Question

Consider you cannot stop the mill to add the chemical. The tank receives some input at 20 L per minutes and feed the mill at the same rate. If the tank as a volume of 3000 L, that initially there is 0.3 kg of chemical per L in the tank, and that the added compound must be at a fixed concentration, what should be that concentration if you want the output of the tank to become at 0.7 kg per L in exactly 120 minutes of operation?

Answer 1

To achieve an output concentration of 0.7 kg/L in the tank after 120 minutes, the input solution must have a concentration of 0.5 kg/L given the 20 L/min flow rate and the 3000 L tank volume.

Step-by-step explanation:

To calculate the required concentration of the chemical compound needed to achieve a concentration of 0.7 kg per L in the tank after 120 minutes, we must consider a continuous flow process where the tank is being fed at 20 liters per minute and simultaneously drained at the same rate. Initially, the tank contains 3000 liters of a solution with a concentration of 0.3 kg/L.

First, we find the total amount of chemical in the tank at the beginning which is 0.3 kg/L × 3000 L = 900 kg.

Next, we calculate the final total amount of chemical needed to achieve the target concentration after 120 minutes. Since 120 minutes is 2 hours, and the tank gets 20 L/min, the volume of solution added will be 20 L/min × 120 min = 2400 L. The target concentration is 0.7 kg/L for the total volume of 3000 L (original tank volume), so we need 0.7 kg/L × 3000 L = 2100 kg of chemical in total.1

To find the difference and thus the amount of chemical needed in the input, we subtract the initial amount from the final total required: 2100 kg - 900 kg = 1200 kg.

Since we are adding 2400 L over the course of 120 minutes, the required concentration of the input chemical solution is calculated by dividing the total chemical needed by the total volume added: 1200 kg ÷ 2400 L = 0.5 kg/L.

Therefore, the input solution should have a concentration of 0.5 kg/L to achieve the desired output concentration of 0.7 kg/L in the tank after 120 minutes of operation.