Chapter 4 – Solutions to Odd Numbered Problems

 

These solutions were provided by Dr. Todd Rayne of Hamilton College.

 

4. 1.      A fluid in an aquifer is 6.5 m above a reference datum, the fluid pressure is 1800 N/m2, and the flow velocity is 3.4 3 1025 m/s. The fluid density is 1.01 3 103 kg/m3.

(A)  What is the total energy per unit mass?

(B)  What is the total energy per unit weight?

   

A.

 

B.

 

 

4.3.      A piezometer is screened 723.4 m above mean sea level. The point-water pressure head in the piezometer is 17.9 m and the water in the aquifer is fresh at a temperature of 20°C.

(A)  What is the total head in the aquifer at the point where the piezometer is screened?

(B)  What is the fluid pressure in the aquifer at the point where the piezometer is screened?

   

A. 

 

     

 

B. 

 

 

 

 

4.5.      A piezometer in a saline water aquifer has a point-water pressure head of 18.73 m. If the water has a density of 1022 kg/m3 and is at a field temperature of 18°C, what is the equivalent fresh-water pressure head?

 

Now, assume fresh water:

 

 

 

 

4.7.      A sand aquifer has a median pore diameter of 0.232 mm. The fluid density is 1.003 x 103 kg/m3 and the fluid viscosity is 1.15 x 10-3 N-s/m2. If the flow rate is 0.0067 m/s, is Darcy’s law valid? What is the reason for your answer?

   

 

 

 

4.9.      A confined aquifer is 8 ft thick. The potentiometric surface drops 1.33 ft between two wells that are 685 ft apart. The hydraulic conductivity is 251 ft/day and the effective porosity is 0.27.

(A)  How many cubic feet per day are moving through a strip of the aquifer that is 10 ft wide?

(B)  What is the average linear velocity?

   

A.

     

 

B. 

 

 

 

 

 

4.11.    An unconfined aquifer has a hydraulic conductivity of 8.7 x 10-2 cm/s. There are two observation wells 597 ft apart. Both penetrate the aquifer to the bottom. In one observation well the water stands 28.9 ft above the bottom, and in the other it is 26.2 ft above the bottom.

(A)  What is the discharge per 100-ft-wide strip of the aquifer in cubic feet per day?

(B)  What is the water-table elevation at a point midway between the two observation wells?

   

A.

 

 

 

 

B.

 

 

 

 

           

 

4.13.    Refer to Figure 4.19. The hydraulic conductivity of the aquifer is 14.5 m/day. The value of h1 is 17.6 m and the value of h2 is 15.3 m. The distance from h1 to h2 is 525 m. There is an average rate of recharge of 0.007 m/d.

(A)  What is the average discharge per unit width at
x 5 0?

(B)  What is the average discharge per unit width at x 5 525 m?

(C)  Is there a water-table divide? If so, where is it located?

(D)  What is the maximum height of the water table?

   

A.

 

Using Equation 4-72:

 

 

 

     B.

Eqn. 4-72 at x = 525 yields:

 

 

C.

 

Yes, there is a water table divide. Using Eqn.4-73:

 

 

  D.

 

Maximum height of water table is at the divide where x = 113.2 m.. Using Eqn.4-74:   

 

4.15.    An earthen dam is constructed on an impermeable bedrock layer. It is 550 ft across (i.e., the distance from the water in the reservoir to the tailwaters below the dam is 550 ft). The average hydraulic conductivity of the material used in the dam construction is 0.77 ft/day. The water in the reservoir behind the dam is 35 ft deep and the tailwaters below the dam are 20 ft deep. Compute the volume of water that seeps from the reservoir, through the dam, and into the tailwaters per a 100-ft-wide strip of the dam in cubic feet per day.

   

Using Equation  4-59:

 

 where

 

 

 

 

 

 

4.17.    Draw a flow net for seepage through the earthen dam shown in Figure 4.20. If the hydraulic conductivity of the material used in the dam is 0.22 ft/day, what is the seepage per unit width per day?

 

 

Solution:

 

            A flow net can be drawn with 5 flow tubes and 25 equipotential lines.

 

Using Equation 5-50:

where