combined project

i
DECLARATION
I hereby declare to the best of my knowledge that this project titled, DESIGN OF A TEST RIG
FOR STUDYING PRESSURE DROP DUE TO FLUID FLOWING ACROSS PIPE FITTINGS,
is the product of the design.
……………………………………..
Godfrey Amos.

ii
SUPERVISOR APPROVAL SHEET.
I hereby certify that the titled DESIGN OF A TEST RIG FOR STUDYING PRESSURE DROP
DUE TO FLUID FLOWING ACROSS PIPE FITTINGS is written by GODFREY AMOS who
was supervised by Prof.O. Kaunde.
PROJECT SUPERVISOR SIGNATURE
Prof.O. Kaunde ……………………………………
Date ……………………………………

iii
ACKNOWLEDGEMENT
First of all, I would like to thank the almighty God who gave me the strength and enable
me to do this project. Conducting a project is not an easy task because it involves a lot of reading,
visiting consultation; some people have contributed in one way or another to make up this project
a success. I would like to thank everybody for his or her valuable contribution given to me. Also
I would like to acknowledge my project supervisor Prof.O. Kaunde to give his time for consultation
in this project and advice during write up of this project. I would also like to acknowledge my wife
and my son Brighton for their prayer and the time they were alone, also special thanks to Dr.
Mwakipesile and my project coordinator Mr.W.Kiunsi for his time not only that but also the
Energy and Production Engineering staffs for their time and my classmates for their support.

iv
List of Symbols and Abbreviation
S/N Symbols and
Abbreviation
Description SI Unit
1 P Pressure 𝑁/𝑚2
3 A Area 𝑚2
4 V Volume 𝑚3
5 Q Flow rate 𝑀3
/𝑠
6 d Internal diameter. m
7 D Diameter m
8 𝜃 Inclination angle 0
9 h Height m
10 b Width mm
11 L Length mm
12 M Mass kg
13 t Time s
14 g Acceleration due to gravity m/s2
15 K Resistance coefficient
16 hL Head loss m
17 f Friction factor
19 T Temperature 0
c
20 Re Reynold number

v
24 µ Coefficient of viscosity Pas
25 ʋ Kinematic viscosity m2
/s
26 ρ density Kg/m3

Table of Contents
DECLARATION ................................................................................................................................................i
SUPERVISOR APPROVAL SHEET..................................................................................................................... ii
ACKNOWLEDGEMENT.................................................................................................................................. iii
List of Symbols and Abbreviation................................................................................................................. iv
CHAPTER ONE...........................................................................................................................................1
INTRODUCTION. .......................................................................................................................................1
1.0 Abstract..............................................................................................................................................1
1.1 Background. ......................................................................................................................................1
1.2 TEST RIG..........................................................................................................................................2
1.3. PROBLEM DEFINITION. .............................................................................................................4
1.4. EXPECTED SOLUTION................................................................................................................4
1.5. PROJECT OBJECTIVES...............................................................................................................5
1.5.1 MAIN OBJECTIVE. .....................................................................................................................5
1.5.2 SPECIFIC OBJECTIVES; ...........................................................................................................5
CHAPTER TWO ..........................................................................................................................................6
LITERATURE REVIEW. ............................................................................................................................6
2.0 What is fluid? ....................................................................................................................................6
2.0.1 Fluid properties..............................................................................................................................6
2.0.2 Laminar versus Turbulent flow....................................................................................................6
2.1. PRESSURE DROP. .........................................................................................................................7
2.1.1 Head Loss......................................................................................................................................11
2.1.2 Forms of Flow Resistance (Head Loss due to Friction)............................................................12
2.1.3 Head losses in a Circular Tube of Constant Diameter .............................................................13
2.1.4 Head Loss Due to Bends..............................................................................................................13
2.1.5 Venturi meter. ..............................................................................................................................14
2.2. VALVES AND FITTINGS..........................................................................................................15
2.2.1 Head Loss due to Valves..............................................................................................................16
2.2.2 Head Losses in Fittings................................................................................................................17
2.2.3 K Factor Method..........................................................................................................................17

2.2.4 Equivalent length of pipe in linear feet (Le) Method. ...............................................................18
2.2.5 Equivalent length tables. .............................................................................................................19
CHAPTER THREE. ...................................................................................................................................23
3.0 METHODOLOGY. ..............................................................................................................................23
3.1 Data collection and analysis. ..........................................................................................................23
3.2 Consultation.....................................................................................................................................23
3.3 Commissioning................................................................................................................................24
CHAPTER FOUR.......................................................................................................................................25
4.0 CONCEPTUAL DESIGN.....................................................................................................................25
4.1.0 DESIGN ALTERNATIVE..........................................................................................................25
4.1.1 ALTERNATIVE 1. ......................................................................................................................25
4.1.2 ALTERNATIVE 2. .....................................................................................................................26
4.1.3 ALTERNATIVE 3. .....................................................................................................................27
4.2 CHOOSING THE BEST ALTERNATIVE..................................................................................28
4.3 SCALE REFORMANCE ...............................................................................................................29
4.4 THE CRITERIA EVALUATION.................................................................................................29
4.5 MATRIX METHOD.......................................................................................................................30
4.6 DESIGN CALCULATION......................................................................................................................31
4.6.1 HEAD LOSSES.................................................................................................................................35
4.6.2 HEAD LOSS DUE TO STRAIGHT PIPE..............................................................................................35
4.6.3 HEAD LOSS DUE TO BENDS. ..........................................................................................................35
4.6.4 HEAD LOSS DUE TO VALVES..........................................................................................................37
2.3 Factors that affect Head Loss. .......................................................................................................38
Conclusion. .................................................................................................................................................40
Recommendation. .......................................................................................................................................40
WORK PLAN.............................................................................................................................................41
COST ESTIMATION:................................................................................................................................42
Stationery Cost......................................................................................................................................42
Design Cost. ...........................................................................................................................................42
References...................................................................................................................................................43

1
CHAPTER ONE
INTRODUCTION.
1.0 Abstract
The purpose of this design project is to design test rig for studying pressure drop due to
fluid flowing across pipe fitting that meets all requirements which will allow students to have
enough understandings on fluid dynamics behavior and to obtain data by performing different
experiments. The prototype will be designed also to meet the requirement. The prototype will be
designed to make fluid dynamics to be performed practically. The prototype must be safe reliable
and easy to use. Pipes and fittings calculations will be performed to make reliable pressure drop
from the pump to the appropriate system. Then the project will be tested and it will work
successfully.
Key words – Test rig, Pressure drop, pipes, bends and valves.
1.1 Background.
MUST (Mbeya University of Science and Technology) is the university found in MBEYA which
offers degree level engineering and business courses. Engineering courses are like mechanical,
civil, electrical and computer engineering.
In mechanical engineering some of the subjects are taught theoretically and others practically.
Example in fluid dynamics, this subject is taught theoretically because in the university students
lack several equipment’s to conduct several experiments and to collect some data.
I have come up with an idea of designing a test RIG for studying pressure drop due to fluid flowing
across pipe fittings and this will help students to attempt several experiments and obtaining several
data which will enable them to write reports for future documentation.

2
1.2 TEST RIG.
 An apparatus used for assessing the performance of a piece of mechanical or electrical
equipment.
 The Losses in Piping Systems apparatus comprises a vertical panel with two separate colored
hydraulic circuits (from figure 1). Each circuit includes various pipe system components. So
students can study flow characteristics through the various pipes and fittings. The circuits
are made of small-bore plastic pipe, commonly used in a wide variety of applications such
as domestic central-heating systems. The small bore allows the circuits to include many pipe
bends and components, while preserving effective upstream and downstream test lengths.
(Hooper, W.B., 1991. In: Mcketta, J.J. (Ed.), Piping Design, Fittings, Pressure Drop.
Encyclopedia of Chemical Processing and Design,vol. 39, pp. 19–27.)
 To measure pressure loss across components, the panel includes piezometer tubes and a
pressure gauge. The pressure gauge (mercury manometer) measures pressure loss across
valves; the piezometer tubes measure pressure loss across the other components. A hand-
pump can be used to adjust the datum position of the piezometers.
Both circuits have common inlet and outlet pipes, controlled by valves. The valves are at the
outlet to minimize flow disruption. (Banerjee, T.K., Das, M., Das, S.K., 1994. Non-Newtonian
liquid flow through globe and gate valves. Can. J. Chem. Eng. 72, 207–21).

3
Figure 1; showing piping systems comprises a vertical panel with two separate
colored hydraulic circuit.
Figure 2; showing how fluid can enter and leave the piping systems.

4
Where;
A Straight Pipe 1.
B 90° Sharp Bend.
C Proprietary 90° Elbow.
D Gate Valve 1.
E venturi meter.
F Orifice meter.
G Smooth 90° Bend 1.
H Smooth 90° Bend 2.
J Smooth 90° Bend 3.
K Valve 2.
L Straight Pipe 2.
1.3. PROBLEM DEFINITION.
 The main problem is lacking of teaching equipment’s which cause students to have small
knowledge on fluid dynamics and small understandings on dynamic behaviors.
The main challenge in this project is that students attends lectures like fluid dynamics theoretically.
This means that they are un able to collect any data concern with fluid dynamics and no report can
be written which is bad for the future generation because there are no written documents. This is
because in the university there are no enough equipment and instruments which can help to collect
data also laboratories for doing those experiments are not well prepared. Therefore, those are
challenges in mechanical engineering department.
1.4. EXPECTED SOLUTION.
 The expected solution is to design a test Rig which will help students to obtain several data
experimentally and those data will help them in learning content.
This will help students to go to the laboratories, perform several experiments and recording some
data which will help them to write reports on those experiments done. Through this method
understanding capacity of students will be high because they will be learning practically. Even the
performance will be high.

5
1.5. PROJECT OBJECTIVES.
The objectives of this project are categorized into two major groups: -
i. Main objective.
ii. Specific objectives.
1.5.1 MAIN OBJECTIVE.
 The main objective of this project is to design, manufacture and commissioning/testing of
a RIG for studying pressure drop due to fluid flowing across pipe fittings.
1.5.2 SPECIFIC OBJECTIVES;
The specific objectives are as follows;
i. To determine fittings which will be used to design a test RIG like pipes, valves, pump,
pressure meter, venture meter.
ii. To manufacture and install the system.
iii. Run experiment to establish functionality

6
CHAPTER TWO
LITERATURE REVIEW.
2.0 What is fluid?
A fluid is any substance that deforms continuously when subjected to shear stress, no matter how
small. Examples of fluids: - water, air, oils, hydrogen gas, paints, blood, glycerin, brine, honey,
etc.
2.0.1 Fluid properties
• Pressure: It is defined as the amount of force exerted on a unit area of a substance.
• Density: is the quantity of matter contained per unit volume of the substance.
• Compressibility: Compressibility is the change in volume of substance when pressure on
it is change.
• Viscosity is that fluid property by virtue of which a fluid offers resistance to shear stresses.
2.0.2 Laminar versus Turbulent flow
 Laminar flow: The highly ordered fluid motion characterized by smooth layers of fluid.
The flow of high-viscosity fluids such as oils at low velocities is typically laminar.
 Turbulent flow: The highly disordered fluid motion that typically occurs at high velocities
and is characterized by velocity fluctuations. The flow of low-viscosity fluids such as air
at high velocities is typically turbulent.
 Ttransitional flow: A flow that alternates between being laminar and turbulent.
Fluids are conveyed through pipelines in which viscous actions lead to friction between the fluid
and the pipe wall. When a fluid flows along a pipe, friction between the fluid and the pipe wall
causes a loss of energy. This energy loss shows itself as a progressive fall in pressure along the
pipe and varies with the rate of the flow. When a fluid is moving in a closed channel such as a
pipe two types of flow can be occurred such as laminar and turbulent flow. At low velocities, fluid

7
is moving without lateral mixing and there is no sign of mixing such as eddies or swirl. This type
of flow regime is called laminar flow. On the other hand, at higher velocities lateral mixing occurs
with eddies and swirls. This type of flow regime is called turbulent flow.
Figure 1; showing laminar flow and turbulent flow.
2.1. PRESSURE DROP.
Pressure drop is defined as the difference in pressure between two points of a fluid carrying
network. Pressure drop occurs when frictional forces, caused by the resistance to flow, act on a
fluid as it flows through the tube. The main determinants of resistance to fluid flow are fluid
velocity through the pipe and fluid viscosity. Pressure drop increases proportional to the frictional
shear forces within the piping network. A piping network containing a high relative roughness
rating as well as many pipe fittings and joints, tube convergence, divergence, turns, surface
roughness and other physical properties will affect the pressure drop. High flow velocities and / or
high fluid viscosities result in a larger pressure drop across a section of pipe or a valve or elbow.
Low velocity will result in lower or no pressure drop. ;( McCabe, W. L. and J. C. Smith, Unit
Operations of Chemical Engineering, 2nd edition, McGraw-Hill1967.)
Pressure Drop in Smooth and Sharp Bends. The change of direction forced on a fluid when it
negotiates a bend produces turbulence in the fluid and a consequent loss of energy. The net loss in
pressure is greater than that for the same length of straight pipes. Abrupt changes of direction
produce greater turbulence and larger energy losses than do smoothly contoured changes. (Dean,
W.R., 1928. The stream-line motion in curved pipes. Philos. Mag. 30, 673–693.)
Pressure Drop through a Venturi Meter. Venturi meter consists of a throttling section which
leads to pressure drop due to the turbulence created at this section. Fluid velocity can be measured
by using Bernoulli equation and equation of continuity in order to calculate the pressure loss
through the pipe. A straight line relation exists between the flow rate and the square root of the

8
pressure drop value, and this principle is utilized in the design of venturi meter. (Ergun, S., Fluid
Flow through Packed Columns, Chemical Engineering Progress, Vol. 48, No. 2, 1952.)
Pressure Drop through an Orifice Meter. An orifice meter consists of a circular disk with a
central hole which is bolted between the flanges on two sections of pipe. Bernoulli’s equation is
applied to the fluid as it flows through the orifice of a reduced area because it is found
experimentally that a contracting stream is relatively stable, so that frictional dissipation can be
ignored, especially over a short distance. As a result, as the velocity of the fluid increases, the
pressure will decrease. (Perry, R.H. and D Green, Perry’s Chemical Engineer’s Handbook, 6th
edition, McGraw-Hill, Japan 1984).
Pipe fittings like valves, bends, elbows, tees, reducers, expander etc. are the integral part of any
piping system. ( Polizelli, M.A., Menegalli, F.C., Telis, V.R.N., Telis-Romero, J., 2003. Friction
losses in valves and fittings for power-law fluids. Braz. J. Chem. Eng. 20, 455–463)
Nipple 450
elbow union
Tee bend reducer

9
Gate valve.
Globe valve. 900
elbow
 Pressure drop across pipe fittings will be measured by using Bernoulli’s principle.
Bernoulli’s theorem states that the total energy of each particle of a body of fluid is the same
provided that no energy enters or leaves the system at any point.
Total head = potential head + pressure head + velocity head
 The pressure drop in pipes can be caused by;
i. Friction.
ii. Vertical pipe difference or elevation.
iii. Changes of kinetic energy.
To determine fluid (liquid or gas) pressure drop along a pipe or pipe components, Reynold number
equation is being considered.
𝑅𝑒 =
𝑫𝝂𝝆
𝝁

10
Where:
Re is Reynold number.
D is a diameter.
µ is a coefficient of viscosity.
υ is kinematic viscosity.
ρ is density.
 Various pipe fittings can be implemented on straight pipes; such as venture meter, orifice
meter as well as smooth and sharp bends. Fluid flow through pipes and fittings can be
investigated with respect to changing liquid flow rate and the effect can be observed via
pressure drop. (Das, S.K., Biswas, M.N., Mitra, A.K., 1991. Non-Newtonian liquid flow in
bends. Chem. Eng. J. 45, 165–171).
Fig 1.
Fig 2. Fig 3.
For an incompressible fluid flowing through a pipe the following equations apply:

11
Where;
Q Volumetric flow rate (m3
/s)
V Mean Velocity (m/s)
A Cross sectional area (m3
)
Z Height above datum (m)
P Static pressure (N/m2
)
hL Head Loss (m)
p Density (kg/m3
)
g Acceleration due to gravity (9.81m/s2
)
The object of this project is to obtain the following relationships:
(a) Head loss as a function of volume flow rate;
(b) Friction Factor as a function of Reynolds Number.
2.1.1 Head Loss.
The head loss in a pipe circuit falls into two categories:
(a) That due to viscous resistance extending throughout the total length of the circuit,
and;
(b) That due to localized effects such as valves, sudden changes in area of flow, and
bends.
The overall head loss is a combination of both these categories. Because of mutual interference
between neighboring components in a complex circuit the total head loss may differ from that
estimated from the losses due to the individual components considered in isolation. The head losses
depend on the type of the flow (laminar or turbulent) and pipe elements (valves, elbows, tees, etc.).
A common approach to characterization of frictional losses is to use the Fanning friction factor f
defined as the friction force per unit surface area divided by the kinetic energy per unit volume (pv
/2).

12
2.1.2 Forms of Flow Resistance (Head Loss due to Friction).
One form of resistance to flow is due to the viscosity of the liquid. Viscosity is the amount of
work needed to move one “box” of liquid against another “box” of liquid. Every liquid has its
own value for this resistance to flow. SAE 30 motor oil has a lower viscosity and flows much
easier than SAE 50 motor oil. The values for water are lower than for the motor oil.
Another characteristic of any liquid is its attraction to a surface. It attaches itself to any surface
and cannot be moved. The liquid in the “box” on the very surface of a pipe does not flow or move.
It always remains stationary. The liquid in the “box” above it has to slide against it and that
requires an amount of energy to overcome friction between the two “boxes”. The higher the
viscosity of the liquid is; the higher the resistance to flow, therefore, the higher the friction loss.
A layer is formed by this non-moving liquid and reduces the inside diameter of the pipe. This
increases the velocity of the liquid passing through it. The head loss from friction is related to the
velocity energy (V2
/2g) of the liquid squared.
The liquid is not moving at the pipe wall but has a much higher velocity at the center of the pipe.
The condition of the inside of a pipe also has a great effect on the head loss of the flow of liquid.
The rougher it is; the thicker the layer of non-moving or slow moving liquid near the pipe wall.
This reduces the inside diameter of the pipe, increasing the velocity of the liquid. With the increase
in velocity comes an increase in friction losses.
Any time a liquid flow changes direction there is resistance. Since all liquids have weight, they
also have momentum. This means the liquid will always try to continue moving in the same
direction. When the liquid encounters a change in direction (such as an elbow), its momentum
carries the flow to the outer edge of the fitting. Because the liquid is trying to flow around the
outer edge of the fitting, the effective area of the fitting is reduced. The effect is similar to attaching
a smaller diameter pipe in the system. The velocity of the liquid increases and the head loss due
to friction increases.
The energy lost by the liquid is converted to heat created by friction. Since the amount of liquid
exiting a pipe has to equal the amount entering the pipe, the velocity must be equal. If the velocity
is equal, then the velocity energy (head) must be equal. This only leaves one place for the energy

13
to come from; pressure energy. The measured pressure entering the pipe will be higher than the
measured pressure exiting the pipe.
2.1.3 Head losses in a Circular Tube of Constant Diameter
The head loss along a length, L, of straight pipe of constant diameter, d, is given by the expression:
where f is a dimensionless constant which is a function of the Reynolds number of the
flow and the roughness of the internal surface of the pipe.
2.1.4 Head Loss Due to Bends
The head loss due to a bend is given by the expression;
where K is a dimensionless coefficient which depends upon the bend radius/pipe radius ratio and
the angle of the bend.
Note:
The loss given by this expression is not the total loss caused by the bend but the excess loss
above that which would be caused by a straight pipe equal in length to the length of the
pipe axis.
For a laminar flow one can solve the Navier-Stokes equations analytically and obtain the
following expression for the friction factor.
Here, Re = Dvp/µ is the Reynolds number (p and µ are the fluid density and viscosity,
respectively).

14
For a turbulent flow the friction losses are given by empirical relationships, such as the Colebrook
equation or the Moody diagram. These relationships involve new parameter s corresponding to the
roughness of the pipe. The roughness depends on multiple factors, including the material from
which the pipe is made and degree of corrosion. The flow network in our lab consists of pipes
made from plastic and galvanized steel.
2.1.5 Venturi meter.
A venturi meter is a tube of non-constant diameter (see Fig. 1). To minimize disturbances to the
flow, the edges of the venturi meter have the same diameter as the pipe into which the meter is
inserted. Variation of the tube diameter leads to variation of the fluid pressure inside the meter.
There are two pressure taps located at the widest and the narrowest locations of the tube. Therefore,
we can determine the flow rate by measuring pressures p and p2 at these locations and substituting
them into the Bernoulli equation. For an incompressible fluid, the pressure drop is related to the
flow rate by the following formula:
Here, Dl and D2 are the pipe diameters at the pressure tap locations and Cd is the discharge
coefficient. In the absence of the friction losses, Crf =1. In most venturi meters, Cd is very close to
1.
Figure 1. Venturi meter.

15
2.1.6 Head Loss due to Sudden Changes in Area of Flow
Sudden Expansion: The head loss at a sudden expansion is given by the expression:
Sudden Contraction: The head loss at a sudden contraction is given by the expression:
where K is a dimensionless coefficient which depends upon the area ratio as shown in Table
2.1. This table can be found in most good textbooks on fluid mechanics.
2.2. VALVES AND FITTINGS.
Valves: Although the great variety of valve designs precludes any thorough classification, most of
the designs may be considered as modifications of the two basic types:
1. the gate type
2. the globe type
If valves were classified according to the resistance which they offer to flow, the gate type valves
would be put in the low resistance class and the globe type valves in the high resistance class. The
classification is not all-inclusive, however, because a large number of modified valve types fall
between the two extremes.
A2/A1 0 0.1 0.2 0.3 0.4 0.6 0.8 1.0
K 0.50 0.46 0.41 0.36 0.30 0.18 0.06 0
Table 2.1 Loss Coefficient for Sudden Contractions

16
Figure above shows two sections of a pipe line of the same diameter and length. The upper section
contains a globe valve. If the pressure drops, ∆P1 and ∆P2, were measured between the points
indicated, it would be found that ∆P1 is greater than ∆P2.
2.2.1 Head Loss due to Valves
The head loss due to a valve is given by the expression:
where the value of K depends upon the type of valve and the degrees of opening.
Fittings: Fittings may be classified as branching, reducing, expanding, or deflecting. Such fittings
as tees, crosses, side outlet elbows, etc., may be called branching fittings.
Reducing or expanding fittings are those which change the area of the fluid passageway. In this
class are reducers and bushings. Deflecting fittings. . .. bends, elbows, return bends, etc. are
those which change the direction of flow.
Some fittings, of course, may be combinations of any of the foregoing general classifications. In
addition. there are types such as couplings and unions which offer no appreciable resistance to
flow and, therefore, need not be considered here.
When a fluid is flowing steadily in a long straight pipe of uniform diameter, the flow pattern, as
indicated by the velocity distribution across the pipe diameter, will assume a certain characteristic
form. Any impediment in the pipe which changes the direction of the whole stream, or even part
of it, will alter the characteristic flow pattern and create turbulence. causing an energy loss greater
than that normally accompanying flow in straight pipe.
Globe Valve, Fully Open 10.0
Gate Valve, Fully Open 0.2
Gate Valve, Half Open 5.6
Table 2.2 gives typical values of loss coefficients for gate and
globe valves

17
Because valves and fittings in a pipe line disturb the flow' pattern, they produce an additional
pressure drop.
The loss of pressure produced by a valve (or fitting) consists of:
1. The pressure drop within the valve itself.
2. The pressure drop in the upstream piping in excess of that which would normally occur if
there were no valve in the line. This effect is small.
3. The pressure drop in the downstream piping in excess of that which would normally occur if
there were no valve in the line. This effect may be comparatively large.
From the experimental point of view, it is difficult to measure the three items separately. Their
combined effect is the desired quantity, however, and this can be accurately measured by well-
known methods.
2.2.2 Head Losses in Fittings
In addition to the pipes, the fluid flow network contains various fittings, including valves, tees,
and elbows. The friction losses due to the fittings are described using the loss factor Kf,
Pipe fittings and valves disturb the normal flow of liquid, causing head loss due to friction. There
are two basic methods currently in use to predict the head loss in pipe fittings and valves. They
are the “K factor “and the “Equivalent length of pipe in linear feet “methods.
2.2.3 K Factor Method.
The fittings, such as elbows, tees, strainers, valves, etc., have all been tested and assigned “K”
factors based on the head loss measured through them. These are normally found in pump
handbooks including the Hydraulic Institute Data Book.
To use this method:
 Find the chart pertaining to the fitting in question
 Determine the “K” factor for the diameter fitting.
 Go to the tables for head loss in pipe and find the correct size pipe for this fitting.

18
 Find the velocity head of the liquid for the flow rate expected through the fitting.
 Multiply the velocity head times the “K” factor.
You have predicted the head loss through that fitting. Continue this procedure for each fitting in
the system. Add all the fitting losses to the expected losses for the pipe and you now have the
head losses due to friction for the entire system.
2.2.4 Equivalent length of pipe in linear feet (Le) Method.
The definition of the Equivalent Length of a pipe fitting is the length of pipe of the same size as
the fitting that would give rise to the same pressure drop as the fitting. It has been found
experimentally that for a given type of fitting (e.g. a long radius elbow) the Equivalent Length (Le)
is larger for larger fittings. But it is found that if Le is divided by the inside diameter of the pipe
(D) the ratio (Le/D) that is obtained is virtually constant for that type of fitting. This has 2
advantages - it dramatically decreases the amount of information that is required and it also
removes the problem of the units used to measure lengths and diameters since the ratio Le/D is
dimensionless. The tables of data in this article can therefore be used with any system of units,
provided that the pipe inside diameter (D) and the Equivalent Length (Le) are measured in the same
units.
It should be noted that the pressure drop across a fitting is determined mainly by how the geometry
of the fitting causes changes in the direction and velocity of the fluid flow. On the other hand, the
friction between the fluid and the fitting walls has a relatively minor effect on the pressure drop.
This means that the material of construction of the fitting has very little effect on the pressure drop
(for example) a plastic globe valve will have the same pressure drop as a steel valve with the same
geometry.
However, the length of pipe that would give a pressure drop equivalent to the globe valve would
depend strongly on the roughness of that pipe. It is therefore important that Equivalent Lengths be
expressed in terms of the actual pipe that is connected to the fitting.
The pipe fittings and valves were tested and values assigned for the head loss measured through
them. Instead of assigning a factor, as in the “K” Factor method, an “equivalent length of pipe in
linear feet” value was assigned.

19
This means that a particular fitting will have a head loss equal to a given length of straight pipe
of the same size. These tables are found in pump handbooks.
To use this method:
 Find the fitting you wish to use in the appropriate table.
 Find the pipe size and record the equivalent length.
 Continue this for all the fittings in the system.
 Add the fitting equivalent length values to get a total equivalent length of pipe.
 Find the pipe diameter, appropriate flow rate (GPM), and head loss per 100’ in the tables.
 Add the total fittings equivalent length of pipe to the total actual length of pipe. This gives
you a total effective length of pipe.
 Divide the total effective length of pipe by 100 and multiply the result by the head loss per
100’ value from the table.
2.2.5 Equivalent length tables.
Equivalent lengths of fittings like.
 elbows - regular 90o
, long radius 90o
, regular 45o
 tees - line flow and branch flow
 return bends - regular and long radius
 valves - globe, gate, angle and swing check
in water piping systems are indicated in the tables below.

20
Screwed Fittings - equivalent length in feet.
Equivalent length (in feet) of straight pipe for fittings like bends, returns, tees and valves. (Pipe
size in inches).
Screwed Fittings - equivalent length in meter.
Equivalent length (in meters) of straight pipe for fittings like bends, returns, tees and valves.

21
Flanged Fittings - equivalent length in feet
Equivalent length (in feet) of straight pipe for fittings like bends, returns, tees and valves.
Flanged Fittings - equivalent length in meter.
Equivalent length (in meters) of straight pipe for fittings like bends, returns, tees and valves.

22
The rig will contains the following parameters which is dimensioned below;
I. Height of the rig 1.5m.
II. Length of a pipe 4.5m.
III. Pipe size ½ inch
IV. Pipe material plastic
V. 900
elbow
VI. Gate valve
VII. Manometer tubes
The Experimental results will be tabulated as follows;
Test number Time to collect 15 kg
of water.
(S)
Manometers readings Pressure
regulator
reading.1 2 3
1.
2.
3.
4.
5.

23
CHAPTER THREE.
3.0 METHODOLOGY.
Different methods of gathering or collection of information and data selection to this project will
be used in order to achieve the objective of this project. The methods used in achieving the
objectives of this project comprises of data collection and analysis (literature review, visiting,
lecture notes and internet browsing), consultation and commissioning.
3.1 Data collection and analysis.
In data collection and analysis different methods will be applied and those methods are as
follows;
 Observation.
Visiting the different areas to observe different rig and get information on how to
use this system to obtain specific, accurate and measurable data.
 Literature review,
Through different books, magazine and pamphlets data will be obtained, and more
detail concern with pressure drop in pipe fittings and Bernoulli’s principle.
 Lecture notes.
The review of the lecture notes in module like fluid dynamics in order to be aware
with several components like venture meter, pumps, orifice meter.
 Internet browsing
Through internet, surfing for different approach was done on the different test Rig
and how to use the system to run several experiments.
3.2 Consultation.
Consultation on my supervisor was done in order to approve data which has been collected.
Also consultation to teachers was done like of engineering materials, strength of the materials
and fluid dynamics, and my fellow students to get information's and clear knowledge on
material to use.

24
3.3 Commissioning.
After collecting some data, the fabrication of the test rig and run it for collecting measureable
data will be done in order to be assure of this project and to make its function ability.

25
CHAPTER FOUR
4.0 CONCEPTUAL DESIGN
In this part, design concepts will be developed, discussed and based on evaluation criteria
and process developed, and a final design will be chosen. However, some features of the selected
design will be modified to further enhance the functionality of the design.
4.1.0 DESIGN ALTERNATIVE
In fluid flow there are several design of rig. Both rigs are used to determine pressure drop across
several fittings. And those will be alternatives to this project. As stated the fluid can be liquid or
gas. But in this project liquid (water) will be used in order to obtain readings.
4.1.1 ALTERNATIVE 1.
A rig with two manometers.
In the experiment, investigation of pressure drop and head loss due to frictional losses will be made
in both laminar and turbulent flow regimes. Other than the main apparatus, a stopwatch to allow
us to determine the flow rate of water, a thermometer to measure the temperature of the water and
a measuring cylinder for measuring flow rates are all needed. ( Sinnott R. K., J. M. Coulson and J.
F. Richardson, Chemical Engineering, An Introduction toChemical Engineering Design,
Pergamon Press, Vol. 6, 1983.)
Figure 2; showing a rig for determination of pressure drop and heat loss.

26
A rig with pumping system and has different fittings.
Various pipe fittings can be implemented on straight pipes; such as venture meter, orifice meter as
well as smooth and sharp bends. Fluid flow through pipes and fittings can be investigated with
respect to changing liquid flow rate and the effect can be observed via pressure drop.
Figure 3; showing a rig for determination of pressure drop due to
water flowing across different fittings.

27
A rig with two piping system and have many manometers.
The Piping Losses Rig has two circuits, but they are used one at a time. Circuits are isolated by
closing off the final valve (choosing the appropriate globe or gate valve). Both circuits are fed by
water pressure at the inlet. The flowrate is set by adjusting the valve until appropriate readings are
shown on the relevant piezometers. Take care not to close the valve too much - the mercury
manometers could be over-pressurized with mains water pressure. This could cause unwanted loss
of mercury out the exit pipe. Ensure there is no trapped air inside the lines and that the air valves
at the top of the piezometers have been opened. Keep checking this and adjusting the flowrate until
the system gives steady and useful data.
 Once there is a steady flow, maintain this and time the flow on the weighing scale (e.g. 1
minute). This will give the data to calculate the flowrate.
 During this steady-state flow, take readings between various points to determine the head
losses due to:
 Length of pipe
 Various elbows and corners
 Changes in diameter
Figure 4; showing a rig for pressure drop in two piping systems.

28
Where;
A Straight Pipe 1
B 90° Sharp Bend
C Proprietary 90° Elbow
D Gate Valve 1
E venturi meter.
F Orifice meter.
G Smooth 90° Bend 1
H Smooth 90° Bend 2
J Smooth 90° Bend 3
K Valve 2
L Straight Pipe 2.
4.2 CHOOSING THE BEST ALTERNATIVE
In set of two alternatives the best alternative is selected depending the following factors.
(a) fulfillment of the function factors
(b) reliability
(c) cost
(d) safety
(e) Maintainability.
(a) Fulfillment of the function factors
the criterion enables to see if the equipment will perform well the intended task of brake operations.
(b) Reliability
These are meant to access the criterion to see if the system will perform its duty smoothly and
quickly.
(c)Cost
The aim of this criterion is to see or enable the operator to operate the system without injuring
when the training process is taking place.

29
(a) Safety
This will enable the machine operator to operate it without being injured / no harm the operator ie:
safe it graded as.
(b) Maintainability
This will enable the operator to trainer to train easily during the driving course
4.3 SCALE REFORMANCE
I have decided to create the scale of performance to be as shown in the table below.
S/N GRADE WEIGHT
1 Excellent 5
2 Very good 4
3 Good 3
4 Average 2
5 Poor 1
4.4 THE CRITERIA EVALUATION
The table below shows the criteria evaluation
S/N CRITERIA WEIGHT
1 Fulfillment 0.30
2 Reliability 0.15
3 cost 0.25
4 safety 0.20
5 Maintainability 0.10
TOTAL 1.00

30
4.5 MATRIX METHOD.
By using the matrix method, the following operation will be considered so as to get best solution.
S/N CRITERIA WEIGHT 1ST
ALTERNATIVE
2ND
ALTERNATIVE
3RD
ALTERNATIVE
SCOPE PRODUCT SCOPE PRODUCT SCOPE PRODUCT
1. Fulfilment 0,30 5 1.5 5 1.5 4 1.2
2. Reliability 0.15 3 0.4 3 0.6 3 0.2
3. Cost 0.25 2 0.5 4 0.4 4 0.5
4. Safety 0.20 2 0.2 4 1.0 3 0.3
5. Maintainability 0.10 3 0.3 3 0.8 2 0.4
TOTAL 4.3 2.6
After the evaluation of all the criteria in the above matrix method, the alternative number 2 was
found to be the best one by considering criteria set for evaluation.
This rig will operate in such a way that, water from the tank will be pumped by using centrifugal
pump, through the pipes will flow to the manometers and several fittings in order to obtain readings
and then it will be back to the tank.
And in order to determine the head loss and friction factor from the rig the following calculations
must be performed;
I. Mass flow rate
II. Volume flow rate
III. Area of flow
IV. Mean velocity
V. Reynold number.

31
4.6 DESIGN CALCULATION.
In order to determine the friction factor and head loss in a pipe circuit the following parameters
must be determined;
i. Mass flow rate.
ii. Volume flow rate.
iii. Area of flow(A).
iv. Mean velocity(v).
v. Reynold number(Re).
Then from that we can obtain the friction factor and head loss of the pipe circuit.
i. Mass flow rate.
From,
Mass flow rate=
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑙𝑖𝑞𝑢𝑖𝑑
𝑡𝑖𝑚𝑒
But, mass =density× volume of water. Where density of water is 1000kg/m3
.
Now, assume at 60 seconds 15 littles can flow through the system at full open of valve
which is equal to 0.015m3
.
Then,
Mass=1000×0.015=15kg,
Then mass flow rate=
15
60
=0.25kg/s.
The mass flow rate is 0.25kg/s.

32
ii. Volume flow rate;
From,
Volume flow rate=
𝑚𝑎𝑠𝑠 𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒
𝑑𝑒𝑛𝑠𝑖𝑡𝑦
Volume flow rate=
0.25 𝑘𝑔/𝑠
1000𝑘𝑔/𝑚3=2.5×10-4
m3
/s.
Volume flow rate is 2.5×10-4m3/s.
iii. Area of flow.
Area =
𝜋𝑑2
4
The diameter of ½ inch pipe from the above table is 0.015m (internal diameter).
Then,
Area=
𝜋×0.0152
4
= 1.84×10-4
m2
.
Area of flow is 1.84×10-4 m2.

33
iv. Mean velocity (v).
From,
Mean velocity=
𝑣𝑜𝑙𝑢𝑚𝑒 𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒
𝑎𝑟𝑒𝑎
V=
2.5×10−4
1.84×10−4 =1.36m/s
Mean velocity is 1.36m/s.
v. Reynold number (Re).
From,
Re=
𝐷𝑉𝜌
𝜇
but
𝜇
𝜌
= 𝜐(kinematic viscosity)
The table below shows kinematic viscosity of different temperatures.

34
From the above table, kinematic viscosity of water at room temperature(250
C) is 0.893×10-6
m2
/s.
Then,
Re=
0.015×1.36
0.893×10−6= 2.28×104
.
Reynold number (Re) is 2.28×104.
Now,
Friction factor will be calculated from Blasius’s Equation, f =
0.0785
𝑅𝑒1/4
In the range 104
< Re < 105
.
Then,
f=
0.0785
(2.28×104)1/4 =6.4×10-3
.
Friction factor of the flow is 6.4×10-3.

35
4.6.1 HEAD LOSSES.
Head losses will be calculated in various parameters which are as follows;
a) Head loss in straight pipe.
b) Head loss due to bends.
c) Head loss due to valves.
4.6.2 HEAD LOSS DUE TO STRAIGHT PIPE.
The head loss along the length L, of a straight pipe of a constant diameter d, is given by;
ℎ𝑙 =
4𝑓𝐿𝑉2
2𝑔𝑑
Then, ℎ𝑙 =
4×6.4×10−3×4.5×(1.36)2
2×9.81×0.015
ℎ𝑙= 0.724 𝑚.
head loss due to straight pipe is 0.724 m.
4.6.3 HEAD LOSS DUE TO BENDS.
The head loss due to bends is given by the expression;
ℎ𝑙 =
𝐾 𝐵 𝑉2
2𝑔

36
For elbow 900
, KB = 0.81 for ½ inch elbow.
Then,

37
ℎ𝑙 =
0.81×(1.36)2
2×9.81
ℎ𝑙 = 0.076 𝑚.
Head loss due to bends (elbow 900) is 0.076 m.
For elbow 450,
KB = 0.43 for ½ inch elbow.
ℎ𝑙 =
0.43×(1.36)2
2×9.81
ℎ𝑙 = 0.041 𝑚.
Head loss due to bends (elbow 450) is 0.041 m.
4.6.4 HEAD LOSS DUE TO VALVES.
Head loss due to valve is given by the expression;
ℎ𝑙 =
𝐾𝑉2
2𝑔
For globe valve the value of K is 9.2.
Then,
ℎ𝑙 =
9.2×(1.36)2
2×9.81
ℎ𝑙 = 0.867 𝑚.
Head loss due to globe valve is 0.867 m.

38
For gate valve the value of K is 0.22.
Then,
ℎ𝑙 =
0.22×(1.36)2
2×9.81
ℎ𝑙 = 0.021 𝑚.
Head loss due to gate valve is 0.021 m.
2.3 Factors that affect Head Loss.
1) Flow Rate.
When the flow rate (GPM) increases, the velocity of the liquid increases at the same rate. The
friction or resistance to flow (due to viscosity) also increases. The head loss is related to the
square of the velocity so the increase in loss is very quick.
2) Inside diameter of the pipe.
When the inside diameter is made larger, the flow area increases and the velocity of the liquid
at a given flow rate is reduced. When the velocity is reduced there is lower head loss due to
friction in the pipe. On the other hand, if the inside diameter of the pipe is reduced, the flow
area decreases, the velocity of the liquid increases and the head loss due to friction increases.
3) Roughness of the pipe wall.
As the roughness of the inside pipe wall increases so does the thickness of the slow or non-
moving boundary layer of liquid. The resulting reduction in flow area increases the velocity
of the liquid and increases the head loss due to friction.
4) Corrosion and Scale Deposits.
Scale deposits and corrosion both increase the roughness of the inside pipe wall. Scale buildup
has the added disadvantage of reducing the inside diameter of the pipe. All of these add up to

39
a reduction in flow area, an increase of the velocity of the liquid, and an increase in head loss
due to friction.
5) Viscosity of the liquid.
The higher the viscosity of the liquid is, the higher the friction is from moving the liquid. More
energy is required to move a high viscosity liquid than for a lower viscosity liquid.
6) Length of the pipe.
Head loss due to friction occurs all along a pipe. It will be constant for each foot of pipe at a
given flow rate. The published tables have head loss values which must be multiplied by the
total length of pipe.
7) Fittings.
Elbows, tees, valves, and other fittings are necessary to a piping system for a pump. It must
be remembered that fittings disrupt the smooth flow of the liquid being pumped. When the
disruption occurs, head loss due to friction occurs. At a given flow rate, the losses for the
fittings will be calculated using a factor that must be multiplied by a velocity head figure, or
as the head loss equivalent to a straight length of pipe.
8) Straightness of the pipe.
Because of momentum, liquid wants to travel in a straight line. If it is disturbed due to crooked
pipe, the liquid will bounce off of the pipe walls and the head loss due to friction will increase.
There is no accurate way to predict the effects since “crooked” can mean a lot of things.

40
Conclusion.
The design of hydraulic platform elevated by a single hydraulic cylinders was carried out
successfully meeting the required design standards. The platform is operated by hydraulic cylinder
which is operated by the hydraulic pump. The scissor lift can have designed is for light load also
because the low capacity hydraulic cylinder is used. The hydraulic scissor lift is simple in use and
does not required routine maintenance. The Pin are subjected to shearing force and should be of
high strength.
Recommendation.
This device affords plenty of scope for modifications for further improvements and
operational efficiency, which should make it commercially available and attractive. Hence, its
wide application in industries, hydraulic pressure system, for lifting of tools in garages,
maintenance of in household, thus, it is recommended for any activity but within the design
conditions.

41
WORK PLAN.
The followings are list of activities during this project.
No. Activities. Duration of research in monthly.
2015 / 2016 2016 / 2017
11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7
1. Tittle selection
2. Literature review
3. Proposal writing
and submission
4. Data collection
and analysis
5. Fabrication of a
RIG
6. Commissioning
7. Report compiling
8. Report submission

42
COST ESTIMATION:
Stationery Cost.
Design Cost.
S/No. Item Quantity Price Amount
1 Pipe ½ inch(50
meter)
50,000 50,000
2 Motor pump 1 100,000 100,000
3 Gate valve 1 15,000 15,000
4 Globe valve 1 15,000 15,000
5 Nipple 2 2,500 5,000
6 Union 2 4,000 8,000
7 Elbow 10 1,000 30,000
8 Tee joint 2 3,000 6,000
9 Connector 3 3,000 9,000
10 Venture meter 1 22,000 22,000
11 Connecting board 1 30,000 30,000
Total 290,000
S/No. Description Quantity Cost/Unit Amount
1 Writing paper A4 2 rim 9,000 18,000
2 Booklet printing 4 5,000 20,000
3 Internet 200 times 20,000 20,000
4 Miscellaneous 20,000
Total 79,000

43
References.
 Banerjee, T.K., Das, M., Das, S.K., 1994. Non-Newtonian liquid flow through globe and gate
valves. Can. J. Chem. Eng. 72, 207–211)
 Das, S.K., Biswas, M.N., Mitra, A.K., 1989. Pressure losses in two-phase Gas–non-
Newtonian liquid flow in horizontal tube. J. Pipelines 7, 307–325.
 Das, S.K., Biswas, M.N., Mitra, A.K., 1991. Non-Newtonian liquid flow in bends. Chem. Eng.
J. 45, 165–171.
 Dean, W.R., 1928. The stream-line motion in curved pipes. Philos. Mag. 30, 673–693.
 Ergun, S., Fluid Flow through Packed Columns, Chemical Engineering Progress, Vol. 48,
No. 2, 1952.
 Hooper, W.B., 1991. In: Mcketta, J.J. (Ed.), Piping Design, Fittings, Pressure
Drop.Encyclopedia of Chemical Processing and Design,vol. 39, pp. 19–27.
 McCabe, W. L. and J. C. Smith, Unit Operations of Chemical Engineering, 2nd edition,
McGraw-Hill1967.
 Perry, R.H. and D Green, Perry’s Chemical Engineer’s Handbook, 6th edition, McGraw-
Hill, Japan 1984.
 Polizelli, M.A., Menegalli, F.C., Telis, V.R.N., Telis-Romero, J., 2003. Friction losses in
valves and fittings for power-law fluids. Braz. J. Chem. Eng. 20, 455–463.
 Sinnott R. K., J. M. Coulson and J. F. Richardson, Chemical Engineering, An Introduction
toChemical Engineering Design, Pergamon Press, Vol. 6, 1983.

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