})
More Information
In drying processes, calculations for moisture content and heat energy are essential for operations like grain drying. The results show the significant energy and air volume required, indicating the efficiency of the drying system.
Tips
- Confusing moisture content (wet basis) with moisture content (dry basis).
- Forgetting to convert units appropriately when calculating total weight or heat energy.
- Not accounting for all the moisture removed from the grain.
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