Conservation Of Mass

Question 1

Steady State

Answer 1

Total mass flow rate in = Total mass flow rate out
Mass of input salt = c1 × Q1 + c2 × Q2 = S
Mass of output salt = c3 × Q3
Output Concentration c3 = (c1 × Q1 + c2 × Q2) / Q1 + Q2

Question 2

Steady State with Nonconservative pollutants

Answer 2

Input rate = Output rate + Decay rate
Input rate = Output rate + kCV
Mass of input salt = c1 × Q1 + c2 × Q2 = S
Mass of output salt = C × Q = C × (Q1 + Q2)
c1 × Q1 + c2 × Q2 = S = C × Q + kCV = C(Q + kV)
C = S / Q + kV

Question 3

Unsteady state condition

Answer 3

C∞ = the concentration in the box at time t = ∞ : C = S / Q + kV
C (0) = concentration at change
C (t) = concentration at given time