Question

a water treatment plant uses alum for coagulation. the rated plant capacity is 5300 m3 /d. alum is dosed as a liquid which is 48.5 wt% dry alum. the density of liquid alum is 1.35 g/ml. (a) what is the concentration of the liquid alum solution (in mg/ml)? [1 mark] (b) given the jar test results below, what is the optimum dosage rate of liquid alum (in ml/min) at the rated plant capacity? [2 marks] (c) determine the amount of liquid alum they will per day use at the treatment plant for an average day flow rate of 3200 m3 /d? [1 mark] (d) if liquid alum costs $50/100 kg, how much does liquid alum cost the treatment plant per year? [2 marks]

Answer 1

The student is calculating the concentration, optimal dosage, daily usage, and annual cost of a liquid alum solution used in a water treatment plant. Concentration is found by multiplying weight percentage by density, whereas dosage, daily use, and cost calculations involve application of basic chemical and economic formulae.

Step-by-step explanation:

The student is tasked with calculating various aspects related to the use of a liquid alum solution in a water treatment plant. The calculations involve the concentration of the solution, the optimal dosage rate, the daily usage, and the annual cost of the liquid alum.

(a) To calculate the concentration in mg/mL, multiply the percentage weight of dry alum by the density and convert to mg/mL:
Concentration = 48.5% x 1.35 g/mL x 1000 mg/g = 654.75 mg/mL

(b) The optimal dosage rate depends on the jar test results, which aren't provided in the question. However, the formula to calculate the dosage rate is:
Dosage Rate (ml/min) = (Plant Capacity (m3/day) x Optimal Dose (mg/L))/(Concentration (mg/mL) x 1440 (min/day))

(c) To calculate the daily usage of liquid alum:
Daily Usage (L/day) = (Average Day Flow Rate (m3/day) x Optimal Dose (mg/L))/(Concentration (mg/mL) x 1000 (mL/L))

(d) The annual cost calculation takes the daily usage, multiplies by the cost per 100 kg, and then by the number of days in a year.