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A batch-type dryer is used to dry dates. The initial and final moisture contents of the dates were measured to be 39% MDB and 14% MWB, respectively. The moisture removal during drying is 185 kg. Determine the capacity in each batch.

Answer :

The capacity of each batch in the batch-type dryer is approximately 173.36 kg. This means that each batch can dry up to 173.36 kg of dates from an initial moisture content of 39% MDB to a final moisture content of 14% MWB.

To determine the capacity of each batch in the batch-type dryer, we first need to calculate the initial and final masses of the dates and then find the difference between them to get the moisture removed.

Given information:

Initial moisture content (X₁) = 39% MDB (dry basis)

Final moisture content (X₂) = 14% MWB (wet basis)

Moisture removed during drying = 185 kg

Let M₁ be the initial mass of the dates and M₂ be the final mass of the dates after drying.

To convert between different moisture basis, we use the following relationship:

MWB = MDB / (1 - MDB) and MDB = MWB / (1 + MWB)

Step 1: Convert the initial moisture content (X₁) from MDB to MWB:

X₁_MWB = X₁ / (1 - X₁)

X₁_MWB = 0.39 / (1 - 0.39)

X₁_MWB ≈ 0.6393 or 63.93% MWB

Step 2: Convert the final moisture content (X₂) from MWB to MDB:

X₂_MDB = X₂ / (1 + X₂)

X₂_MDB = 0.14 / (1 + 0.14)

X₂_MDB ≈ 0.1228 or 12.28% MDB

Step 3: Calculate the initial mass (M₁) of the dates:

M₁ = Moisture removed / (X₁_MWB - X₂_MDB)

M₁ = 185 kg / (0.6393 - 0.1228)

M₁ ≈ 185 kg / 0.5165

M₁ ≈ 358.36 kg

Step 4: Calculate the final mass (M₂) of the dates:

M₂ = M₁ - Moisture removed

M₂ = 358.36 kg - 185 kg

M₂ ≈ 173.36 kg

For more such question on moisture visit;

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