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Clarkson University
Implementation of a Garden Irrigation System
Analysis of the Design, Cost, and Energy Expenditures of a Water Distribution
System
Demetrius Boone
0698468
ES 330 Fluid Mechanics
Dr. Bohl
11/02/2020
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01. Executive Summary
This report suggests a design methodology that includes mechanisms for turning the flow on/off
and the analysis behind making my current design work for the village given at as cheap a cost as
possible. After critical analysis of the Bill of materials the reported price is $11,516.08. This allowed for
the required 20gpm to be met at a whopping 41.6935gpm. Furthermore, the design needed to take into
consideration of the cost estimate for the implementation of the irrigation system and its material parts to
ensure a suitable and cheap solution for the community garden which was found to be a grand total of
around $20,000.Finally the pump to try and double the needed flow rate was found to be the Proline
Hy-Drive 4000 GPH Water Pump, allowing for about an extra 46gpm to flow through to the garden.
01. Introduction
A small remote village in a developing country needs to design and build an irrigation
system for their community garden. The source of there water is a small lake on one side of their
village. The community garden is on the complete other side with a 5.5 m drop in elevation. Therefore,
the system design is intended to be gravity fed. The goal in this project is to minimize the cost while
achieving a maximum flow rate through the system of at least 20 GPM. All parts involved will be
properly addressed and shown where the origin of it arises from.Also, a side discussion of a pump to
help double the flow rate to help meet new needs of the garden is a possibility that will be explored.
02. Materials and Methods
A. Assumptions
● The temperature of the water is approximately 20 degrees celsius. Therefore Viscosity is .001002
● The body of water has a laminar flow. This assumption is shown in equation 3.
● A few cost assumptions are made due to lack of specific information (renting excavators etc.)
● Roughness is considered to be .000007 when dealing with PVC piping.
● This village is somewhere in NY (we are a sad developing country ofc)
● Pressure does not change throughout this system. This assumption is demonstrated in equation 2.
B. System Design
Figure 1. Map of Irrigation System Layout
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C. Types of Piping Used
In total, 680 meters of 3” diameter PVC pipe are needed and 7 90 degree elbow pipes with
diameters of 3”. According to (usplastic.com), the source for the prices and the supplier of the PVC
Pipe, the cost of a 1ft, 3” diameter PVC pipe is $4.22(due to discount of mass purchase). The cost of 680
meters or 2230.97 ft of this pipe is $9414.69. Finally, for the 7 pvc elbow pipes, according to the source
and supplier (usplastic.com), the total cost for the 7 3” diameter elbow pipes would be $1089.97.
Attachments will be further priced and shown in the BOM.
D. System Losses
We must account for the total losses within the system, therefore we must alter the energy
equation as shown in the givens, equations 1 through 5. The equation for the velocity out of the pipe is
shown in equation 6. The A is the cross-sectional area of a single branch.Therefore, equation 5 must
then be changed to be equation 7:
2
2
(1)
𝑍1 + (𝑃1/ρ𝑔) + (𝑉1 /2𝑔) = 𝑍2 + 𝑃2/ρ𝑔 + (𝑉2 /2𝑔) + ℎ𝐿
(2)
𝑉1= 0
𝑃1= 𝑃2
𝑍1= ℎ = 5. 5𝑚, 𝑍2= 0
(3)
(4)
2
(5)
ℎ = (𝑉2) /2𝑔 + ℎL
2
2
(6)
𝑉2= ∀/12𝐴 = ∀/(12π𝑑 /4) = ∀/3π𝑑
2 2
2
2
(7)
ℎ = 1/(2𝑔) * (∀/3π𝑑 ) + ℎL= (∀ /18π𝑔𝑑 ) + ℎL
Where h is the total head loss caused by the friction through each pipe (h1,h2), the change in pipe
diameter (hD), and finally the branching of the pipe (hB). Furthermore, h1 is the main pipe that goes
through the village, and h2 is the forked part of the pipe where it is split into 12 equal branches. The
equation for h can thus be considered in equation 8. For h1, you use equation 9 and 10, where 𝑉i= ∀/𝐴i
2
2
(8)
ℎ = (∀ /18π𝑔𝑑 ) + ℎ1+ ℎ2+ ℎD+ ℎB
2
ℎ1= 𝑓(𝑅𝑒i, ε1/𝐷1)(𝐿1/𝐷1)((𝑉1) /2𝑔))
(9)
2
(10)
𝑅𝑒1= ρ𝑣1𝐷1/µ = ρ∀𝐷1/π * (𝐷1) /4 * µ = 4ρ∀/π𝐷1µ
Therefore, h1 can be re-written as shown in equations 11 through 12
2
2
(11)
ℎ1= 𝑓(4ρ∀/π𝐷1µ , ε1/𝐷1) * (𝐿1/𝐷1) * (∀ /(2𝑔𝐴1) )
2
5
2
= 8/π 𝑔 * 𝑓(4ρ∀/π𝐷1µ , ε1/𝐷1) * (𝐿1/(𝐷1) ) * ∀
(12)
For h2, each individual pipe gets there own loss so the equation will slightly differ, ∀ is replaced
with (1/12)∀then the whole equation is multiplied by 12, which gives us equation 13:
2
5
2
ℎ2= 2/3π 𝑔 * 𝑓(ρ∀/3π𝑑µ , ε3/𝑑) * (𝑙/𝑑 ) * ∀
(13)
The resulting equation for h, altering equation 8 and substituting the equations for h1 and h2 is
written as:
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2
2
2
5
2
2
5
2
ℎ = ∀ /18π𝑔𝑑 +8/π 𝑔 * 𝑓(4ρ∀/π𝐷1µ , ε1/𝐷1) * (𝐿1/(𝐷1) ) * ∀ + 2/3π 𝑔 * 𝑓(ρ∀/3π𝑑µ , ε3/𝑑) * (𝑙/𝑑 ) * ∀ + ℎ
(14)
D+ ℎB
hD can be simplified by using the equation 15, and while using the source of
(www.engineeringtoolbox.com), Cc is found to be approximately 0.64. Equation 15 thus can be
re-written as equation 16 by substitution of values
2
2
(15)
ℎD= 𝑉 /2𝑔 * (1/𝐶𝑐 − 1)
2
2
4
2
(16)
ℎD= 8∀ /π 𝑔(𝐷2) * ((1/0. 64) − 1)
Finally, hB, the head loss from the branching component, can be computed using the equations
shown in equation 17 through 20.
2
(17)
ℎB = 𝑘 * (𝑉 /2𝑔)
Next, replacing V with (∀/12𝐴), where A is the cross-sectional area of the small pipe. Using the
equations for A and V shown in equations 18 and 19, hB from equation 17 can be rewritten as shown in
equation 21.
2
2
(18)
𝐴 = π(𝑑/2) = π𝑑 /4
2
(19)
𝑉 = ∀/3π𝑑
2 2
2
4
(20)
ℎB= 𝑘/2𝑔 * (∀/3π𝑑 ) = 𝑘∀ /18π𝑔𝑑
After combining each of these equations together, we receive the resulting equation for total loss,
h, shown in equation 21.
2
2
2
2
5
2
2
5
2
2
2
4
ℎ = ∀ /18π 𝑔𝑑 + 8/π 𝑔 * 𝑓(4ρ∀/π𝐷1µ , ε1/𝐷1) * (𝐿1/(𝐷1) ) * ∀ + 2/3π 𝑔 * 𝑓(ρ∀/3π𝑑µ , ε3/𝑑) * (𝑙/𝑑 ) * ∀ + 8∀ /π 𝑔(𝐷2) * ((1/
2
4
+ (𝑘∀ /18π𝑔𝑑 )
(21)
Coefficients for minor losses were discovered on
(https://www.plumbingsupply.com/ed-frictionlosses.html)
Calculations using the parts that make up Equation 22 and its Variables Can Be Seen on Sheet
1(Total Loss)(Hard to fit and be able to understand)
E. Flow Rate Range
The flow rate range for this PVC piping system for a PVC pipe with diameter of 3”, the
maximum flow rate in gallons per minute is approximately 41.6935 (.002630436m^3/s) (converted
value using unitjugglar.com), which is calculated through the excel sheet labeled Vdot. The minimum
flow rate is estimated to be around 0 if the system were to freeze over and no longer be able to run till
insulated or heated (this is upstate Ny…). In non frozen conditions however it seems the lowest it will
really go is dependent on the previous number and should stay somewhere close to that number of
41.6935gpm, from playing with it in excel it seems the lowest it could go is about 39gpm.
F. Bill of Materials
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To start the previous materials mentioned: 3” diameter 20 feet long PVC pipe IN(26509), 2231 ft
of this pipe is $9414.82, then 7 3in diameter elbow pipes IN(34253) would be $1089.97. For the new
information and remainder pieces to the puzzle: 111 PVC couplings IN(28457) for $2.75 is priced at
$305.25 (usplastic.com), a single reducer coupling IN(26256) from 3in to 1in is priced at
$80.69(usplastic.com), 3in bolted full port valve with 3in flow Size IN(30656) be able to turn the system
on and off at the source is priced at $142.42(usplastic.com). This leads to a total cost of materials to be
$11033.15, this is purely the raw cost and shipping seems to be estimated at around 40$ and the current
sales tax rate in NY is 4% so after adding the shipping cost then including tax the final material price is
$11,516.08.
G. Overall Financial Estimate
Of course the final material price of $11,516.08 is only factoring the material cost of the project,
the total cost of this system is dependent upon the cost of the construction of the pipeline.The cost of
pipe construction is correlated with the price to rent the proper tools to excavate and install, from
(www.pricecomparisonadvisor.com) it is estimated that it would cost around $2000 a week due to hiring
an operator and the distance they are required to travel since there are none in the nearby area (closest
are some in syracuse). I would estimate the project would take around 1 month (4weeks) as there isn't a
lot of complexity to the matter as its dig up lay the piping and cover. (I extended it by 2 weeks due to the
act that most construction workers take longer on projects then needed.) Therefore with these estimates
it would cost around $8000 for the construction. Thus, the total cost of the project is around $20,000.
H. Pump Recommendation for Doubled Flow Rate
Proline Hy-Drive 4000 GPH Water Pump is the ideal pump for doubling this cases gpm, as the
4000GPH can be converted to 66.67 gpm and while that is over double the current gpm for the system
discussed above it is important to remember the efficiency of pumps of this gpm rate are around 65-70%
(https://tacoadvancedhydronics.wordpress.com/).Using the average (68%) this puts the outlet to about
45.34gpm which is just around the double mark for this current system. It's IN is 94057 and it's priced
at $265.52 from the www.usplastic.com website.
04. Conclusion
To close out this project, a report of all that was addressed:
● A map of the irrigation system layout (Figure 1.)
● Detailed analysis put together both in excel and throughout the report explaining the logistics behind
each decision.
● The Bill of Materials addressed all points required and provided the total cost of the project's materials.
● A rough cost estimate was provided given available knowledge on civil projects in rural areas.
● The potential pump was also properly recommended and reported in a similar fashion to the Bill of
Materials.
● And a final thank you for reading and analyzing this project.
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05. References
“PVC Pipe.” PVC Pipe | U.S. Plastic Corp., www.usplastic.com/catalog/item.aspx?itemid=23979.
https://www.usplastic.com/catalog/item.aspx?itemid=26832&catid=726
https://www.usplastic.com/catalog/item.aspx?itemid=38457&catid=592
https://www.usplastic.com/catalog/item.aspx?itemid=23374&catid=726.
“Manning's Roughness Coefficients.” Engineering ToolBox, www.engineeringtoolbox.com/mannings-roughness-d_799.html.
“PVC Pipes - Friction Loss and Flow Velocities Schedule 80.” Engineering ToolBox,
www.engineeringtoolbox.com/pvc-pipes-friction-loss-d_803.html
https://www.engineersedge.com/physics/water__density_viscosity_specific_weight_13146.htm
How Much Does it Cost to Rent a Mini Excavator? (n.d.). Retrieved November 02, 2020, from
https://www.pricecomparisonadvisor.com/mini-excavators/how-much-does-it-cost-to-rent-mini-excavator.html
PlumbingSupply.com®. (n.d.). Friction Loss Tables. Retrieved November 02, 2020, from
https://www.plumbingsupply.com/ed-frictionlosses.html
Achieving High Pump Efficiency. (2011, June 14). Retrieved November 02, 2020, from
https://tacoadvancedhydronics.wordpress.com/2011/05/09/achieving-high-pump-efficiency-3/