The solution in the first pipe has a concentration of c1 mg/L and that in the second pipe has a concentration of c2 mg/L. the flow rate of the pipes are Q1 and Q2 respectively. The concept of mass or material balance can be applied to determine the concentration of the mixed solution discharged from the tank because under steady-state conditions, the total amount of salt entering the tank must be equal to the total amount leaving the tank. In other words, since the salt neither decays nor reacts with other substance (in this example), the concentration of salt in the mixture in the tank stay constant over time.
The product of concentration of volume flow rate equals the mass flow rate because mg/L X L/d = mg/d where the volume flow rate in this example is expresses in terms of liter per day, or L/d. for convenience here, consider that the time interval is 1 day. Then the product of c1 X Q must equal the mass of salt entering the vessel in 1 d from the first pipe. Similarly, c2 X Q equals the mass of salt entering the tank from the second pipe. The total mass of salt entering the tank in 1 d, that is, the input, must be equal to the sum from the two pipes, or input = c1 X Q1 + c2 X Q2.