Chapter 10 Solutions to the Odd Numbered Problems

 

Solutions provided by Dr. Todd Rayne of Hamilton College

 

1.  A saline solution with a concentration of 1823 mg/L is introduced into a 2-m-long sand column in which the pores are initially filled with distilled water. If the solution drains through the column at an average linear velocity of 1.43 m/day and the dynamic dispersivity of the sand column is 15 cm, what would the concentration of the effluent be 0.7 day after flow begins?

   

Step 1:  Calculate  from Eqn. 10-6 (assume )

                       

 

Step 2: Using Eqn. 10-8 to calculate C:

 

    

 

 

since  ignore second term.

 

 

From Appendix 13 or EXCEL,

 

 

 

 

Note: If this problem is solved in EXCEL, the final answer is different because EXCEL can calculate erfc(3.87) and use the second term of Eqn. 10-8. The Excel answer is C=86.7 mg/L.

 

 

3. A landfill is leaking an effluent with a concentration of sodium of 1250 mg/L. It seeps into an aquifer with a hydraulic conductivity of 9.8 m/day, a gradient of 0.0040, and an effective porosity of 0.15. A down-gradient monitoring well is located 25 m from the landfill. What would the sodium concentration be in this monitoring well 300 days after the leak begins? Note: In this problem you will need to find erfc(2x), which is equal to 1 1 erf(x).

   

Step 1:  Determine average linear velocity:

                       

            Step 2:  Determine DL (longitudinal dispersion coefficient)

 

            Using Eqn. 10-9:         

                                               

                                               

            and                              

                                               

 

 

 

            Step  3:  Determine C using Eqn. 10-8

 

 

 

5.   What is the relative velocity of a solute front of a solute-soil system with a distribution coefficient of 83 mL/g, a dry bulk density of 2.12 gm/cm3, and a volumetric water content of 0.26?

   

 

Using Eqn.10-15:

 

 

7. A capture well is pumping at a rate of 37,000 ft3/day from a confined aquifer with a hydraulic conductivity of 920 ft/day, an initial hydraulic gradient of 0.0027, and an initial saturated thickness of 40 ft.

(A)  What is the maximum width of the capture zone?

(B)  What is the distance from the well to the stagnation point?

   

A.  Calculate maximum width of capture zone using Eqn.10-18:

 

 

B.        Calculate the distance from the well to the stagnation point using Eqn. 10-17: