1. Find: z [ft] z 5 8 C) 10 D) 12 Q pump 3 [ft] water sand L=400 [ft]
Ksand=1*10-6 [m/s]
Q=10,000 [gal/day] Q z
pump
3 [ft]
water
Find the the depth z, in feet. [pause] In this problem, ---
sand

2. Find: z [ft] z 5 8 C) 10 D) 12 Q pump 3 [ft] water sand L=400 [ft]
Ksand=1*10-6 [m/s]
Q=10,000 [gal/day] Q z
pump
3 [ft]
water
a 400 foot long trench is shored on both sides, ---
sand

3. Find: z [ft] z 5 8 C) 10 D) 12 Q pump 3 [ft] water sand L=400 [ft]
Ksand=1*10-6 [m/s]
Q=10,000 [gal/day] Q z
pump
3 [ft]
water
and a pump pumps at 10,000 gallons per day ---
sand

4. Find: z [ft] z 5 8 C) 10 D) 12 Q pump 3 [ft] water sand L=400 [ft]
Ksand=1*10-6 [m/s]
Q=10,000 [gal/day] Q z
pump
3 [ft]
water
to lower the water surface elevation in the trench by a depth z.
sand

5. Find: z [ft] z 5 8 C) 10 D) 12 Q pump 3 [ft] water sand flownet
L=400 [ft] 5 8
C) 10
D) 12
Ksand=1*10-6 [m/s]
Q=10,000 [gal/day] Q z
pump
3 [ft]
water
The water moves through a sand layer with a given hydraulic conductivity and flow net. [pause]
sand
flownet

6. Find: z [ft] z 5 8 C) 10 D) 12 Q pump 3 [ft] water sand L=400 [ft]
Ksand=1*10-6 [m/s]
Q=10,000 [gal/day] Q z
pump
3 [ft]
water
Since this diagram is symmetrical, we’ll only view the left half, for now.
sand

7. Find: z [ft] z Q water 3 [ft] sand L=400 [ft] Ksand=1*10-6 [m/s]
Q=10,000 [gal/day] Q z
water
3 [ft]
[pause]
sand

8. Find: z [ft] z Q = K * hL * Q water 3 [ft] sand L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND Q z
water
3 [ft]
Flow through a flownet is calculated as ---
sand

9. Find: z [ft] z Q = K * hL * Q water 3 [ft] sand L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND Q z
water
3 [ft]
the hydraulic conductivity, ---
sand

10. Find: z [ft] z Q = K * hL * Q water 3 [ft] sand L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND Q z
water
3 [ft]
times the headloss, ---
sand

11. Find: z [ft] z Q = K * hL * Q water 3 [ft] sand L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND Q z
water
3 [ft]
times the number of flow channels divided by the number of drops from the flownet, ---
sand

12. Find: z [ft] z Q = K * hL * Q water 3 [ft] sand L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND Q z
water
3 [ft]
times the length of the structure into and out of the viewing plane.
sand

13. Find: z [ft] z Q = K * hL * Q water 3 [ft] sand L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND Q z
water
3 [ft]
For this problem, ---
sand

14. Find: z [ft] z Q = K * hL * given Q water 3 [ft] sand L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND Q
given z
water
3 [ft]
we have been given the flowrate, hydraulic conductivity, flownet and length, ---
sand

15. Find: z [ft] z Q = K * hL * given Q hL = K*L Q water 3 [ft] sand
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND Q
given z
water Q ND
hL =
3 [ft] *
K*L NF
So we’ll solve for the head loss across the flow net, ---
sand

16. Find: z [ft] z Q = K * hL * given Q hL = K*L Q water 3 [ft] sand
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND Q
given z
water Q ND
hL =
3 [ft] *
K*L NF
and the z value we’re trying to find is that headloss.
sand

17. Find: z [ft] z = z Q = K * hL * given Q K*L Q water 3 [ft] sand
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND Q
given z
water Q ND
z =
3 [ft] *
K*L NF
---
sand

18. Find: z [ft] z = z = z Q = K * hL * 7.48 given Q K*L K*L Q water
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z
water Q ND
z =
3 [ft] *
K*L NF
The flowrate is converted to cubic feet per day, ---
1,337 [ft3/day] ND
z = *
K*L NF
sand

19. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28
the hydraulic conductivity is converted to feet per day, --- m
1,337 [ft3/day] ND
z = *
0.283[ft/day]*L NF
sand

20. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28
and the length is plugged into the equation without conversion. m
1,337 [ft3/day] ND
z = *
0.283[ft/day]*L NF
sand

21. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28
From the flownet, we count the number of drops across the soil. m
1,337 [ft3/day] ND
z = *
0.283[ft/day]*L NF

22. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28 1 m 1
1,337 [ft3/day] ND
z = *
0.283[ft/day]*L NF

23. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28 2 m 1
1,337 [ft3/day] ND
z = *
0.283[ft/day]*L NF 2

24. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28 3 m 1
1,337 [ft3/day] ND
z = *
0.283[ft/day]*L NF 2 3

25. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28 4 m 1
1,337 [ft3/day] ND
z = *
0.283[ft/day]*L NF 2 4 3

26. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28 5 m 1
1,337 [ft3/day] ND
z = 5 *
0.283[ft/day]*L NF 2 4 3

27. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28 6 m 1 6
1,337 [ft3/day] ND
z = 5 *
0.283[ft/day]*L NF 2 4 3

28. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28
7 [pause] 7 m 1 6
1,337 [ft3/day] ND
z = 5 *
0.283[ft/day]*L NF 2 4 3

29. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28
7 drops 7 m 1 6
1,337 [ft3/day]
z = 7 5 *
0.283[ft/day]*L NF 2 4 3

30. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28
Lastly, we count the number of flow channels in the net, and we count, --- 7 m 1 6
1,337 [ft3/day]
z = 7 5 *
0.283[ft/day]*L NF 2 4 3

31. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28 1 1 7 m 1 6
1,337 [ft3/day]
z = 7 5 *
0.283[ft/day]*L NF 2 4 3

32. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28 1 2 2 7 m 1 6
1,337 [ft3/day]
z = 7 5 *
0.283[ft/day]*L NF 2 4 3

33. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28 1 2 3 3 7 m 1 6
1,337 [ft3/day]
z = 7 5 *
0.283[ft/day]*L NF 2 4 3

34. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28 4 1 2 3
4 [pause] 7 m 1 6
1,337 [ft3/day]
z = 7 5 *
0.283[ft/day]*L NF 2 4 3

35. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28 4 1 2 3
4 channels on the left side of the trench, --- 7 m 1 6
1,337 [ft3/day]
z = 7 5 *
0.283[ft/day]*L 4 2 4 3

36. Find: z [ft] z = z = z Q = K * hL * 7.48 given 86,400 Q K*L 3.28 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28 4 1 2 3
plus an additional 4 flow channels on the right side of the trench, since we’re only viewing half the flow net. [pause] The headloss across the flow net, 7 m 1 6
1,337 [ft3/day]
z = 7 5 *
0.283[ft/day]*L
4+4 2 4 3

37. Find: z [ft] z = z = z = 10.3 [ft] z Q = K * hL * 7.48 given 86,400 Q
L=400 [ft]
Ksand=1*10-6 [m/s] NF
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28 4 1 2 3
our value z, is equal to 10.3 feet. 7 m 1 6
1,337 [ft3/day]
z = 7 5 *
0.283[ft/day]*L
4+4 2
z = 10.3 [ft] 4 3

38. Find: z [ft] z = z = z = 10.3 [ft] z 5 Q = K * hL * 8 C) 10 7.48 D) 12
L=400 [ft]
Ksand=1*10-6 [m/s] NF 5 8
C) 10
D) 12
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28 4 1 2 3
Looking back at our possible solutions, --- 7 m 1 6
1,337 [ft3/day]
z = 7 5 *
0.283[ft/day]*L
4+4 2
z = 10.3 [ft] 4 3

39. Find: z [ft] z = z = z = 10.3 [ft] z AnswerC 5 Q = K * hL * 8 C) 10
L=400 [ft]
Ksand=1*10-6 [m/s] NF 5 8
C) 10
D) 12
Q=10,000 [gal/day]
Q = K * hL *
* L ND
gal
7.48
ft3 Q
given z s
water
86,400 Q ND
z =
day
3 [ft] *
K*L NF ft
3.28 4 1 2 3
The answer is C. 7 m 1 6
1,337 [ft3/day]
z = 7 5 *
0.283[ft/day]*L
4+4 2
z = 10.3 [ft] 4
AnswerC 3

40. ? Index σ’v = Σ γ d γT=100 [lb/ft3] +γclay dclay 1
Find: σ’v at d = 30 feet
(1+wc)*γw
wc+(1/SG)
σ’v = Σ γ d d
Sand
10 ft
γT=100 [lb/ft3]
100 [lb/ft3]
10 [ft]
20 ft
Clay
= γsand dsand
+γclay dclay A W S
V [ft3]
W [lb]
40 ft
text
wc = 37% ? Δh
20 [ft]
(5 [cm])2 * π/4