Mass flow rate of outside air through a duct is 735 kg h⁻¹. Absolute humidity of air is 0.025 kg water vapour per kg dry air at 40 °C. This air is mixed with equal quantity of moist exhaust air coming out of a counter current dryer at 55 °C. The mixed air is heated up to 75 °C to dry barley, fed at 174 kg h⁻¹, at an initial moisture content of 31 % (wet basis) to a final value of 7 % (dry basis). The absolute humidity of the exhaust air from the dryer in 'kg water vapour per kg dry air' will be ________.
Official Answer Key:
0.086 to 0.089
Step-by-Step Solution & Explanation
Moisture removed from grain. Dry matter = 174 (1 − 0.31) = 120.06 kg h⁻¹.
Initial water = 174 × 0.31 = 53.94 kg h⁻¹; final water = 0.07 × 120.06 = 8.40 kg h⁻¹ (7 % dry basis).
W = 53.94 − 8.40 = 45.54 kg h⁻¹.
Dry air flow. Outside moist air 735 kg h⁻¹ ⇒ dry air = 735/(1 + 0.025) = 717.1 kg h⁻¹.
Recycled exhaust is of equal quantity, so total dry air through the dryer = 2 × 717.1 = 1434.1 kg h⁻¹.
Mixing. H_mix = (0.025 + H_e)/2.
Dryer moisture balance. H_e = H_mix + W/(dry air through dryer)
H_e = (0.025 + H_e)/2 + 45.54/1434.1 = 0.0125 + 0.5 H_e + 0.03176
0.5 H_e = 0.04426 ⇒ H_e = 0.0885 kg water vapour per kg dry air — within the official range 0.086–0.089.
Common error: reading 7 % as wet basis, which changes W to 40.4 kg h⁻¹ and H_e to 0.081.
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