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Wet towels at the Biltmore Hotel are dried in a continuous dryer after washing for use by hotel guests. The towels contain 45% water (by mass) when they enter the dryer and 3% water (by mass) when they exit the dryer. The slightly damp towels (3% water) exit the dryer at a rate of 850 kg/day. Hot, perfectly dry air (115°F, 1 atm) is also fed into the dryer. When the air leaves the dryer is has cooled to 100°F (1 atm still) and has a relative humidity of 55%.Determine the volumetric flowrate of air (m3/day) entering the dryer.Determine the mass flowrate of towels (kg/day) entering the dryer.

Question

Wet towels at the Biltmore Hotel are dried in a continuous dryer after washing for use by hotel guests. The towels contain 45% water (by mass) when they enter the dryer and 3% water (by mass) when they exit the dryer. The slightly damp towels (3% water) exit the dryer at a rate of 850 kg/day. Hot, perfectly dry air (115°F, 1 atm) is also fed into the dryer. When the air leaves the dryer is has cooled to 100°F (1 atm still) and has a relative humidity of 55%.

Determine the volumetric flowrate of air (m3/day) entering the dryer.

Determine the mass flowrate of towels (kg/day) entering the dryer.

check_circleAnswer
Step 1

Let the basis of the calculation for the given process be 850 kg/day of the dry towels. Water is represented by ‘W’ and Solids by ‘S’. The schematic flow diagram for the given process of drying is shown below:

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Step 2

It is given that the relative humidity of the exit wet air (stream 4) is 55%. At 100°F, the vapor pressure of water from steam table is 49.157 mmHg. The partial pressure of water in the exit wet air is calculated as:

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Step 3

Now, the mole fraction of water in the stream 4 is calculated from p...

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