Steady State Plug Flow Question

Question

Chlorine can be used to disinfect drinking water.  A water pipeline is 2 feet in diameter and 4000 ft. long, and has a water flow rate of 10,000 gallons per minute (gpm).  Chlorine is added at the beginning of the pipeline at a concentration of 3 mg/L, and it decays with a first order rate constant k=0.09 min^-1.  Assume steady state and plug flow conditions.  Calculate the concentration of chlorine (mg/L) at the end of the pipeline.

 

Showing all units and any conversion.

Answer 1

First let's calculate the volume of the pipe line at 4000*pi cubic feet. We have to convert this to gallons.

4000*pi cubic feet*12^3 inches^3*2.54^3 cm^3* 1ml         *1 liter  *.264 gallons

                            --------------     ----------------   ----------- --------- --------------- = 93894.13 gallons

                            1ft^3                inches^3          cm^3      1000ml  liter

At 10000 gallons per minute that's 9.3894 minutes to fill the pipeline.

 

Concentration decays at V0*e^-tk were V0=3mg/L. Here tk=9.3894*.09=.845. e^-.845=.4296.

.4296*3=1.29mg/L.

 

Hope that helps,

Deanna