Potato flakes (moisture content = 75% wet basis) are being dried in a concurrent flow drier. The moisture content of the air entering the drier is 0.08 kg of water per 1 kg dry air. The moisture content of air leaving the drier is 0.18kg water per 1kg of dry air. The airflow rate in the drier is 100kg dry air per hour. As shown in the figure below, 50kg of wet potato flakes enter the drier per hour. At steady state, what is the mass of “dried potatoes”?
no figure.
Well, let's do some calculations and find out!
Now, we know that the airflow rate in the drier is 100 kg dry air per hour, and the moisture content of the air entering the drier is 0.08 kg of water per 1 kg dry air. So, we can determine the amount of water entering the drier as 100 kg dry air/hour multiplied by 0.08 kg water/kg dry air.
This gives us 8 kg of water entering the drier per hour.
Next, we need to calculate the amount of water leaving the drier. We know that the moisture content of air leaving the drier is 0.18 kg water per 1 kg dry air. So, we can determine the amount of water leaving the drier as 100 kg dry air/hour multiplied by 0.18 kg water/kg dry air.
This gives us 18 kg of water leaving the drier per hour.
Now, we know that 50 kg of wet potato flakes enter the drier per hour, and the moisture content of the potato flakes is 75% (moisture content = 75% wet basis).
To find the mass of "dried potatoes," we need to calculate the amount of water removed from the potato flakes in the drier. This can be calculated as 50 kg wet potato flakes/hour multiplied by 0.75 (moisture content in decimal form).
This gives us 37.5 kg of water removed from the potato flakes in the drier per hour.
Now, to find the mass of "dried potatoes," we need to subtract the amount of water removed from the total mass of wet potato flakes entering the drier. So, the mass of "dried potatoes" is 50 kg wet potato flakes - 37.5 kg water removed = 12.5 kg.
Therefore, the mass of "dried potatoes" at steady state is 12.5 kg.
To determine the mass of "dried potatoes" at steady state, we need to calculate the mass of water removed from the wet potato flakes by the drying air.
Step 1: Calculate the moisture content of wet potato flakes entering the drier:
Mass of water in wet potato flakes = Moisture content x Mass of wet potato flakes
Mass of water in wet potato flakes = 0.75 x 50 kg
Mass of water in wet potato flakes = 37.5 kg
Step 2: Calculate the mass of water in the drying air entering the drier:
Mass of water in drying air = Moisture content x Mass of dry air
Mass of water in drying air = 0.08 kg water/kg dry air x 100 kg dry air
Mass of water in drying air = 8 kg
Step 3: Calculate the mass of water in the drying air leaving the drier:
Mass of water in drying air = Moisture content x Mass of dry air
Mass of water in drying air = 0.18 kg water/kg dry air x 100 kg dry air
Mass of water in drying air = 18 kg
Step 4: Calculate the mass of water removed from the wet potato flakes:
Mass of water removed = Mass of water in wet potato flakes - Mass of water in drying air leaving the drier
Mass of water removed = 37.5 kg - 18 kg
Mass of water removed = 19.5 kg
Step 5: Calculate the mass of dried potato flakes:
Mass of dried potato flakes = Mass of wet potato flakes - Mass of water removed
Mass of dried potato flakes = 50 kg - 19.5 kg
Mass of dried potato flakes = 30.5 kg
Therefore, the mass of "dried potatoes" at steady state is 30.5 kg.
To find the mass of "dried potatoes" at steady state, we need to determine the moisture content of the potato flakes entering and leaving the drier.
Given information:
- Moisture content of wet potato flakes entering the drier: 75% (on a wet basis)
- Moisture content of air entering the drier: 0.08 kg water per 1 kg dry air
- Moisture content of air leaving the drier: 0.18 kg water per 1 kg dry air
- Airflow rate in the drier: 100 kg dry air per hour
- Potato flakes entering the drier per hour: 50 kg
Let's calculate the moisture removal rate and the amount of water evaporated from the potato flakes.
1. Moisture content in wet potato flakes: 75% (0.75 on a wet basis)
Therefore, the moisture content in dried potato flakes would be: 100% - 75% = 25% (0.25 on a wet basis)
2. Moisture removal rate:
The moisture removal rate can be calculated using the formula:
Moisture removal rate = wet potato flakes entering the drier per hour × (moisture content in wet potato flakes - moisture content in dried potato flakes)
Moisture removal rate = 50 kg/hour × (0.75 - 0.25)
= 50 kg/hour × 0.5
= 25 kg/hour
3. Water evaporated from the potato flakes:
The amount of water evaporated from the potato flakes can be calculated using the formula:
Water evaporated = moisture removal rate × moisture content in dried potato flakes
Water evaporated = 25 kg/hour × 0.25
= 6.25 kg/hour
Therefore, at steady state, the mass of "dried potatoes" per hour would be equal to the amount of water evaporated from the potato flakes, which is 6.25 kg/hour.