1. Find: minimum # of stages
gal
min
Elev2=825 [ft]
Q=500
n=1,780 [rpm]
s=0 [ft]
ns>1,500 3 4 5 6
Elev1=
Find the minimum number of stages for the pump. [pause] In this problem, ---
415 [ft]
#stages?

2. Find: minimum # of stages
gal
min
Elev2=825 [ft]
Q=500
n=1,780 [rpm]
s=0 [ft]
ns>1,500 3 4 5 6
Elev1=
Groundwater is pump from an aquifer into an elevated storage tank.
415 [ft]
#stages?

3. Find: minimum # of stages
gal
min
Elev2=825 [ft]
Q=500
n=1,780 [rpm]
s=0 [ft]
ns>1,500 3 4 5 6
Elev1=
The elevation of the groundwater table, and the elevation of the water surface elevation in the tank are provided. There is no drawdown ---
415 [ft]
#stages?

4. Find: minimum # of stages
gal
min
Elev2=825 [ft]
Q=500
n=1,780 [rpm]
s=0 [ft]
ns>1,500 3 4 5 6
Elev1=
in the groundwater table resulting from the pumping.
415 [ft]
#stages?

5. Find: minimum # of stages
gal
min
Elev2=825 [ft]
Q=500
n=1,780 [rpm]
s=0 [ft]
ns>1,500 3 4 5 6
Elev1=
The flowrate, actual motor speed, and minimum specific speed are also provided. [pause]
415 [ft]
#stages?

6. Find: minimum # of stages
gal
min
Elev2=825 [ft]
Q=500
n=1,780 [rpm]
s=0 [ft]
ns>1,500
n * Q
ns=
Δh3/4
Elev1=
In English units, ---
415 [ft]
#stages?

7. Find: minimum # of stages
gal
min
Elev2=825 [ft]
Q=500
n=1,780 [rpm]
s=0 [ft]
ns>1,500
n * Q
ns=
Δh3/4
Elev1=
the specific speed, n sub s, of a pump, equals ----
415 [ft]
specific
#stages?
speed

8. Find: minimum # of stages
gal
min
Elev2=825 [ft]
Q=500
n=1,780 [rpm]
s=0 [ft]
ns>1,500
motor speed [rpm]
n * Q
ns=
Δh3/4
Elev1=
the actual motor speed, n, in revolutions per minute, times ---
415 [ft]
specific
#stages?
speed

9. Find: minimum # of stages
gal
min
Elev2=825 [ft]
Q=500
n=1,780 [rpm]
s=0 [ft]
ns>1,500
motor speed [rpm]
n * Q
gal
flowrate
ns=
min
Δh3/4
Elev1=
the square root of the flowrate, in gallons per minute, divided by ---
415 [ft]
specific
#stages?
speed

10. Find: minimum # of stages
gal
min
Elev2=825 [ft]
Q=500
n=1,780 [rpm]
s=0 [ft]
ns>1,500
motor speed [rpm]
n * Q
gal
flowrate
ns=
min
Δh3/4
Elev1=
the head added by the pump, in feet, raised to the 3/4s power.
415 [ft]
added
specific
head [ft]
#stages?
speed

11. Find: minimum # of stages
gal
min
Elev2=825 [ft]
Q=500
n=1,780 [rpm]
s=0 [ft]
ns>1,500
motor speed [rpm]
n * Q
gal
flowrate
ns=
min
Δh3/4
Elev1=
Since the problem statement provides the ---
415 [ft]
added
specific
head [ft]
#stages?
speed

12. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500
motor speed [rpm]
n * Q
gal
flowrate
ns=
min
Δh3/4
Elev1=
flowrate, motor speed, and minimum specific speed, we’ll solve for the added head ---
415 [ft]
added
specific
head [ft]
#stages?
speed

13. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500
motor speed [rpm]
n * Q
gal
flowrate
ns=
min
Δh3/4
Elev1=
and identify the minimum number of stages required. [pause] Solving for the added head, the added head equals ---
415 [ft]
added
specific
head [ft]
#stages?
speed

14. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500
n * Q
ns=
Δh3/4
Elev1=
the actual speed to the 4/3s power, times the flowrate, to the 2/3s power, divided by the specific speed, to the 4/3s power. [pause]
415 [ft]
n4/3 * Q2/3
Δh=
ns4/3
#stages?

15. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 h
Elev1=
If we look at a pump curve we recall that ----
415 [ft]
#stages? Q

16. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft] A B
ns>1,500 h
pump A
pump B
Elev1=
the total flowrate, resulting from multiple pumps operating in parallel, ---
415 [ft]
#stages? Q

17. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft] A B
ns>1,500 h
pump A
pump B
Elev1=
is the sum of the flowrates, from each individual pump, for a given head. Similarly,
415 [ft]
system
Qsys=QA+QB
#stages? Q

18. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 h D C
Elev1=
the total head, resulting from multiple pumps operating in series, ---
415 [ft]
pump C
#stages?
pump D Q

19. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 h D C
system
Elev1=
is the sum of heads, from each individual pump, for a given flowrate. When a single pump is fitted with multiple stages----
hsys=hC+hD
415 [ft]
pump C
#stages?
pump D Q

20. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 h D C
system
Elev1=
each set of impellers, or bowls, can be thought of as separate pumps operating in series. Therefore, ---
hsys=hC+hD
415 [ft]
pump C
#stages?
pump D Q

21. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 h D C
system
Elev1=
if the change in head, or lift, generated by the pump is a fixed quantity, then the required lift for ----
hsys=hC+hD
415 [ft]
pump C
#stages?
pump D Q

22. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 h D C
system
Elev1=
each stage, is inversely proportional to ---
hsys=hC+hD
415 [ft]
pump C
#stages?
pump D Q

23. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 h
4 stages
3 stages
2 stages
Elev1=
the number of stages in the well casing. [pause] Therefore, if the value of delta h is known, ---
415 [ft]
1 stage
#stages? Q

24. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 h Δh
Elev1=
and the pump has 4 stages, as shown here, then for a given flowrate, Q, ---
415 [ft]
#stages? Q

25. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 h Δh
Elev1=
the total head produced by the pump is shared equally ----
415 [ft]
#stages? Q Q

26. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 h Δh
Elev1=
Δh4
between the four stages. [pause] If there were only 3 stages,
415 [ft]
Δh3
Δh2
#stages?
Δh1 Q Q

27. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 h Δh
Elev1=
each individual stage would be required to add more head to the system. [pause] Same is true for if there were only ---
Δh3
415 [ft]
Δh2
#stages?
Δh1 Q Q

28. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 h Δh
Elev1=
2 stages, or 1 stage.
415 [ft]
Δh2
#stages?
Δh1 Q Q

29. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 h Δh
Elev1=
[pause] From before, the equation for the specific speed ---
415 [ft]
Δh1
#stages? Q Q

30. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500
n4/3 * Q2/3 = Δh h
ns4/3 Δh
Elev1=
of the pump, n sub s, assumes there is only 1 stage. However, for a pump with multiple stages, ----
415 [ft]
Δh1
#stages? Q Q

31. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500
n4/3 * Q2/3 = Δh h
ns4/3 Δh
Elev1=
the specific speed, is based on the head lift per stage, ---
Δh3
415 [ft]
Δh2
#stages?
Δh1 Q Q

32. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 = h
# stages
ns4/3 Δh
Elev1=
and increases as the number of stages increases. [pause] The question asks to find the minimum ----
Δh3
415 [ft]
Δh2
#stages?
Δh1 Q Q

33. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 = h
# stages
ns4/3 Δh
Elev1=
number of stages, such that the the specific speed is at least ---
Δh3
415 [ft]
Δh2
#stages?
Δh1 Q Q

34. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 = h
# stages
ns4/3 Δh
Elev1=
1,500. [pause]
Δh3
415 [ft]
Δh2
#stages?
Δh1 Q Q

35. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 = h
# stages
ns4/3 Δh
Elev1=
The minimum number of stages is a function of the ----
Δh3
415 [ft]
Δh2
#stages?
Δh1 Q Q

36. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 = h
# stages
ns4/3
Δh * ns4/3 = Δh
# stages
Elev1=
the total head, the minimum specific speed, the motor speed, and the flowrate. [pause]
n4/3 * Q2/3
415 [ft]
#stages? Q Q

37. ? Find: minimum # of stages = = n4/3 * Q2/3 ns4/3 n4/3 * Q2/3
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 = h
# stages
ns4/3 ?
Δh * ns4/3 = Δh
# stages
Elev1=
The last unknown variable is the change in head, delta h, which equals ---
n4/3 * Q2/3
415 [ft]
#stages? Q Q

38. ? Find: minimum # of stages + + - + + ρ*g ρ*g = = n4/3 * Q2/3 ns4/3
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 =
# stages
ns4/3 ?
Δh * ns4/3 =
# stages
Elev1=
the total head of the water in the tank minus the total head of the ground. [pause] Assuming the pressure head and velocity head are negligible ---
n4/3 * Q2/3
415 [ft]
Ptank
Pgw v2 v2
tank gw
Δh = +
ytank + - +
ygw +
ρ*g
ρ*g
2*g
2*g

39. ? Find: minimum # of stages + + - + + ρ*g ρ*g = = n4/3 * Q2/3 ns4/3
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 =
# stages
ns4/3 ?
Δh * ns4/3 =
# stages
Elev1=
in the tank and in the ground, the total head equation reduces to ---
n4/3 * Q2/3
415 [ft]
Ptank
Pgw v2 v2
tank gw
Δh = +
ytank + - +
ygw +
ρ*g
ρ*g
2*g
2*g

40. ? Find: minimum # of stages = = n4/3 * Q2/3 ns4/3 n4/3 * Q2/3
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 =
# stages
ns4/3 ?
Δh * ns4/3 =
# stages
Elev1=
the change in elevation head between the two sources.
n4/3 * Q2/3
415 [ft]
Δh = ytank - ygw

41. ? Find: minimum # of stages = = n4/3 * Q2/3 ns4/3 n4/3 * Q2/3
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 =
# stages
ns4/3 ?
Δh * ns4/3 =
# stages
Elev1=
Plugging in the given values for elevation, delta h equals, ---
n4/3 * Q2/3
415 [ft]
Δh = ytank - ygw

42. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 =
# stages
ns4/3
Δh * ns4/3 =
# stages
Elev1=
410 feet. [pause] We’re now ready to solve for the minimum number of stages.
n4/3 * Q2/3
415 [ft]
Δh = ytank – ygw= 410 [ft]

43. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 =
# stages
ns4/3
Δh * ns4/3 =
# stages
Elev1=
The variables on the right hand side are plugged into the equation, and the number of stages equals, ----
n4/3 * Q2/3
415 [ft]
Δh = ytank – ygw= 410 [ft]

44. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 =
# stages
ns4/3
Δh * ns4/3 =
# stages
Elev1=
5.18. [pause] Since the problem stated 1,500 is the ---
n4/3 * Q2/3
415 [ft]
# stages = 5.18
Δh = ytank – ygw= 410 [ft]

45. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 =
# stages
ns4/3
Δh * ns4/3 =
# stages
Elev1=
minimum specific speed, then 5.18 is the minimum ----
n4/3 * Q2/3
415 [ft]
# stages = 5.18
Δh = ytank – ygw= 410 [ft]

46. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 =
# stages
ns4/3
Δh * ns4/3 =
# stages
Elev1=
number of stages required for the well pump, and is round up to ----
n4/3 * Q2/3
415 [ft]
# stages > 5.18
Δh = ytank – ygw= 410 [ft]

47. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 =
# stages
ns4/3
Δh * ns4/3 =
# stages
Elev1=
6 stages.
n4/3 * Q2/3
415 [ft]
# stages > 5.18
# stages = 6
Δh = ytank – ygw= 410 [ft]

48. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 =
# stages
ns4/3
Δh * ns4/3 = 3 4 5 6
# stages
Elev1=
When reviewing the possible solutions, ---
n4/3 * Q2/3
415 [ft]
# stages > 5.18
# stages = 6
Δh = ytank – ygw= 410 [ft]

49. Find: minimum # of stages
gal
Elev2=825 [ft]
Q=500
min
n=1,780 [rpm]
s=0 [ft]
ns>1,500 Δh
n4/3 * Q2/3 =
# stages
ns4/3
Δh * ns4/3 = 3 4 5 6
# stages
Elev1=
the answer is D.
n4/3 * Q2/3
415 [ft]
# stages > 5.18
# stages = 6
Δh = ytank – ygw= 410 [ft]
AnswerD

50. ? 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