CE440_HW#3_SOLUTION_2024
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California Polytechnic State University, San Luis Obispo *
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440
Subject
Industrial Engineering
Date
Feb 20, 2024
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19
Uploaded by CoachParrotMaster1060
1 CE 440 Hydraulic Systems Engineering H O M E W O R K # 3 Total 200 points Winter 2024
S
ubmit all Problems as a group. But feel free to discuss with others. You are
encouraged to use MS Excel whenever necessary.
Problem #1 (10+10+15+5 points) Mapped below is a pipe network. Use Linear theory method to develop matrices for solving the network. Pump curve is given as E
p
=
−
2.1
Q
2
−
0.1
Q
+
100
. Given C = 120 for all
pipes.
2 C
= 120 n
= 1.85
3 - 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85
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4 -11.46 -0.07 -0.07 -11.46 - + -
97.8 -
440.10 -
20.07 -
82.21 + 15.05
- 15.05
+ 373.24
-
440.10 -
57.64 -
82.21 -
57.64 -97.8 - 440.10 -20.07 + 15.05 - 15.05 + 373.24 - 440.10
5 Pipe # C L (m) D (m) K 1 120 600 0.30 320.511 2 120 300 0.15 4686.285 3 120 500 0.60 9.134 4 120 400 0.30 213.674 5 120 300 0.30 160.255 6 120 100 0.15 1562.095 7 120 200 0.30 106.837 8 120 200 0.30 106.837 Pipe # D D' E E' q (cms) n K A B Hc 1 97.80 -5.39 ~ ~ 0.12 1.85 320.51 ~ ~ ~ 2 440.10 -6.07 ~ ~ 0.03 1.85 4686.29 ~ ~ ~ 3 0.00 0.00 ~ ~ 0.00 1.85 9.13 ~ ~ ~ 4 20.07 -0.28 ~ ~ 0.03 1.85 213.67 ~ ~ ~ 5 15.05 -0.21 ~ ~ 0.03 1.85 160.26 ~ ~ ~ 6 373.24 -15.43 ~ ~ 0.09 1.85 1562.10 ~ ~ ~ 7 0.00 0.00 ~ ~ 0.00 1.85 106.84 ~ ~ ~ 8 0.00 0.00 -0.10 100 0.00 1.85 106.84 -2.10 -0.10 100
6 Problem #2 (35 points)
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7 (a)
Using the given parameters, determine the pump head required (ft). (b)
From the pump curve given, select the best impeller diameter. For this diameter and required pump head, at what discharge, power and efficiency will the pump operate? (c)
If the water is at 40 °F, the total head loss from lower reservoir to pump = 9 ft, and the pump is 10-ft higher than the lower reservoir, determine the NPSH
avail (ft) for the pump. (d)
Does the pump selected in (b) fit this criterion? If so, up to what height above the lower reservoir could the pump be located? If not, to what height must the pump be lowered? Assume the head loss remains constant. Solution
8 Problem #3 (25 points) (Use of MS Excel is mandatory) A pump manufacturer’s testing lab is sketched on the next page. Several experiments are run to determine a new pump’s characteristic and efficiency curves. The data from those experiments is shown in the table below. Using this data, derive & plot the characteristic curve and the efficiency curve for this pump. Present the two curves together in one plot (Be sure to properly account for minor and friction losses in the experimental apparatus).
9
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10
11 Problem #4 (50 points) (
from Fall 2011 MT#
1) Apply Linear Theory method to the pipe network given below. The initial assumed flow rates and flow directions for each pipe are listed in the table below. Write down the matrices derived using the linearization. Other necessary data you require are listed in tables below. Minor losses are negligible. Pumps are on pipes 1 and 6 and pumping in the assumed direction of flow. K1 0.453 K2 0.453 K3 0.453 K4 0.453 K5 0.453 K6 0.453 KT1 0.054 KT5 0.054 KT6 0.054 Q1 (cfs) 4.0 Q2 (cfs) 5.0 Q3 (cfs) 4.0 Q4 (cfs) 6.0 Q5 (cfs) 6.0 Q6 (cfs) 10.0 QT1 (cfs) 4.0 QT5 (cfs) 6.0 QT6 (cfs) 10.0 D2 (cfs) 15 D3 (cfs) 5 Za (ft) 140 Zb (ft) 160 Zc (ft) 200 1
2
3
4
5
6
T
1
T
6
T
5
1
6
3
4
5
2
Z
a
Z
c
Z
b
D
2
D
3
1
1
D
2
Z
a
Node
Pipe
Fixed-head node
Demand
Assumed flow direction
for both pumps Pump 1
Pump 2
2
)
2
(
A
g
D
fL
K
=
12
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13
14 Pipe # D D' E E' q (cfs) n K A B H
c
1 3.62 -7.25
-13
226 4.0 2.0 0.453 -1.0
-5.0
210 2 4.53 -11.33
~ ~ 5.0 2.0 0.453 ~ ~ ~ 3 3.62 -7.25
~ ~ 4.0 2.0 0.453 ~ ~ ~ 4 5.44 -16.31
~ ~ 6.0 2.0 0.453 ~ ~ ~ 5 5.44 -16.31
~ ~ 6.0 2.0 0.453 ~ ~ ~ 6 9.06 -45.30
-25
310 10.0 2.0 0.453 -1.0
-5.0
210 T1 0.43 -0.86
~ ~ 4.0 2.0 0.054 ~ ~ ~ T5 0.65 -1.94
~ ~ 6.0 2.0 0.054 ~ ~ ~ T6 1.08 -5.40
~ ~ 10.0 2.0 0.054 ~ ~ ~ 1.08 202.9 184.51
15 Problem #5 (20+30 points)
Diagrammed below is a simple pipe network system. The system has 2 different modes of operation: a daytime mode where most of the system’s pressure and flow are supplied by the elevated tank, and a nighttime mode where the pumps provide all of the flow and pressure and the tank is refilled. At both the pumping station and the elevated tank are sets of valves that are opened and closed in the two modes to enforce flow directions and bring the second pump on- and off-line. Pump #2 is identical to Pump #1. When formulating the set of equations to describe this network, you may treat everything between Tank A and Node 1 as being a single pipe. You may also treat everything between Tower B and Node 3 as being a single pipe. It is important to change the characteristics of these two pipes appropriately between the day and night cases. (a) Write the set of equations that you will use to solve for system flows for (i) the daytime
case and (ii) the nighttime case.
(20 points)
(b) If the correct flow in Pipe 1 is 0.98 cfs in the day and 22.91 cfs at night and the correct
flow in Pipe 5 is 14.02 cfs in the day and 17.91 cfs at night, what will be the flows in Pipes
2, 3, and 4 for (i) the daytime case and (ii) the nighttime case.
(30 points)
See next page for details. Day Night
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16 Pipes 1 and 5 may both be assumed to be 200 ft long no matter the state of valves along the pipe. Pipes 2, 3, and 4 are each 2000 ft long. All pipes are 24 inches in diameter and have friction factor f = 0.013. You should consider appropriate minor losses in your calculations. K
gatevalve
= 0.2, K
checkvalve
= 2.0. Neglect entrance and exit losses. Pumps #1 and #2 are identical, and each has the characteristic curve shown next page.
17
18
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19