**UNIVERSITY OF NAIROBI **

**PROJECT NO: GON 03/2015 **

**DESIGN OF A PENSTOCK FOR A MICRO HYDRO PLANT **

**AUTHORED BY: **
**MOMANYI DUNCAN ** **F18/29933/2009 **
**MOKO ANTONY ** ** F18/20005/2009 **
**PROJECT SUPERVISOR: **
**ENG. G. NYANGASI **
**SUBMITTED: APRIL, 2015 **

**SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE **
**AWARD OF THE DEGREE OF BACHELOR OF SCIENCE IN MECHANICAL AND **

**MANUFACTURING ENGINEERING **

**DECLARATION **

The work presented in this project is my original work and to the best of my knowledge, it has not been submitted either in the same or different form anywhere for certification in any other university for academic qualification.

Signed ……….. MOMANYI DUNCAN Signed ……….. MOKO ANTONY ……… Signed Supervisor Eng. G. NYANGASI ………

**DEDICATIONS **

This project is dedicated to our parents for their love for our education and their positive
**influence towards its completion. **

**ACKNOWLEDGEMENTS **

This project might not have been a success were it not for the countless effort from people we are obliged to acknowledge here.

First and foremost, we would like to acknowledge our supervisor, Eng. Nyangasi for his guidance and for all the literature material provided by him that were a huge guide.

We also acknowledge the operations officer at KENGEN Kenya, eastern region,Mr. Joel Ngugi for allowing us to visit their power plant at Sagana, Nyeri county to carry the field study that laid the basis for this research project.

Abundant gratitude goes to Miss. Ruth of the operations office at KENGEN for her great facilitation to see that the trip to their plant was a success.

Above all, we wish to thank our parents for the financial and moral support provided by them to ensure that we completed this research project.

**ACCRONYMS **

Ki - turbulence loss coefficient

�� - Velocity

Q - Discharge

UPVC - Unplasticised polyvinyl chloride

CFM/cfm - Cubic feet per minute

FPM/fpm - feet per minute

Kw - Kilowatts

Hp - Horsepower

Fd - Loss coefficient for pipe entry

�� - Capture velocity

� - Height between the vessel and the exhaust hood

� - Velocity Pressure

- Fitting coefficient of friction

� - Coefficient of friction due to angle of bend

- Coefficient of friction due to Reynolds number

� - Density

- Acceleration due to gravity

ℎ - static height

**Contents **
DECLARATION ... 2
DEDICATIONS... 3
ACKNOWLEDGEMENTS ... 3
ACCRONYMS ... 4
ABSTRACT ... 9
CHAPTER 1: INTRODUCTION ... 10
1.1 Background information ... 10
1.2 Problem statement ... 11
1.3 Objectives ... 12

CHAPTER 2: LITERATURE REVIEW ... 13

2.1 Materials used for penstocks ... 13

2.1.1 Ductile iron ... 13

Figure 2.1: Ductile iron ... 13

2.1.2 Prestressed concrete ... 13

Figure 2.2: Concrete Penstock... 13

2.1.3 Mild steel ... 13

Figure 2.3: Steel penstocks ... 14

2.1.4 UUPVC (Unplasticised polyvinyl chloride ... 14

Figure 2.4: uPVC penstock ... 15

2.2 Factors to be considered when selecting material ... 15

2.2.1 Design Pressure ... 15 2.2.2 Surface Roughness ... 16 2.2.3 Weight of material ... 16 2.2.4 Ease of transportation ... 16 2.2.5Method of jointing ... 16 2.2.6 Cost of material ... 17

2.3 Determination of penstock dimensions and losses ... 17

2.3.1 darcy-weischbach method ... 17

Figure 2.5: Moody diagram ... 19

Table 2.1: Materials ... 20

(courtesy engineeringtool-box.com) ... 20

**Pipe equation** ... 21

CHAPTER 3: EXISTING PENSTOCK OF KENGEN SAGANA PLANT ... 1

3.1 specifications. ... 1

Table 3.1: Plant Specifications ... 2

Figure 3.1: AUTOCAD drawing of the SAGANA hydo plant’s pensto k indi ating the uried part. ... 3

Figure 3.2: dimensioned CAD drawing of the SAGANA plant ... 3

Figure 3.3: CAD drawing of the SAGANA hydro plant penstock outlay ... 4

3.2 Performance of existing plant ... 4

3.3 Net head available at turbine ... 5

3.4 Determining the plant efficiency ... 6

3.5 Percentage head loss... 6

3.6 Penstock efficiency ... 6

CHAPTER 4: REVIEW OF THE EXISTING PENSTOCK ... 7

4.1 Mild steel ... 8

4.1.1 Penstock loss calculations ... 8

4.1.2 Steel penstock efficiency ... 8

4.1.3 Steel penstock diameter ... 9

Table 4.1: Iterating for different diameters, ... 10

4.1.4 expected power output at optimum penstock ... 10

=25.3x36.19x60.36x9.81 ... 10

4.2uPVC ... 10

4.2.1 PENSTOCK LOSS CALCULATIONS ... 10

4.2.2 pvc penstock efficiency ... 11

4.3 Proposed outlay of new penstock ... 1

Figure 4.2: AUTOCAD Proposed outlay of new penstock ... 3

Figure 4.3: AUTOCAD Proposed outlay of new penstock... 4

CHAPTER 5: CONCLUSION AND RECOMMENDATION ... 5

5.2 Recommendation ... 6

REFERENCES ... 7

**ABSTRACT **

The objective of the project was to conduct a literature review regarding the specifications and design parameters required to design a penstock. After review of the field data required to design the component were derived from KENGEN SAGANA HYDRO POWER STATION. This is because of poor performance of the existing penstock at the plant. To achieve this objective a review of the existing system was done as well as factors to be considered evaluated. This was followed by a design of a penstock that would presumably be more efficient leading to increased power output.

From the review of the existing penstock, it was found that it can be improved to yield a higher output regarding the amount of water it will discharge to the turbine. Improving the current penstock involved designing for the best material with lesser losses and suggesting the best outlay. A simulated model of the proposed penstock was also designed to show how it’s going to work.

Data such as that obtained from the site and use of penstocks design handbooks enabled us to determine the optimum parameters for the penstock as well as suggest the efficient turbine. Also, route consideration was of factor to aid in elevation changes which are very important in determining the optimum head and economical penstock length.

A turbine and generator was selected to match the flow and pressure at the bottom of the penstock. Inaccurate flow versus pressure measurements existed for the old penstock route. In order to estimate the available hydraulic power which can be expected from the new penstock route, both routes were mapped with special attention paid to elevation changes. Total head was found to be 37.5 meters over a distance of roughly 648 meters. The effects of fittings and pipe dimensions, materials and ages on pressure dissipation were accounted for via minor loss correlations and both Darcy-Weisbach and Hazen-Williams equations. For each penstock route, total head loss was calculated at various flow rates from which total hydraulic power could be estimated. The head loss calculated in the old route was compared with the existing measurements. At the permitted average water flow rate of 25.4 meters cubic per second, hydraulic power is predicted to be 543.44 kw using the new material and a Francis turbine is

recommended. While the original measurements corroborate this finding, corrections made to the measurements suggest that 530 kw is a more reasonable power estimate

*(source of figures: Kengen Kenya,Sagana plant) *
**CHAPTER 1: INTRODUCTION **

**1.1 Background information **

The penstock is the pipe which conveys water under pressure from the forebay tank to the turbine. The penstock often constitutes a major expense in the total micro hydro budget, as much as 40 % is not uncommon in high head installations, and it is therefore worthwhile optimizing the design. The trade-off is between head loss and capital cost. Head loss due to friction in the pipe decrease dramatically with increasing pipe diameter. Conversely, pipe costs increase steeply with diameter. Therefore a compromise between cost and performance is required.

The design philosophy is first to identify available pipe options, then to select a target head loss, 5 % of the gross head being a good starting point. The details of the pipes with losses close to this target are then tabulated and compared for cost effectiveness. A smaller penstock may save on capital costs, but the extra head loss may account for lost revenue from generated electricity each year.

The materials used in penstock are usually steel, HDPE (High Density Polythene) and increasingly PVC (Poly Vinyl Chlo-ride). It is one of the most important components of the MHS (Micro Hydro-power System) because it is at this point that the potential energy of the water is converted into kinetic energy. The velocity of water at the penstock is typically 3m/s and is often located at a slope over 45 degrees (Sanchez & Rodriguez, June 2011). Due to the risk of contraction and expansion of penstock pipes due to fluctuation in seasonal temperature, sliding type of expansion joints are placed between two consecutive pipe lengths. Anchor block, which is basically a mass of concrete fixed into the ground, is used to restrain the penstock from movement in undesirable directions.

Traditionally, steel penstocks have been considered as very high pressure conduits, usually of large diameter, and operating with frequent surges during the normal condition. Penstocks may also be subject to pulsations of varying frequency and amplitudes transmitted from the turbine or pump.

When penstocks are installed above ground, this can sometimes cause excessive vibration. These are the perceived differences between a penstock and an ordinary pipeline. Based on these

conditions, penstocks have been designed to standards initially established with minor revisions based on an allowable design stress at normal conditions of 2/3 of yield or 1/3 of tensile strength.

In the last 25 years there have been many changes in steel making practice, pipe manufacturing methods and welding procedures. These lines have usually been buried lines operating at working pressure of 150 to 350 p.s.i. plus transient pressures. Many lines, however, have been installed since 1960 with working pressure as high as640 p.s.i. using high strength low alloy steels with an allowable design stress of 50% of yield atworking pressure and up to 75% of yield at transient pressures.

Today there are many penstocks installed utilizing thousands of feet of pipe with operating pressures varying from no pressure at the inlet structure, to low or moderate pressures, or to very high pressures at the power plants. Most of these penstocks are buried and many parallel to the stream from which the water was diverted. They are usually in remote locations. With certain types of turbines and an adequate control valve system, sometimes involving a synchronous bypass system. Transient pressures can be limited. A buried penstock will not be subject to the problem of harmonic vibrations sometimes associated with the traditional penstock.

For many of these installations, when carefully evaluated by the engineer, the normal quality and the design standards of KEBS steel standards should be considered adequate and will provide the most economical material for this service. As working pressure and pipe diameter increase, the use of high strength low alloy steel will become economical. At design stresses over 21,000 p.s.i. at normal conditions, additional testing, including 100% ultrasonic or radiographic inspection of welds, is appropriate.

**1.2 Problem statement **

Penstocks are the single major component of a hydro-power plant that comprises the significant cost (about 40 per cent) to install and maintain. Therefore looking for the best way of selecting the best material and having the best dimensions that will convey sufficient thrust to the turbine is very necessary.

Our case study was based on Sagana micro hydro power plant that was commissioned in the pre-independence period with three penstocks feeding three Francis turbines each producing 500KW of electrical power at full load.

The penstocks are all made of ductile iron and their outlay is illustrated in this study which gives us conviction of providing a better design of a penstock that can perform better than the existing as shall be shown herein.

The existing penstocks at Sagana micro hydro-power plant have been presumed not to be fully optimized to yield the best of their ability. We are therefore going to use the existing data about the currently installed penstocks and turbines to come up with a presumably more efficient through theoretical workings and show how a more optimized penstock to be suggested here can be utilized for that reason.

Cost is also going to be of a major factor here as every project is usually evaluated by its economic viability. It shall be shown here basing on figures obtained of the current penstock how the newly installed penstock shall be of economic significance relative to the former on matters installation and maintenance.

**1.3 Objectives **

The research study was aimed at reviewing the design of the penstock at Sagana KenGen micro hydro power plant

Suggest most suitable material for use to design the new penstock giving consideration to:

i) Design Pressure

ii) surface roughness

iii) weight of material

iv) Method of joining

v) Cost of material

**CHAPTER 2: LITERATURE REVIEW **
**2.1 Materials used for penstocks **

**2.1.1 Ductile iron **

These pipes can have an internal coating of cement, affording better corrosion protection and
low friction loss. Ductile iron is a heavy material, however, which leads to a difficult and more
costly installation. Ductile iron allows for multiple jointing options, including mechanical joints
**(bolted gland), push-in spigot and socket with a flexible seal, or occasionally flanged. **

**Figure 2.1: Ductile iron **
**2.1.2 Prestressed concrete **

Several factors come into play with concrete penstocks which make them typically unsuitable for use, even at moderate pressure. Concrete’s friction loss characteristics can be highly variable. Further, the material’s excessive weight makes transportation and installation difficult. However, steel reinforced concrete pipes, particularly when they are pre-stressed, can serve as a cost-effective alternative for low and medium head sites. Concrete penstocks typically have rubber ring joints.

**2.1.3 Mild steel **

Mild steel is likely the most widely utilized penstock material for small hydro systems. Its low
cost and ease of acquisition add to its appeal. Mild steel provides a greater versatility for pipe
diameter and thickness. It has moderate friction loss. Mild steel penstocks are resistant to
mechanical damage but can be more susceptible to corrosion when the pipelines are buried.
While these pipes are heavy, they can easily be manufactured in smaller segments, thus making
transportation and installation easier. The jointing on mild steel pipes can be achieved by on-site
**welding, flanges, or mechanical joints **

**Figure 2.3: Steel penstocks **

**2.1.4 UUPVC (Unplasticised polyvinyl chloride **

UPVC is a commonly used penstock material. It has low friction loss and a high resistance to corrosion. UPVC is available in a large range of sizes and pressure ratings and the cost is

relatively low. Additionally, the material is lightweight, increasing the ease of transportation and installation. However, UPVC is relatively fragile and susceptible to mechanical damage from impacts, particularly at low temperatures. Further, UPVC will deteriorate when exposed to

ultraviolet light; the sun exposure will cause surface cracking, which in turn, will have a significant consequence on the pressure rating of the pipe. As such, the pipe must always have protection from direct sunlight by burying, covering with foliage, wrapping, or painting. UPVC also requires continuous support along the length of the penstock due to its high vulnerability to stress fatigue. If the UPVC is allowed to bend, there will be an introduction of internal forces against the wall of the pipe; further, vibrations induced by water flow can be enough to cause a stress fatigue failure after only about 5 to 10 years of operation. Because of this, it is

recommended that UPVC pipe be run along the ground or preferably buried. UPVC pipe segments can be joined using spigot and socket with UPVC pipe cement or using spigot and socket with a flexible sealing ring.

**Figure 2.4: uPVC penstock **

**2.2 Factors to be considered when selecting material **
**2.2.1 Design Pressure **

Almost any type of pipe will work as a penstock, at least to some degree. The most common types are white polyvinyl chloride (PVC) and “poly pipe” (black polyethylene, PE; or high-density polyethylene, HDPE), which come in several pressure ratings. Common drainpipe is thin-walled and not rated for pressure. Though it can accommodate up to about 30 feet of head if you are careful opening and closing valves, drainpipe is not normally a recommended choice. In selecting pipe with the correct pressure rating, be sure to allow an extra 40% above the static water pressure in the pipe. For example, with 66 m of head, the static pressure is about 87 pounds per square inch (psi). Multiply that by 1.4 (140%) to reach the needed pipe pressure

rating of 122 psi. To compute the static pressure for the proposed penstock (in psi), divide the total head (in feet) by 2.3.

To save on penstock costs, a system can use pipes of increasingly higher pressure ratings as it gets closer to the bottom of the run, where pressure is highest. In that case, calculate the pipe pressure ratings for different total heads as you move down the pipeline.

Some hydro installers will disagree, but my strong preference for penstocks is to use PVC pipe in 20-foot lengths with a bell end for gluing lengths together. Splices used for other pipe types are not reliable at high pressure or for unrestrained pipe movement. Thin-wall poly pipe comes in a long roll and can be easy to use, especially if your penstock has to weave through trees and over rocks to the turbine, and if you can complete the entire run without splices. Thick-wall poly pipe requires special butt-welding equipment. The welds will leave a bead on the inside of the pipe that will affect flow. In our area, the critters tend to like chewing on poly pipe, but in other parts of the country, they seem to have a taste for the white PVC.

Aluminum pipe can be easy to get in agricultural areas but generally should only be used for pressures up to about 125 psi. It should not be buried unless treated to deal with the acidity in soils. Steel will handle very high pressure but should also not be buried, since it will rust out over time. Common PE poly pipe and HDPE have pressure ratings around 80 psi. They are available at even higher pressure ratings but can be hard to get in larger sizes.

**2.2.2 Surface Roughness **

Materials with higher surface roughness are very undesirable for the task of conveying water as their friction factor is high thus have increased resistance to the water flowing through them. An example with very high surface roughness undesirable for large flow rates is prestressed concrete and can thus be unsuitable for service as a penstock.

**2.2.3 Weight of material **

Materials with enormous weights are very undesirable for use due to challenges of handling them from transportation to installation which can pose a challenge on the economic viability of the whole project.

**2.2.4 Ease of transportation **

The material to be used for a penstock must provide ease of transport to the installation site as area of manufacture to the site could be miles away thus relatively light and posses a a smaller diameter while performing the same expected function.

Materials such as upvc are most suitable as they are light as well as easy to join compared to materials like prestressed concrete.

**2.2.5Method of jointing **

Pipes are generally supplied in standard lengths and have to be joined together on site. There are several ways of doing this and the following factors should be considered when choosing the best joint system for a particular scheme:

suitability for chosen pipe material,

skill level of personnel installing the pipe,

whether any degree of joint flexibility is required,

relatively costs,

ease of installation.

Methods of pipe jointing fall roughly into four categories:

flanged,

spigot and socket,

mechanical,

welded.

**2.2.6 Cost of material **

This is the most fundamental factor to consider in the whole selection process because as explained above the penstock cost comprises close to 40% of the hydro plant cost thus decisive selection of the most reasonably priced material that can still perform as optimally as expected is of invaluable essence.

**2.3 Determination of penstock dimensions and losses **
**2.3.1 darcy-weischbach method **

The flow of liquid through a pipe is resisted by viscous shear stresses within the liquid and the turbulence that occurs along the internal walls of the pipe, created by the roughness of the pipe material. This resistance is usually known as pipe friction and is measured is feet or metres

head of the fluid, thus the term head loss is also used to express the resistance to flow.

Many factors affect the head loss in pipes, the viscosity of the fluid being handled, the size of the pipes, the roughness of the internal surface of the pipes, the changes in elevations within the system and the length of travel of the fluid.

The resistance through various valves and fittings will also contribute to the overall head loss. A method to model the resistances for valves and fittings is described elsewhere. In a well designed system the resistance through valves and fittings will be of minor significance to the overall head loss, many designers choose to ignore the head loss for valves and fittings at least in the initial stages of a design.

**The Darcy-Weisbach equation **

Weisbach first proposed the equation we now know as the Weisbach formula or
Darcy-Weisbach equation:
hf* = f (L/D) x (v*2/2g)
where:
hf = head loss
(m) f = friction
factor

L = length of pipe work (m)

d = inner diameter of pipe work (m) v = velocity of fluid (m/s) g = acceleration due to gravity (m/s)

or:

(ft) f = friction factor

L = length of pipe work (ft)

d = inner diameter of pipe work (ft) v = velocity of fluid (ft/s) g = acceleration due to gravity (m/� )

The friction factor is obtained from a moody diagram.

The Moody Chart or sometimes the Friction Factor Chart, enables a user to plot the Reynolds number and the Relative Roughness of the pipe and to establish a reasonably accurate value of the friction factor for turbulent flow conditions.

The Moody Chart encourages the use of the Darcy-Weisbach friction factor and this is the method of choice for hydraulic engineers.

**Figure 2.5: Moody diagram **

**2.3.2 Hazen william method **

The Darcy-Weisbach equation can be difficult to use because the friction factor was difficult to estimate. In 1906, Hazen and Williams provided an empirical formula that was easy to use.

The general form of the equation relates the mean velocity of water in a pipe with the geometric properties of the pipe and slope of the energy line.

where:

*V is velocity *

*k is a conversion factor for the unit system (k = 0.849 for SI units) *

*C is a roughness coefficient *

*R is the *hydraulic radius

*S is the slope of the energy line (*head loss per length of pipe or hf/L)

*The conversion factor k was chosen so that the values for C were the same as in the Chézy *
*formula for the typical hydraulic slope of S=0.001*.*The value of k is 0.001*−0.04

*Typical C factors used in design, which take into account some increase in roughness are as *
follows

**Material ** **C Factor low C Factor high **

Cast iron new 130 130

Concrete 100 140
Copper 130 140
Steel 90 110
Galvanized iron 120 120
Polyethylene 140 140
Polyvinyl chloride (PVC) 150 150
Fibre-reinforced plastic (FRP) 150 150
**Table 2.1: Materials **
(courtesy engineeringtool-box.com)

**Pipe equation **

The general form can be specialized for full pipe flows. Taking the general form

Rearranging gives

*The flow rate Q = V A, so *

The hydraulic radius* R (which is different from the geometric radius r) for a full pipe of *

*geometric diameter d is d/4; the pipe's cross sectional area A is * , so

When used to calculate the head loss, becomes:

where:

*S = Hydraulic slope *

hf = head loss in meters (water) over the length of pipe

*L = length of pipe in meters *

*Q = volumetric flow rate, m*3/s (cubic meters per second)

*C = pipe roughness coefficient *

**CHAPTER 3: EXISTING PENSTOCK OF KENGEN SAGANA PLANT **

In this chapter, the specifications of the existing penstock at sagana micro hydro plant are discussed in detail.

Sagana micro hydro power plant is owned by KENGEN limited and was commissioned in 1957. The plant has a capacity of 1.5MW at full load. It has three Francis turbines. Each turbine is supplied by a 0.5 m diameter 648m long ductile iron penstock.

All the available specifications for the penstock are given below and a schematic of it drawn below.
**3.1 specifications. **

i) Available head

ii) available flow rate iii) Length of pipeline iv) material of penstock

v) diameter of penstock
Total Head
**available ,H **
Flow Rate
**Q **
Length of
**penstock, L **
Material of
**penstock, M **
Power output,
**P **
Penstock
diameter,
**D**
37.5 m 25.4� /s 648 m Ductile iron 500 KW 0.5 m

**Figure 3.1: AUTOCAD drawing of the SAGANA hydo plant’s penstock indicating the buried **
**part. **

**Figure 3.3: CAD drawing of the SAGANA hydro plant penstock outlay **

**3.2 Performance of existing plant **

To evaluate the performance and efficiency of the penstock, the Darcy-Weisbach equation for head loss due to friction and the equation for head loss due to minor losses from geometric irregularities such as gate slots and bend was used. Avoidable head losses can be directly related to overall

power/energy loss and subsequent loss of revenue for the plant. These equations are defined as follows: Avoidable head loss due to friction, Δhf (ft), from the Darcy-Weisbach equation:

∆ℎ = ∆ �

Where: ·

* Δf is the difference in Darcy friction factors computed for the existing roughness conditions and *
roughness conditions after potential upgrade

**L **is the length of the conveyance component

**V **is the average flow velocity or flow rate per cross-sectional area
** D is the hydraulic diameter **

**g **is the acceleration due to gravity

Friction Losses – 0.5 m section of pipe

D= 0.5 m *f = 0.027 *
μ = 1.002x10-3
L = 648 m
ρ = 998 kg/m3
g = 9.81
m/s2
C = 64 H = 42m

Velocity = V = [flow rate] / (π r2

) = 25.4 m3/s / (π (0.5 m)2/2) = 129.6 m/s

Le = 10 d = 4.064 m

Avoidable head loss due to minor losses (e.g., gate slots), Δhm

∆ℎ = ∆��
V = 64.6M/S,
*K*L* = *
0.001
∆ℎ = .
Where: ·

* ΔK is the difference in minor head loss coefficients computed for existing wall irregularities from gate *
slots and for conditions with irregularities removed by use of slot fillers after potential upgrades.

**V**is the average flow velocity or flow rate per cross-sectional area

** g is the acceleration due to gravity **

Other key values required to complete the computations for avoidable head losses include the
*dimensionless Reynolds number, Re, Darcy friction factor, f, kinematic viscosity, v and equivalent *
roughness ε (m). If the Reynolds number and relative roughness of the penstock shell

or tunnel interior are known, the Darcy friction factor can be determined using the Moody diagram. If
exact relative roughness measurements are unavailable, an approximate Darcy friction factor can be
*determined by comparing the existing conditions with charts found in publications such as Friction *
*Factors for Large Conduits Flowing Full [3], which provide data of measured Darcy friction factors *
for various construction materials.

Avoidable power loss, ΔP (MW), associated with Δhf or Δhm

**3.3 Net head available at turbine **

Given the available head and after calculating losses in the pipe, we can calculate the net head available at the turbine by subtracting the total losses from the total head available.

H=37.5-(4.064+0.212) H=33.224m

Its evident from above that major losses are incurred. Mostly courtesy of the frictional losses resulting from a high roughness factor of ductile iron.

**3.4 Determining the plant efficiency **
From the formulae:

= ��g

Given all the parameters in table 3.1 above , we can calculate for efficiency by making it the subject,

� = � � . � . � .

� = . %

**3.5 Percentage head loss **

This is an expression of the percentage head loss from frictional factors and minor losses of the gross head .This is so as to express the how desirable or undesirable the material used is.

%�� = � X100

%�� = . _{.} X100

=11.4%

This is an indication that the material currently in use is very inefficient due to a high percentage head loss as a desirable material should have a percentage head loss of less than 8%.

The penstock efficiency of the penstock is given as the net head available over the gross head
available.,
� =_{�}�
= .
. x100
� =88.59%

This is the penstock efficiency of the ductile iron penstock at SAGANA KENGEN Micro hydro plant.

**CHAPTER 4: REVIEW OF THE EXISTING PENSTOCK **

In this chapter a review of the existing penstock is carried out by evaluating the fixed elements at the plant and variable elements and incorporating the two to try optimize the design.

a)fixed elements-these refers to elements at the site that have already been pre-determined and can not be changed. These are: i) Head

ii)Length iii)Discharge

b)variable elements-refers to factors about penstock that can be altered to optimize the performance of the penstock. We shall review these in detail in this section.. they include:-

i)material of penstock ii)size of diameter

From existing plant, since the head is fixed, we can only work to minimize the losses experienced in the penstock by trying out different materials and obtain one with the minimum frictional losses. Optimizing the diameter is also very paramount to attain the best discharge while minimizing material used. Same applies to wall thickness.

The material to be proffered should also relevant in terms of cost. The cheapest with the best flow ability and durable is desirable.

Using the given fixed parameters about the plant, we shall try with steel and upvc as prestressed concrete was already eliminated due to unnecessary bulkiness, to try realise one with most minimum head loss and optimum diameter for purposes of best efficiency and cost effectiveness.

**4.1 Mild steel **

**4.1.1 Penstock loss calculations **

Flow Q 25.4 � /�

Gross head _{Hg } 37.5 m

Penstock length L 60

m Penstock internal diameter d

500 mm
Length L
**648m **
**Calculations**
Velocity in penstock V=
�
**,129.6m/s **

Friction head loss in penstock � = ∆fLV2 D g

From moody diagram in fig 2.1, obtain f, as 0.005 From Darcy’s equation ,

� = . x _{x x .}x . x .

**4.1.2 Steel penstock efficiency **
� =_{�}�
� =� -�
** =37.5-3.04 **
=34.46
� = .
. x100
� =91.89%

**4.1.3 Steel penstock diameter **

**Presume new pipe to be steel penstock ,648 m long has a design flow of 25.42 m3/s and a gross **
head of 37.5 m. Calculate and diameter and wall thickness. head loss < 5% of gross head.
Select diameter as , D =500 mm

Flow velocity V = 4.Q / pi .D2 =129.6 m/s Reynolds no = V.D x 106 = 1.8x 106 Surface roughness of mild steel is, f = 0.3 So , K/D = 0.3/300 = 1x 10-3

from Moody chart f = 0.005, From Darcy’s equation ,

h f = ½ x 129.6 x 500 x 0.0046 / 9.81x 25.4= 3.04 m in our case gross head = 37.5 m

H f = (3.04 /37.5 )x 100 =8.1 %

increase D by 50 mm ,
now V = 106.9m/s
K/D = 0.3/310 = 9.6 x 10-4
Re = V X D = 106.9 X 550= 1.7 x 10 6
corresponding f = 0.005
hf = 2.01 m
**%hf = 5.4 % **
**Iterations ** **Diameter(mm) ** � **V(m/s) ** **%� **
**1 ** **500 ** **3.04 ** **129.6 ** **8.1 **
**2 ** **550 ** **2.01 ** **106.9 ** **5.4 **
**3 ** **600 ** **1.31 ** **88.6 ** **3.4 **

**Table 4.1: Iterating for different diameters, **

From table 4.1 above, the iterations reveal that the optimum steel diameter that can produce the least
**frictional losses is 600mm. **

**4.1.4 expected power output at optimum penstock **

= ��g

=25.3x36.19x60.36x9.81 =543.44 Kw

Percentage increase= . �

**4.2uPVC **

** 4.2.1 PENSTOCK LOSS CALCULATIONS **

Flow Q 25.4 � /�

Gross head _{Hg } 37.5 m

Penstock length L 648m

Penstock internal diameter,d 500 mm
**Calculations**

**Velocity in penstock V= **�

�** ,**129.6m/s

Friction head loss in penstock � = ∆fLV2 D g

From moody diagram in fig 2.1, obtain f, as 0.0025

� = . x _{x x .}x . x .
** ** =2.93m
**4.2.2 pvc penstock efficiency **
� =_{�}�
� =� -�
=37.5-2.93=34.57
� = .
. x100
� = . %

**4.3 Proposed outlay of new penstock **

The outlay of the penstock is very key in reducing much losses. However much the topography of the site will have pre determined the penstock route, a lot has to be done to eliminate so much bends in order to reduce head loss due to bends.

From the design software used,(AUTOCAD and AutoDesk INVENTOR), an optimum suggestion of the optimum layout was drawn as shown below with numerous benefits compared to the previous outlay. key among them being:

i) reduced length from 648m to 598m

ii) 2.increased flow rate per second

iii) 3.reduced bend loses

** Figure 4.2: AUTOCAD Proposed outlay of new penstock **

**Figure 4.3: AUTOCAD Proposed outlay of new penstock **

Above are sample suggested designs that were designed by AUTOCAD and INVENTOR™

**CHAPTER 5: CONCLUSION AND RECOMMENDATION **
**5.1 Conclusion **

All three objectives addressed in this report were satisfied by the end of the project.

The total head losses resulting from the use of ductile iron as the penstock were calculated and its subsequent efficiency determined then compared to that of steel and uPVC and it was noted that ductile iron is not as efficient as both steel and uPVC.

Ultimately, the most optimal diameter of the steel penstock that has the least percentage of head losses was determined by iterating from the initial diameter at the provided length.

Considering all the factors discussed in chapter two on factors to consider on selection of penstock material, steel was settled on more so due to its ease of availability relative to uPVC and durability as well as method of joining.

The optimal diameter of this steel proposed penstock was determined as 600mm. At this optimum penstock, power is noted to have a very reasonable 8.7% increase and

considering a new material has been implemented with more efficiency than initial, its worth the cost.

A CAD designed penstock layout was established as shown herein.

The route was accurately mapped, with consideration to both overall length and elevation changes, using several different methods. Both Darcy-Weisbach and Hazen-Williams

correlations were used to predict friction head loss. Minor head loss was estimated via the minor loss correlation.

From head loss and flow rate, available power could be estimated. Discrepancies between the estimates produced by the two different friction head loss correlations were shown to be a result

of the differing sensitivity of each correlation to flow velocity. Sample calculations for available power were used to clarify this point.

The below chart was used to determine an appropriate turbine which is the francis turbine due to low head high flow installation.

**Figure 5.1.Broadly generalized chart using flow rate and head combinations to estimate **

available power. The useful point demonstrated here is turbine selection

**5.2 Recommendation **

It was recommened that a steel penstock be implemented due to its suitable efficiency which results in a significant output as exhibited. Ultimately it reduces the cost of the plant set up as it’s the penstock that covers the biggest cost of setting up the plant.

It was also recommended that the designed new outlay of the penstock be endossed as it exhibits reduced bends-thus minimized turbulence losses, ,reduced overall length,thus reduced cost of overall material, and a new material(steel) that is easy to install with lesser frictional losses be installed.

The Francis turbine at the site can be retained as its relevance to deliver a higher out put at the new elevation and increased flow rate is valid.

**REFERENCES **

“Design of Large Pipelines” by Herman Schorer, Transactions, 98:lOl. ASCE, 1933.
*White, Frank. Fluid Mechanics. 7th. New York: McGraw-Hill, 2009. Print *

“Welded Steel Penstocks” Engineering Monograph No. 3, U.S. Bureau of Reclamation, 1967. “Welded Steel Penstock-Design and Construction” by P. J. Bier, Engineering Monograph No. 3,

U.S. Bureau of Reclamation, September 1960. (Revised 1966).

* "Darcy-Weisbach Equation." Wikipedia. N.p., n.d. Web. 1 Jun 2012. *
<http://en.wikipedia.org/wiki/Darcy–Weisbach_equation>

*"Major Loss in Ducts." Engineering Toolbox. N.p., n.d. Web. 1 Jun 2012. *
<http://www.engineeringtoolbox.com/major-loss-ducts-tubes-d_459.html>

KS0574:1997 Standard for Steel Water Pipe 6 In. and Larger

“Optimum Penstock Diameter in Hydro-Electric Plants” by Edward J. Low - Journal, Power Division, ASCE Proceedings, July 1962

“Hydraulic Losses in Pipe Fittings” by D. Thoma, Transactions of the Munich Hydraulic Institute, Bulletin No. 3.