1. CIVL 215 Design Project
Daniel W. Kerkhoff
41531161
Dec. 2, 2016
Dr. Noboru Yonemitsu

2. TABLE OF CONTENTS
1.0 INTRODUCTION
2.0 EQUATIONS AND CALCULATIONS
2.1 Minimum Pressure/ Hill Equation
2.2 Horizontal Length vs. Arc Length Error
2.3 Global Critical Values
3.0 STANDARD SOLUTION
3.1 A Short Description
3.2 Graph of Solution
3.3 Tabulated Results
3.4 Solution With No Excess Head
4.0 OPTIMIZED SOLUTION
4.1 A Short Description
4.2 Graph of Solution
4.3 Tabulated Results
5.0 CONCLUSION

3. 1.0 INTRODUCTION
The following report is a pre-feasibility design for a water pipeline that is designed to
carry water from one reservoir to another. The first of the two reservoirs is located at an
elevation of 300m, whilst the second is located 415 km away at an elevation of 500m. The
topography between these two reservoirs can be approximated as a parabola that attains its
maximum elevation of 660m 249 km away from the first reservoir. The specifics of the project
require the pipeline to be built from a certain set of pipe diameters ranging from 0.9m to 1.4m.
To prevent cavitation or pipeline rupture, the pressure in the pipe cannot fall below 70% of
atmospheric pressure nor can it exceed the equivalent of 150m of head. For this report, minor
losses associated with changes in pipe diameter, pumps, or any other factors will be ignored on
the assumption that they are negligible on the scale of this project.
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4. 2.0 EQUATIONS AND BASIC CALCULATIONS
2.1 MINIMUM PRESSURE/HILL EQUATION
The equations for both the hill and the minimum pressure line are essentially the same.
The following calculations show how this parabolic equation is derived.
The design criteria give three conditions that must satisfy the parabolic equation
y=Ax2 + Bx + C: the pipeline starts at 300m, reaches a maximum of 660m at 249 km, and must
end with an elevation of 500m. These points correspond to those conditions: (0,300), (249000,
660), and (415000, 500). The coefficients A, B, and C can be determined by the row reduction of
the following matrix:
Figure 1: Row Reduction of Hill Equation
Therefore, the equation of the hill is:
The equation for minimum pressure is the same as the hill, except for the C value. The
allowable pressure in the pipe is 70% of atmospheric pressure, so taking Patm = 101,300 Pa, the
max pressure is 70,917 Pa. Dividing the max pressure by density * gravity to get equivalent
head (taking density to be 1000 kg/m3 and g to be 9.8 m/s2) yields h=7.24m. This means that
the HGL can fall no lower than 7.24m below the centerline of the pipe, or, the HGL cannot fall
below the equation:
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5. 2.2 HORIZONTAL LENGTH VS. ARC LENGTH ERROR
The true length of the hill can be found by determining the arc length of the above
determined parabola. The arc length formula is commonly known, yielding the following
calculation:
Figure 2: Integration to Find True Hill Length
By further using a calculator, the exact result was found to be: 415,000.9189. This gives
a percentage error of 2.2x10-6 %, much to small to be of any real significance.
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6. 2.3 GLOBAL CRITICAL VALUES
The following critical values are global in the sense that they apply to both the non-
optimized and the optimized solution. The calculation done here is for a pipe with a diameter of
1.4m. The values for all the other pipes can be found in the table below.
Relative Roughness = E/D = 0.05/140 = 3.57 x 10-4
V: velocity, D: diameter, v: kinematic viscosity of water (taken to be 10-6 m2/s)
Re = 9.05 x 10-6
Using a Moody Diagram, f = 0.02
A Bernoulli analysis between the first and second reservoir yields the equation:
When the above equation is simplified, the total head that the pumps need to supply is:
Frictional head Loss = 127.64 m
Frictional head Loss/ Total Length = 3.07577 x 10-4 [m/m]
Table 1: Key Values for Different Pipelines
Total Cost
($/km)
Pipe Diameter
(m)
Relative
Roughness
Reynolds
Number
f Total
Head Loss
Frictional
head
Loss/Meter
50,000.00
0.90 0.00056 1.41E+06 0.016 930.0803 0.002241
80,000.00
1.00 0.00050 1.27E+06 0.016 549.2031 0.001323
120,000.00
1.10 0.00045 1.15E+06 0.016 341.0119 0.000821
150,000.00
1.20 0.00042 1.06E+06 0.018 248.3015 0.000598
180,000.00
1.40 0.00036 9.06E+05 0.020 127.6447 0.000307
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7. 3.0 STANDARD SOLUTION
3.1 A SHORT DESCRIPTION
The following solution is the most simplistic way to solve the problem of delivering
water from the first reservoir to the second. This solution only uses 1.0m diameter pipe, with the
defining condition that the exit head be minimized. Also, the HGL is only allowed to touch the
hill line instead of going beneath into the negative pressure zone – this will ensure the safety of
the pipe by making cavitation nearly impossible.
3.2 GRAPH OF SOLUTION
Figure 3: HGL, EGL, Min. Pressure and Hill Height vs. Horizontal Distance
*Note: the EGL lies just above the HGL, too close to be seen on this plot
Head Difference at Exit: 51 m.
Legend
Blue Line = 1.0 m diameter pipe
Red Parabolas: minimum and maximum pressure boundaries
Black Parabola: hill
Horizontal Distance (m)
Elevation(m)
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8. 3.3 TABULATED RESULTS
Table 2: Pipeline Costs
Total Pipe
Length
Cost/ km of
1.0 m
Diameter
Pipe
Total Pipeline
Cost
415 km $80,000 $33,200,000
Table 3: Location of Pumps
Pump
Number
1 2 3 4 5 6 7 8
Pump
Position
0.00 km 24.6 km 51.0 km 80.0 km 112 km 149 km 194 km 257 km
Total Pump Cost: $80,000,000
TOTAL COST: $113,200,000
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9. 3.4 SOLUTION WITH NO EXCESS HEAD
The following solution is identical to the previous solution except for the 0.9m diameter
pipe that is attached to the latter portion of the pipeline to ensure the HGL meets the centerline of
the pipe at the exit to the second reservoir.
Figure 2: HGL, EGL, Min. Pressure and Hill Height vs. Horizontal Distance
Green line = 0.9m diameter pipe
*Note: the EGL lies just above the HGL, too close to be seen on this plot
Table 4: Pipeline Costs
Total 1.0m
Diameter
Total 0.9m
Diameter
Cost/ km of
1.0m
Diameter
pipe
Cost/ km of
0.9m
Diameter
Pipe
Total Pipeline
Cost
359.6 km 55.4 km $80,000 $50,000 $31,538,000
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Horizontal Distance (m)
VerticalDistance(m)

10. Table 5: Location of Pumps
Pump
Number
1 2 3 4 5 6 7 8
Pump
Position
0.00 km 24.6 km 51.0 km 80.0 km 112 km 149 km 194 km 257 km
Total Pump Cost: $80,000,000
TOTAL COST: $111,538,000
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11. 4.0 OPTIMIZED SOLUTION
4.1 A SHORT DESCRIPTION
The key differences between the following optimized design and the previous design are
these three. One, this solution employs a twinned 0.9m diameter pipe for the first 384 km, cutting
frictional head losses in half and making the pipeline $80,000/km cheaper when compared to
1.4m diameter pipe. The remainder of the way is done with a single 0.9m diameter pipe. Two,
the first pump is placed nearly 2 km from the origin. This gives the possibility of removing one
of the pumps. Three, the HGL is allowed to reach the minimum pressure line rather then the hill
line before a pump is placed, potentially allowing the removal of a pump.
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12. 4.2 GRAPH OF SOLUTION
Figure 4: HGL, EGL, Min. Pressure and Hill Height vs. Horizontal Distance
*Note: the EGL lies just above the HGL, too close to be seen on this plot
.
Head Difference at Exit: 0.0m.
Legend
Blue Line = twinned 0.9 diameter pipe
Green Line = single 0.9m diameter pipe
Red Parabolas: minimum and maximum pressure boundaries
Black Parabola: hill
Elevation(m)
Horizontal Distance (m)
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13. 4.3 TABULATED RESULTS
Table 6: Pipeline Costs
Twinned
Horizontal
Distance
Total
Twinned
Pipe Length
Total Single
Pipe Length
Total
Combined
Pipe Length
Cost/ km of
0.9m
Diameter
Pipe
Total Pipeline
Cost
383.77 km 767.54 km 31.23 km 798.77 km $50,000 $39,938,500.00
Table 7: Location of Pumps
Pump
Number
1 2 3 4 5 6 7
Pump
Position
1.809 km 27.85 km 56.22 km 87.71 km 123.6 km 166.5 km 223.9 km
Total Pump Cost: $70,000,000.00
TOTAL COST: $109,938,500.00
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14. 5.0 CONCLUSION
By following the guidelines given and by taking into considerations all restraints,
both the non-optimized and the optimized solutions as shown above will successfully
deliver 1m3
/s of water from the first to the second reservoir. It is recommended that you
proceed with the optimized solution, as it will both reduce construction costs by $3,261,500
from the original single pipeline design and will more accurately deliver the required
amount of water to the second reservoir. This report is correct to the best of my knowledge,
and I trust that the information provided herein is sufficient for your purposes. Should you
have any further questions or concerns, please do not hesitate to contact me at
daniel.kerkhoff@kerkhoffconsultants.ca.
Kerkhoff Consultants
Daniel W. Kerkhoff
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