2020

Pipe Design for Thermo-Fluid

Coursework
LAGRANGE GROUP
Part A
In order to complete the first stage of this exercise, we need to understand how we can get
the head H for flow Q from a pipe with a diameter of 1.2m. What we are given in Table one
from the coursework sheet is a list of values for the flow coefficient KQ and the head
coefficient KH, additionally we see that we have the efficiency values for each of the
coefficient mentioned earlier. These are listed in table 1 annexe B.
In order to continue, the relationship between the Head of the system and the flow rate
must be found. This can be done by relying on the equations for the Flow and Head
coefficients. The equations are mentioned below:

𝑔𝐻 𝑄
𝐾𝐻 = 𝐾𝑄 = (1)
𝑁 2 𝐷2 𝑁𝐷2
Where:

- g is the gravitational constant at sea level

- H is the Head of the system
- Q is the flow rate
- N is the Pump seed (measured in Revolutions per second)
- D is the pump diameter

In order to find H and Q, we must rearrange the equations given above, so that they are in
terms of the two coefficients KQ and KH. Using standard algebraic methods, we receive:

𝑁 2 𝐷2 𝐾𝐻
𝐻= 𝑄 = 𝑁𝐷2 𝐾𝑄 (2)
𝑔

Using the information given in table 1, we can now proceed with answering question 1. This
is done by inputting the values we have been given in the coursework description, assuming
the pump speed is 800RPM.
Thus, the values for head H, flow rate Q and Efficiency, are given in table 2 in Annex B:
(Appendix A for full spreadsheet).
Using information from the course textbook (p.802 & p.876-877, Douglas, 2007), the three
sets of values are plotted on the graph. This can be done as the flow rate can be assumed as
the x-axis, which allows the two other values to be graphed concerning the flow rate. The
answer to Part A question 1, which is Graph 1, demonstrates this.
Now that question one has been
answered, question 2 can be focused
on. Here, one is asked to write down an
expression for the head loss in the
piping system.
The pipes head loss in the system comes from an understanding of friction. As fluid is
transported through an enclosed region, in this case, a pipe, the fluid will experience
friction, generally leading to a loss in pressure. The pipe head loss represents the frictional
loss in this pipe and expresses it in terms of the Head of the system (Subsea Pipelines and
Risers, 2005).
In order to find an expression for the head loss, we must first investigate and find an
equation where head loss is represented. On inspection of the course materials, a
relationship between head loss and the dynamic Head can be found. Total dynamic Head of
a system is what determines the losses in the piping system that the pump must overcome
(Rain Collection Supplies, n.d.). This relationship is demonstrated in equation set three:

𝐻𝑃 = ∆𝑧 + ∑ 𝐻𝐿 (3)

Where:
- ∆𝑧 is the static head, given in the question to equate to 100
- ∑ 𝐻𝐿 is the sum of head loss or total head loss
- 𝐻𝑝 is Total dynamic Head.

By analysing the above equation, we see that the pipe head of a system is dependent on the
sum of all the head losses. Therefore, in order to answer question two of part A, we must
expand equation 3.
In order to find the sum of the head losses, we need to inspect the Darcy Weisbach formula.
In fluid dynamics, the Darcy–Weisbach formula is an empirical equation, which relates the
head loss/ pressure loss, due to friction along a given length of pipe to the average velocity
of the fluid flow for an incompressible fluid (Darcy–Weisbach equation, n.d.) (Subsea
Pipelines and Risers, 2005).

𝑄 4𝑄
𝑉= = 2 (4)
𝐴 𝜋𝑑
𝐿 𝑉2 8𝑓𝐿𝑄 2
𝐻𝑙 = 𝑓 ∗ ∗ = (5)
𝑑 2𝑔 𝑔𝑑 4 𝜋 2
𝑉2 8𝑄 2
ℎ𝑙 = 𝐾𝑙 ∗ = (𝑛𝑒 𝑘𝑒 + 𝑛𝑣 𝑘𝑣 ) ∗ 4 2 (6)
2𝑔 𝑔𝑑 𝜋
Where:
- F is the Friction factor
- L is the length of the pipe
- d is the pipe diameter
- V is the flow velocity
- KL is the loss coefficient
- 𝑛𝑒 is the number of elbows in the system.
- 𝑘𝑒 is the loss coefficient for elbows
- 𝑛𝑒 is the number of valves in the system.
- 𝑘𝑒 is the loss coefficient for the valves
 - 𝐴 is the area of the pipe
- 𝑄 is the flow rate
- 𝐻𝑙 is the major head loss
- ℎ𝑙 is the minor head loss
-

These two equations show the frictional loss in the pipe and the additional componentry.
This is demonstrated in the major head loss equation 𝐻𝑙 which shows the frictional loss in
the pipe. The Minor head loss equation, ℎ𝑙 , shows the friction loss through the
componentry such as the elbows and valves.
Since Flow Velocity is not provided, it was represented in terms of Flow rate and pipe
diameter.
Now a complete equation for the head loss can be found, and the expression is shown in
equation 7:
8𝑓𝐿𝑄2 8𝑄2
𝐻𝑃 = 100 + + (𝑛𝑒 𝑘𝑒 + 𝑛𝑣 𝑘𝑣 ) ∗ (7)
𝑔𝑑 2 𝜋2 𝑔𝑑 4 𝜋2

As shown in the previous paragraphs and equations, Total head loss is the sum of the Major
Pipe loss and Minor head loss. This relationship is demonstrated in equation 7. This is useful
information as question three asks us to plot a head loss curve against the flow rate in a
system with a pipe of 0.7-meter diameter.
Using all of the information and the equations above, velocity can be found first. In Annexe
B table 3, the calculations for the value were completed with the flow rate and velocity
relationship (Equation 4).
Once those values had been found, this group focused on finding the Darcy friction Factor
for use in the Head loss equation. To continue, the Reynolds number must be found. Based
on the velocity in table 3, the Reynolds number can be found using the equation
(Engineering ToolBox, 2004):
𝜌𝑣𝑙
𝑅𝑒 = (8)
𝜇
where:
- 𝜌 is the Density of water
- 𝑣 is the flow velocity
- 𝑙 Is the pipe length
- 𝜇 is the dynamic viscosity of water
- 𝑅𝑒 is Reynolds number

After some research, the value of μ was found to be 1.306mPa.s. This integer came from
online searching for dynamic viscosity of water at 10-degree Celsius (Engineering ToolBox,
2003).
Now that Reynolds number is found for the ranges of flow rate, as seen in Annexe B table 4,
the Darcy Friction Factor can be calculated. To do this, it is useful to understand that there is
turbulent flow in the pipe. As demonstrated by the Reynolds numbers all being more
significant than 2300. Therefore, the pipe is considered to be smooth. Additionally, in order
to calculate the friction factor correctly, the equation required is shown below. This
equation was chosen as a result of the Blasius relationship (p.338-339, Douglas, 2007).
4 × (0.079) 0.316
𝑓= 0.25 = (9)
𝑅𝑒 𝑅𝑒 0.25
After getting the friction factor, as seen in table four, the major head loss can be calculated.
The question requires the plotting of a graph of head loss H (system performance curve) vs
Q, see Graph 2. Note that the system performance curve takes into account the static head
of the system (Keiser, 2016).
Question four in part A
requires the determination of
the flow rate in the system.
This is done by working out the
intersection of the Head vs
Flow curve with the system
performance graph (p.877,
Douglas, 2007). This will
determine the operating point
and, subsequently, the flow rate in the system. In order to do this precisely and accurately, a
polynomial trendline of both curves will be created. Ensuring the R2 coefficient is virtually
equal to one, to allow for an accurate equation. The equations with the corresponding R2
values are shown in graph 2.
Therefore, by using simple algebraic principles, we can determine that the x (the flow rate)
value to be 4.626m3/s, allowing for a 283.407m Head. Now that an appropriate flow rate
and head have been found, the power required to run the pump can be calculated. This is
done by using the following equation:
𝜌∗𝑄∗𝐻
𝑃= (10)
ℵ
Where:

- 𝑃 is Power
- 𝜌 is Density of water
- ℵ is pump efficiency

Using equation 10, the Power works out to be 3,277,517 Watts

Part B
Introduction
This group has been tasked with designing a pump-piping system to fill a tank. The requirements of
this system state that two tanks are to be connected by a pump which is 2200 meters long and gains
100 meters in height. Additionally, the pipe must have four valves, and ten elbows of various angles.
On top of that, the system must fill a secondary tank of 80,000 m3 with 100,000m3 of water
throughout the day. However, the pump powering the system can only run for 8 hours during a day.
Therefore, there is a minimum and required flow rate in the system. This is because the system must
be able to pump 100,000m3 of water in eight hours. By dividing 100,000 by 28,800, the required flow
rate is worked out to be 3.472 m3/s. This leads to the aim of this research paper; which is to design a
pump with a specific efficiency, Power, pipe material (made from either concrete or steel) and pump
diameter along with the simulation of the associated costs of the system that meets or exceeds the
required flow rate.

Despite the previous requirements, an additional task has been assigned, which involves a decision
matrix to decide on the power generation method that will be used to run the pump and the system.
Consequently, this group has an additional task to evaluate the carbon footprint. These two tasks
have been assigned to allow the suitability of our proposed project to be evaluated.

As is common in most design projects, this group has had to prioritise certain variables. These are
the design factors that have been mentioned previously: Efficiency, cost, carbon footprint and flow
rate. Using the factors and information stated previously, the main priority of this report would be to
design a system that has reduced the carbon footprint and the cost while maximising flow rate and
efficiency.

Method
There are four independent variables of the experiment, which are pipe diameter, the material of
the pipe, pump diameter and pump speed.
To begin any analysis, a suitable range of values must be made. Thus, this group decided to state the
use of a range of values for pipe and pump
diameters (from 0.2 to 2.0 meters) and pump
speed (600-1800 RPM). We can assume,
therefore, that these will be the independent
variables of the system.

As well as the given values, this research

paper must understand what is controlling
the experiment. In order to do this, one must
understand the dependant variables that are
within the experiment. This is because these
are the values which are being measured and
Figure 1
tested. The dependent variables of this
particular system are Head, Flow rate, Head loss, Total Head loss, power output, the roughness of
the pipe, Carbon footprint and cost of the system. The changing of independent variables is what will
aid in the selection of the optimal values of the independent variables to design the system.
Now that the independent and dependant variables have been assigned, one can finally list and
understand the control variables. These are the constant values of the experiment. The control
variables of the system, are thus,
the size of the reservoir tank
80,000 m3, a temperature of 10
degree Celsius, filling time of 8
hours per day, the total length of
the pipe, the number of elbows
and butterfly valves, Density of
water, the dynamic viscosity of
water 1.3076x10-3Pa and finally the
roughness for the Concrete pipe
being 0.08.
In part A by using the given equation of flow and head coefficient (Equations 1 and 2), the head and
flow rate were calculated. However, for this analysis, the Pump diameter and speed will be set as
variables, unlike Part A, which required those values to be constant.
First, the Total Head loss for both concrete and steel pipes will be calculated. This will help to
understand the difference in performance and characteristics between the steel and concrete pipes.
In order to calculate the major head loss for the steel pipe, the Darcy friction factor is required. Since
the friction factor can be calculated for both turbulent and laminar flow, the Reynolds number of
steel is recommended. This is because of the
Darcy Friction Factor equation mentioned in
Part A (Equation 9). This method is only
required for a steel pipe as concrete pipes
are assumed to have a constant friction
factor of 0.08. Refer to equation 8 for a full
description of this method.
After Calculating the Reynolds number for
the steel pipe (refer to Annex A, Table 1), it is observed that the flow in the pipe is turbulent. This is
because all values of the Reynolds number are more significant than 4000. As seen in the course
textbook: "In straight pipes of constant diameter, flow can be assumed to be turbulent if the
Reynolds number exceeds 4000." (p.102, Douglas, 2007). Therefore, when calculating the friction
factor for steel, the Darcy Weisbach equation for turbulent flow is applied (see equation 9). The
values for the friction factor can be verified with the use of a Moody chart (see figure 1). Note that
the flow is entirely turbulent, and thus the complete turbulence line in figure one is used.

Using equation 9, the friction factor is

calculated, allowing for the subsequent
calculation of the major head loss (refer
equation 5) for both steel and concrete pipes.
For the minor head loss, it is easily calculated
by inserting the values into the given equation
(refer to equation 6).
Once the values for both steel and concrete
pipes are obtained, one can graph the
following relationships: Head vs Flow rate,
efficiency vs flow rate and system performance curve (Friction Loss vs Flow rate).
One of these relationships, Head vs flow rate, can be seen in graphs four and five. By analysing these
graphs, we can understand the characteristics of the pipes and how the change in pipe diameter,
pump diameter and pump speed affect the
dependent variables. The difference between
concrete and steel pipes can be seen by the
Head vs flow and system performance curve
(p.802, Douglas, 2007).

Using graphs four and five, the operating point

flow rate of the system can be calculated for
both steel and concrete pipes. The operating
point flow rate is completed by equating the
lines of Head vs Flow rate and the system
performance curve. This will produce a quadratic equation, and solving for x will give the operating
point flow rate. This method is then completed for varying pipe diameters between the range of 0.2
– 1.4m with a difference of 0.2m. These values can then be graphed to show the relationship that
pipe diameter has to the operating point flow
rate according to each pipe material (graphs
six and seven). The pump diameter is kept
constant for these graphs in order to show
the pipe diameters influence. However, the
pipe speed was changed from 600 to 1800
RPM also to demonstrate its influence over
the system. No other speeds were used as
they would fall between these sets of values
and within the domain of the system.

In order to aid the analysis, the graphs can also demonstrate the carbon footprint of concrete pipes
against diameter. This is done as Table 3 in the coursework sheet gives a range of pipe diameters
and carbon footprint values. Thus, by extrapolating these given values, and assuming a linear
relationship, one can view how the pipe diameter affects the system.
What is observed from the graph is that the operating point flow rate significantly increases with a
pump speed of 1800 RPM than that of 600RPM with changes in pipe diameter. Additionally, the
operating point flow rate increases as diameter
increases; these are true for both concrete and
steel pipes. However, these change at a different
rate depending on the pump speed and material.
Next, in order to analyse more of the
independent variables, this group has calculated
the head loss (use equation 7) for pipe diameters
within the range of 0.2 - 1.4m with a difference of
0.2 m. At the same time, pump diameter and
speed are kept constant. This is done for both
concrete and steel pipes (The values can be found in annexe A table 2). These values are plotted
against the Flow rate to demonstrate their relationship. See graphs eight and nine.
These graphs display how the pipe diameter and roughness can affect the system performance
curve. This is very useful in deciding what pipe diameter and material to use. As the diameter of the
pipe increases, it will have a lower head loss and higher flow rate.
By using equation two, it is possible to see the effect of Pump diameter on the system. This can be
done by calculating the Head and Flow rate for a range of different pump sizes. These will vary
between 0.2 – 1.4 m with a difference of 0.2m. This occurs while the pump speed and pipe diameter
are kept constant. Please note that there has not been a separation for steel and concrete pipes
because the pipe diameter is constant. As well as that the roughness of the pipes are not considered
when calculating the Head and flow
rate. Therefore, the head and flow rate
curve will be the same for both pipe
materials. The obtained values are
plotted on a graph of Head vs Flow
rate, see graph 10.
According to graph 10, both flow rate
and Head increase as the diameter of
the pump increase. This relationship between Head and flow rate to pump diameter is useful for
which pump diameter is optimal for the system. Similar characteristics can be seen for a varying
pump speed and constant pipe and pump diameter.

Analysis
In this project, there are four components which are prioritised; they are high flow rate, good
operating point efficiency, cost efficiency, and a low carbon footprint. The idea is to optimise all
these objectives to make an ideal system. Relating to the introduction, it is known that this system
must meet a minimum and required flow rate of 3.472m3/s. Therefore, this group shall design a
system that prioritises this flow rate and the other considerations as detailed above. To start
designing the system, one must evaluate the effect of each variable, starting with pipe diameter.

Graph eight and nine show the relationship between Head loss and Flow rate as a result of a change
in pipe diameter with a constant RPM. These curves demonstrate that larger diameters have a more
significant effect on the flow rate. What can be demonstrated is for an increase Pipe diameter, there
will be a proportional increase in flowrate. However, the graphs also demonstrate that there is an
inversed relationship between Pipe diameter and head loss. The graph can represent this for the
smallest diameter, 0.2. This shows that for a small increase in flowrate, there will be an un-
proportional change in the head loss. The opposite is seen as pipe diameter increases. This is
because higher diameters have less friction which results in less Head and thus an increase in flow
rate.

Additionally, Graph 10 demonstrates the direct relationship between the pump diameters, flowrates
and Head. This is because an increase in pump diameter increases the Flow rate of the system. As
well as that, this relationship can be seen for a varying pump speed. An increase in pump speed will
result in a higher flowrate. This is useful since one of the priorities in designing the system is to have
a flow rate high enough to meet the required operating point. Therefore, the graph provides useful
information to select the right pump diameter and speed as they directly control the system flow
rate.

Graphs 6 and 7 show the operating point flowrate against diameter for two different pump speeds,
with a constant head and flowrate. These two graphs show an "S" shape relationship for both pump
speeds. This relationship shows that when small diameters are increased there is a more
considerable increase in operating point flowrate. However, for a diameter of 0.7 m, there is an
inflexion point, for both RPM values. This demonstrates that when larger diameters are increased
there is less of a proportional change to operating flowrate. This relationship demonstrates that
there is little point in having a pipe diameter greater than one as the gains for flow rate are minimal
at best.

The graphs also show that higher pump speeds have higher operating flowrates. This is because the
values at 1800 RPM are almost three times greater
than the flow rate values at 600RPM. It can be
observed that the required operating flowrate of
3.5 is easily achievable with 600 RPM, so there is
little point in wasting money with a higher pump
speed. Thus, aiding in the achievement of the goal
of this research paper.

Graphs six and seven also demonstrate that the

difference between the pipe materials creates
different changes in operating point flow rates.
This can be seen through the concrete pipe's operating flow rate is more generous than that of the
steel pipe. This is as a result of the friction factor for concrete being significantly smaller.
Additionally, graphs six and seven show that the Carbon footprint of the system increases at
different rates with pipe diameter depending on the material. By inspecting and extrapolating the
carbon footprint values for each pipe material, one can see a difference in the gradients. This is
important because the steel pipe has a much
larger gradient for carbon footprint than
concrete pipes, as seen on graphs 14 and 15.
Therefore, a small change in pipe diameter will
lead to a larger than proportional change in
carbon footprint. Therefore, this analysis should
help in selecting a pipe diameter and a material
that will yield a high operating flow rate and
have a lower carbon footprint, for an
environmentally friendly yet workable system.

An absolute priority of this paper is costs. In order to analyse this, a relationship must be established
between the costs and the independent variables. In Table 3 of the coursework sheet, there is a
range of pipe and pump diameters with corresponding prices. By using the same extrapolating
method used for the carbon footprint graph, one can again assume a linear relationship. Therefore,
by using this method, graphs 11 and 12 were created.

Graph 11 demonstrates the cost vs Pump diameter relationship. This is a fixed cost required to build
the pump. By closer inspection, one can see that the gradient of this curve is very high, as illustrated
by the equation of the line. Thus, one would expect the pump to be designed with as small of an
impeller diameter as possible, to limit the costs of the system and meet the outlined requirements.

Graph 12, on the other hand, shows the relationship between cost and Pipe diameter. This draws
the same conclusion as graph 11. That in order to keep costs to a minimum, the pipe size must be as
small as possible.

However, on closer inspection, the Pipe diameter-cost equation (the equation of the line on graph
12) exhibits a gradient which is much greater than the pump diameters. Therefore, it is more
important to have a smaller pipe diameter. As an increase in pipe diameter will have a greater
increase in cost than it would for a similar change in the size of the pump.
System Design Proposal
As a consequence of all the previous data and explanations, one can now start on deciding the sizes
and specificity of the pipe system. One can first start with finding the correct flow rate as this pipe
system must have a minimum operational flow rate of 3.47 m3s-1. This group started by finding a
system which met this. By using the analysis discussed previously, a concrete pipe with a diameter of
0.75 m, a pump diameter of 1.02 m and an RPM
of 900 was chosen. Which combined to give an
efficiency of around 35%. These values can be
pictorially shown in graph 13.

These values have been chosen because, firstly,

the intersection of Head vs Flowrate and system
performance shows that the operational
flowrate is 3.6 m3s-1. This is high enough to
achieve the 100,000 m3 usage and the maximum 8-hour filling time, thus meeting the first set of
requirements.

Additionally, by extrapolating the values, one can see that the system has an adequate efficiency of
roughly 35%. Therefore, the initial parameters of this paper have been met with this initial proposed
design. As well as that concrete pipes were chosen as they have a smaller carbon footprint than
using steel pipes. According to graphs six and seven, the carbon footprint for concrete is 3.75 times
smaller than steel pipes if used in our pump-piping system.

One of the major priorities when designing this pump piping system is to make it as environmentally
friendly as possible. This paper will analyse this feature by ensuring the system has a low carbon
footprint. One method of ensuring this, as previously mentioned (graphs six and seven), is to change
the pipe material and diameter. This group decided to settle with a concrete pipe of a diameter of
0.75m. This is because, for a 0.75m pipe diameter, the carbon footprint emission for the concrete
pipe is 194.441 KgCO2/m while the steel pipe is 505 KgCO2/m. Therefore concrete is selected over a
steel pipe.

However, to meet the final set of requirements that were set out, this group has to test the cost of
the system. This was done by forming a linear equation using the information from table 2 of the
coursework sheet about estimated capital costs. The equation derived is shown below:

𝐶𝑜𝑠𝑡𝑠 = (4000 + 1500 ∗ 𝐷) + 4 ∗ (500 + 120 ∗ 𝑑) + 10 ∗ (100 + 50 ∗ 𝑑) + (2.2 ∗ 2200 ∗ 𝑑)

By inputting the proposed system's values, an initial cost was worked out to be £596,500. This
group, however, did simulate many other system designs. Although, for larger diameters, the costs
were significantly higher. This relates to the previous analysis section. Therefore, we continued with
the given parameters listed at the beginning of this section.

Now that the piping system design has been agreed upon, this group must determine the running
costs of the system. This can be done by finding the operating point in graph 13. By doing this, one
finds that the Head is 201m, and the flow rate is 3.6m3/s. With these values, one can calculate the
power required to run the pump using equation 10, which equates to 2,057,143 Watts. This can
subsequently allow for the calculation of kilo-watt-hours by dividing the power equation by a
thousand and then multiplying it by eight. This will give a value of 16,457.14 kWh.
According to table two of the coursework sheet, the electrical costs are 8p per kilo-watt-hour.
Therefore, to find the electrical costs and the subsequent running costs, one must multiply the
previous value to give a value of £1316.57 per day.

These costs are relatively high and not ideal. However, we have succeeded in maximising the other
three priorities, as a consequence of this group designing a system that achieved the required
flowrate, good efficiency and a low carbon footprint.

This group believes it has found an ideal solution as, for example, our other design was to reduce the
pump speed to 600 RPM, increase the pipe diameter to 0.9 and increase pump diameter to 1.2. This
will keep a similar flowrate of about 3.7 m3s-1. This allows for a significant reduction in the running
costs to £950 per day. However, this design would increase initial costs to £710,800. This would be a
worse design assuming the system will have a long life span. This is because our proposed design will
save a total of £114,300 in capital costs as well as that this new system with the added width of the
pump and pipe diameter will significantly increase the carbon footprint from the materials,
according to graph 6. However, as the climate is of increasing concern, this group does not want to
compromise on the carbon footprint priority. Therefore, the proposed design will trade costs to
allow the carbon footprint to be a minimum.

Lastly, an additional requirement of this research paper was to look at the power provider for the
system. Through closer inspection, this group has chosen nuclear Power because it is the most
environmentally friendly energy provider of providers available. This is because Nuclear Power emits
the smallest carbon footprint, which is 5 gCO2/kWhr compared to Coal and Gas, which emit 800 and
500 gCO2/kWhr respectively (refer to Table 3 Annexe C). The reason nuclear Power has the smallest
carbon footprint is that operating reactors emit minimal amounts of carbon dioxide. However, if this
research paper allowed this group to choose other sources of Power outside of table 3, there would
have been significant interest in wind and hydroelectric power systems. This is because these are
renewable and would reduce our carbon footprint, even more, thus maximising our design proposal.

Conclusion
In the introduction, this group was tasked with designing a piping system. The coursework asked this
group to detail the parameters, costs of the componentry and make a system that was economical in
the capital costs, operating expense and considered the carbon footprint. To ensure these goals
were met, this group set conditions that our design must meet. This entailed a design that: has a
high flow rate, good efficiency, low costs, and a low carbon footprint. To design a system that meets
those requirements, this group made a series of graphs and calculations that studied the piping
materials and analysed the variables controlling the piping system. After the inspecting the data,
this group concluded that our system must have a concrete pipe with a diameter of 0.75m, Pump
impeller size of 1.02m and a flow rate of 900RPM. As said in the analysis, this design is ideal for the
fact that it has the least trade-offs than any other system design this group tested.

However, this is far from an ideal system. This is because the design still has high operating and
capital cost. Therefore, in order to complete further analysis of this design, it would be ideal to use
more up to date technologies to simulate and analyse the piping system properly. For example, a
tool such as Applied Flow Technologies Fathom may be ideal in completing a more in-depth analysis.
Additionally, this analysis did not consider an extended amount of power generation methods, such
as wind and solar energy. This perusal would increase the research papers suitability for the worlds
broadening increase in more environmentally suitable methods of power generation.
Annexe A: Part B Tables

Reynolds number Friction factor Major Head loss Minor Head loss Head loss sum

0 0 0 0 100
1068593.851 0.009828425 23.61303765 2.555413127 126.1684508
2137187.703 0.008264687 79.42447486 10.22165251 189.6461274
3205781.554 0.007467988 161.4782579 22.99871814 284.476976
4274375.405 0.006949746 267.1510248 40.88661003 408.0376348
5342969.257 0.006572664 394.77475 63.88532816 558.6600782
6411563.108 0.006279804 543.1459528 91.99487256 735.1408254
7446763.402 0.006049162 705.7857863 124.0997455 929.8855317
8515357.253 0.005849737 892.4516839 162.2712291 1154.722913
9583951.104 0.00567938 1097.571236 205.5535389 1403.124775
10652544.96 0.005531256 1320.605473 253.946675 1674.552148
11721138.81 0.005400633 1561.086081 307.4506373 1968.536718
12789732.66 0.005284108 1818.600273 366.0654259 2284.665699
Table 1: Table of Total Head loss for steel pipe

Friction factor Major Head loss Minor Head loss Total Head loss

0.008 0 0 100
0.008 19.22020129 2.555413127 121.7756144
0.008 76.88080518 10.22165251 187.1024577
0.008 172.9818116 22.99871814 295.9805298
0.008 307.5232207 40.88661003 448.4098307
0.008 480.5050323 63.88532816 644.3903605
0.008 691.9272466 91.99487256 883.9221191
0.008 933.3997951 124.0997455 1157.499541
0.008 1220.501552 162.2712291 1482.772781
0.008 1546.043711 205.5535389 1851.59725
0.008 1910.026273 253.946675 2263.972948
0.008 2312.449238 307.4506373 2719.899875
0.008 2753.312605 366.0654259 3219.378031
Table 2: Table of Total Head loss for concrete pipe
 Head loss Head loss Head loss Head loss Head loss Head loss
Head loss 1 Flow rate
0.2 0.4 0.6 0.8 1.2 1.4
100 100 100 100 100 100 100 0
4868.146682 257.3181443 121.8115825 105.4357895 101.8663304 100.7842485 100.3786726 0.995328
19172.58673 729.2725771 187.2463301 121.7431582 107.4653215 103.136994 101.5146904 1.990656
43013.32013 1515.863298 296.3042427 148.9221058 116.7969734 107.0582365 103.4080533 2.985984
76390.34691 2617.090308 448.9853203 186.9726326 129.861286 112.547976 106.0587615 3.981312
119303.667 4032.953607 645.2895629 235.8947384 146.6582594 119.6062126 109.4668149 4.97664
171753.2805 5763.453194 885.2169706 295.6884234 167.1878935 128.2329461 113.6322134 5.971968
231657.7796 7739.916012 1159.246276 363.9808378 190.6354914 138.0858338 118.3896577 6.936192
302881.9707 10089.85579 1485.05679 445.177944 218.5138014 149.8005458 124.0460795 7.93152
383642.4551 12754.43186 1854.490469 537.2466293 250.1247721 163.0837548 130.4598466 8.926848
473939.2329 15733.64422 2267.547313 640.1868937 285.4684036 177.9354608 137.6309589 9.922176
573772.304 19027.49286 2724.227322 753.9987371 324.5446958 194.3556638 145.5594163 10.917504
683141.6685 22635.9778 3224.530496 878.6821597 367.3536488 212.3443639 154.2452189 11.912832
Table 3: Table of Head loss of Concrete pipe

Head loss Head loss Head loss Head loss Head loss Head loss
head loss 1 Flow rate
0.2 0.4 0.6 0.8 1.2 1.4
100 100 100 100 100 100 100 100
4156.315164 257.4842898 123.8123145 106.2738309 102.2393479 100.9681474 100.4776236 4156.315164
13913.07133 640.2936373 182.1849796 121.7639263 107.8031309 103.3870855 101.6770435 13913.07133
28414.22384 1212.89882 269.9401124 145.1499237 116.2338706 107.0643901 103.5057339 28414.22384
47238.67991 1959.650884 384.7970985 175.8502651 127.3300691 111.9153072 105.9229416 47238.67991
70118.694 2870.599676 525.3058436 213.495176 140.9636072 117.8859476 108.9027543 70118.694
96861.08761 3938.566157 690.4201042 257.8178636 157.0420467 124.9374298 112.4264761 96861.08761
126309.7691 5117.644397 873.0738038 306.9284373 174.8819458 132.7708332 116.3450927 126309.7691
160246.6003 6479.516778 1084.411682 363.8322818 195.5777759 141.8677778 120.8999927 160246.6003
197677.6145 7984.723667 1318.360946 426.9053988 218.5423212 151.9714569 125.9631679 197677.6145
238516.2986 9630.049996 1574.453043 496.0283076 243.734184 163.0644581 131.5262457 238516.2986
282687.48 11412.70215 1852.280845 571.0971899 271.1173933 175.1316511 137.5819509 282687.48
330124.9002 13330.21778 2151.485497 652.0205379 300.6602438 188.1597001 144.1238709 330124.9002
Table 4: Table of Head loss of Steel pipe
Annexe B: Part A Tables
Table 1

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
KQ 0 032 064 096 128 16 192 223 255 287 319 351 383
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
KH 419 433 442 447 437 433 419 403 386 357 326 279 233
Effici
ency 0 13 25 35 44 48 51 53 54 55 53 50 45

Table 2 Table 3

Q (X-AXIS) H (Y-AXIS) Efficiency Q (X-AXIS) Pipe Area V

0 393.629 0 0 0.3848451 0
0.3686 406.782 13 0.442368 0.3848451 1.14947
0.7373 415.237 25 0.884736 0.3848451 2.29894
1.106 419.934 35 1.327104 0.3848451 3.44841
1.769472 0.3848451 4.59788
1.475 410.539 44
2.21184 0.3848451 5.74735
1.843 406.781 48
2.654208 0.3848451 6.89682
2.212 393.629 51
3.082752 0.3848451 8.01037
2.569 378.598 53
3.52512 0.3848451 9.15984
2.938 362.628 54
3.967488 0.3848451 10.3093
3.306 335.383 55
3.675 306.261 53 4.409856 0.3848451 11.4588

4.044 262.106 50 4.852224 0.3848451 12.6083

4.412 218.892 45 5.294592 0.3848451 13.7577

Table 4

Reynolds number Friction Factor

0 0
6.15E+05 1.13E-02
1230686.806 0.009487
1846030.209 0.008573
2461373.612 0.007978
3076717.014 0.007545
3692060.417 0.007209
4288174.339 0.006944
4903517.742 0.006715
5518861.145 0.00652
6134204.547 0.00635
6749547.95 0.0062
7364891.353 0.006066
Annexe C: Course work Tables
Appendix A.

Spreadsheet for Part B

Cost Evaluation for Part B

Costs Spreadsheet for Part B

Spreadsheet for Part A

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