ABSTRACT

This report deals with the study different types of losses in

a pipe network. A pipe network contains straight pipelines, The result of this zero velocity at the wall is observed in
some bends of different types, and different types of the form of an irregular and non-uniform plot. The profile
valves. Major losses were determined for straight pipes, shape depends upon nature of flow, and whether the fluid
and minor loss coefficients were calculated for different is within the entrance region or fully developed. In these
types of bends and valves. Friction factor and minor loss cases, exert resistive shear stresses is exerted by the walls
coefficients were determined at different values of flow of a duct on the fluid. This effect creates a decrease in
rates. It was found that friction factor decreases with pressure of the fluid as the fluid flows from upstream to
increasing Reynold number. In order to correctly analyze downstream. This phenomenon is termed as head loss. It is
the data, curve fitting was applied on different graphs using shown in figure below:
MATLAB, and several results were derived.

NOMENCLATURE
P Pipe diameter
L Pipe length
𝜌 Density of fluid Figure 1: Pressure loss in pipe

g Gravitational acceleration There are a number of components in a proper piping

Ke Minor loss coefficient system. These components include elbows, throttle valves,
tees, miters, long elbow, short elbow. The components to
f Friction coefficient be used in the system depends on the length of pipe, its
curvature or joints, and the intended purpose of the usage.
p Pressure
With the addition of these components, there is continuous
hl Major head loss increase in the losses in pipes. These losses can be
classified into two categories; major losses and minor
hm Minor head loss losses. The types of losses that are associated with the pipe
hT Total head loss itself is known as major losses. This type of loss is
associated with the length of the pipe, the velocity of
1. INTRODUCTION flowing fluid and the roughness of the pipe section. On the
other hand, minor losses are the losses that are associated
The fluid transport in a pipe or a piping system is very
with the additional components in the piping system. The
valuable for regularity of daily life tasks. In this case, fluid
names of these components are given above and the loss in
is in direct contact with the boundary when it flows
each of the components is different from other
through a duct. A no-slip condition is developed in that
components. The two losses act together to reduce the
case. For a fixed duct, velocity of fluid layer which touches
overall head and the summation of these two losses-overall
the surface of the pipe, is zero.
loss, is known as the total head loss.
1.1 Objectives: is the correction factor of K.E of the fluid. Finally, the
Th head loss in a pipe system is studied in this quantity
experiment.. The objectives of the experiment are: 𝑃 1
𝜌
+ 2 𝛼𝑉 2 + 𝑔𝑧
 Determine the major loss and determine the
friction factor. represents mechanical energy which is useful. Equation
 Calculate the minor loss of a sudden expansion, (2.2) is known as mechanical energy equation. The term
sudden contraction, bend, and valve. “losses” is the sum of major and minor losses. Total loss
 Measure the minor loss coefficient for each (ht) is the sum of major loss (hl) and minor loss (hm). For
component. fig.2
ht = h1–h2 Eq. (2.3)
2. Theoretical Background:
The Mechanical Energy equation: Major Loss:
The mechanical energy equation states that the rate of Consider a straight pipe having a uniform cross-sectional
change of internal energy if a system is a function of heat area having no abrupt changes in its area, then the minor
removed or added to the system and the work done on/by loss in that pipe will be zero (hm) =0. Furthermore, major
the system. The value of internal energy may be kept loss is determined from
constant by changing one of the variables in such a way 𝐿𝑉 2
that its sum with other variable makes the overall sum ℎ𝑙 = 𝑓 𝐸𝑞. (2.4)
2𝑔𝐷
constant.
Minor loss in sudden expansion:
A sudden expansion cross-sectional area is shown in fig.3
below:

Figure 2: Pipe flow

Its integral form applied to control volume in fig.2 is

Figure 3: Expansion
written as,
𝜕 This results in a reduction of downstream velocity V2. It
. .
∫ 𝑒𝜌𝑑𝑉 + ∫ 𝑒𝜌𝑉. 𝑛𝑑𝐴 = 𝑄𝑖𝑛 + 𝑊𝑖𝑛 𝐸𝑞. (2.1) is determined from expression below:
𝜕𝑡
𝐴1
If flow is assumed to be steady and incompressible, and 𝑉2 = 𝑉1 𝐸𝑞. (2.5)
there are unidirectional inlets/outlets. Now, if we consider 𝐴2
that the heat transfer to/by the fluid and the corresponding 𝑃 1 𝑃 1
( + 𝛼𝑉 2 + 𝑔𝑧) 2 − ( + 𝛼𝑉 2 + 𝑔𝑧) 1 = ℎ𝑙 + ℎ𝑚 𝐸𝑞. (2.6)
changes in the internal energy, the above equation will be 𝜌 2 𝜌 2
simplified to,
If pipe is horizontal, z1=z2. Equation (2.7) simplifies to
𝑃 1 𝑃 1
Σ ( + 𝛼𝑉 2 + 𝑔𝑧) 𝑖𝑛 + 𝑤𝑠ℎ𝑎𝑓𝑡 = Σ ( + 𝛼𝑉 2 + 𝑔𝑧) 𝑜𝑢𝑡 + 𝑙𝑜𝑠𝑠𝑒𝑠 𝐸𝑞. (2.2)
𝜌 2 𝜌 2 𝑃2 − 𝑃1 𝑉12 − 𝑉22
+ = ℎ𝑙 + ℎ𝑚 𝐸𝑞. (2.7)
Where the work done with subscript shaft is the work 𝜌 2𝑔
done by pump/turbine in the system. This work may be In this case, as the length of fitting is short, the major loss
positive or negative depending on whether energy is can be neglected. Thus, the minor loss can be rewritten
extracted /added to the system. The other quantity alpha as:
 v1  D1 4  Where, hm,b is minor loss. Using the major head in
hm,e  h1  h2  1  ( )  Eq. (2.8) equation 2.4, the minor loss is given by:
2g  D2 
hm,b  h1  h2  hl Eq. (2.13)
Furthermore, the minor loss through sudden expansion
can be written as: Furthermore, the minor loss through a bend is determined
by:
v1
hm,e  K e Eq. (2.9)
2g v
hm,b  K e Eq. (2.14)
2g
Where, Ke is minor loss co-efficient due to expansion.

Minor loss in a sudden Contraction

In pipe flows the sudden contractions also, such as shown
in the figure the phenomenon is the opposite of the
expansion. As the cross-sectional area decreases the flow
stream velocity v2 increases. Consequently, minor head
loss is given by relation:

Figure 5:Bend

Minor loss in a valve

Valves in the fluid systems serve the purpose of opening,
closing and partially obstructing the flows. The amount of
head loss is dependent on the state of the valve i.e. it is
opened, closed or partially obstructed.

Figure 4: Contraction

v2  D2 4 
hm,c  h1  h2  ( )  1 Eq. (2.10)
2 g  D1 

Similarly, the minor loss is given by: Figure 6: Valve

𝑣̅ 2 Applying the mechanical equation, the pressure loss

ℎ𝑚,𝑐 = ℎ1 − ℎ2 + 2𝑔2 Eq. (2.11)
through valve is given

p1  p2
hT  hl  hm,v  Eq. (2.15)
Where Kc is the minor loss co-efficient due to contraction. g

Minor Loss in Bend Where h m,v is the minor due flow across a valve. As the
Consider a straight pipe having a uniform cross-sectional axial distance is too small, major loss is neglected.
area having no abrupt changes in its area, then the above Equation (2.15) becomes
basic equation gets the simplified form:
p1  p2
hm,v  Eq. (2.16)
hT  h1  hm,b  h1  h2 Eq. (2.12) g
Moreover, the minor loss can also be calculated by:

v
hm,v  Ke Eq. (2.17)
2g

3. Experimental details
The experimental setup contains two piping systems.
These piping systems are represented by dark and light
lines to distinguish them from each other. The flow
components are shown in the table below:
Table 1 :Properties of Components in Figure 7

Letter Description Tap

No.
Dark Blue
A Straight pipe, 𝜙13.7 mm 3-4
B Mitre Bend, 90° 5-6
C Standard elbow bend, 90 1-2
B Gate valve 19-20
Light Blue
E Sudden expansion, 𝜙 13.7 mm x 𝜙 26.4 mm 7-8
F Sudden contraction 𝜙 26.4 mm x 𝜙 13.4 mm 9-10
G Bend, 90° x R50.8 mm 15-16
H Bend, 90° x R101.6 mm 11-12
J Bend, 90° x R152.4 mm 13-14
K Glove Valve 17-18
L Straight pipe, 𝜙 26.4 mm 8-9
R Flow Meter In-line
Figure 7: Layout of Water Friction Panel

4. Equipment
The pipe system is attached to a pump that is responsible
for the flow throughout the system. The pump has a
maximum limit of providing Q = 6 gal/min. There is a
task at the end of the system to collect the water. The
capacity of this tank is 10L. The specifications of the five
bends are collected in the table:
Table 2:Geometric Properties of joints

Bend Radius Circuit Tap Length Length

(mm) No. between between
Taps, Panel Taps, Panel No.
No. 1 2
B Mitre Bend Dark Blue 5-6 940 935
C STD elbow Dark Blue 1-2 930 925
G 50.8 Light Blue 15-16 920 930
H 101.6 Light Blue 11-12 935 930
J 152.5 Light Blue 13-14 880 920

3.1 Priming of the System

The system is primed before initiating an experiment
using the following steps:
Step 1: Supply side of the pump was connected to the inlet 5. Data Reduction:
and the holding tank was connected to the outlet. State all results in SI units
Step 2: Water inlet hose and return hose were placed into 1. Straight Pipes: Compute the friction factor in the
the tank. pipes A and L for all volumetric flow rates. Plot
Step 3: Pump was switched on. the graph friction factor f vs. Reynold Number Re.
4Q
Step 4: Water was allowed to flow for few minutes. Re 
 D
Step 5: Gate valve was closed and all trapped air was
Fit the data in the power function:
removed into piezometers. Piezometer should show zero
pressure difference.
f ( x)  ao  a1 x n
3.2 Procedure: 2. Sudden Expansion: Compute the minor loss co-
In order to perform the experiment, a series of steps is efficient for expansion fitting E for all volumetric
performed: flow rates. Plot graph minor loss co-efficient Ke
Step 1: Pump was switched on and the system was vs. Reynold Number Re
primed as mentioned in the section 3.2. 3. Sudden Contraction: Compute the minor loss co-
efficient for contraction Kc fitting F for all
Step 2: The valve K was closed. Along with this, the volumetric flow rates. Plot graph minor loss co-
other valve D was opened to let the water flow through efficient for contraction Kc vs. Reynold Number
the dark circuit shown in the figure. Re
4. Bends: Compute the minor loss co-efficient for
Step 3: Volumetric flow was adjusted using gate valve D
bend Kb for bends B, C, G, H and J. Plot graph
so that the rotameter R shows the 10% volumetric flow
minor loss co-efficient for bend Kb vs. Reynold
rate.
Number Re
Step 4: The height of the water was noted in piezometer f  0.0785Re0.25
tube from Taps ranging from Tap 1 to 6 and pressure 5. Valves: Compute the minor loss co-efficient for
difference for Taps 19 to 20. globe valve K and gate valve K, for all
Step 5: Flow rate was measured by noting the time for 2L volumetric flow rates. Plot graph minor loss co-
flow of water in the graduated cylinder. efficient for valves Kv vs. Reynold Number Re
6. Error Analysis: For each of the computed values
Step 6: Steps 3 to 5 were repeated for different values of perform error analysis as mentioned in section
flow rate. 3.1
Step 7: Gate valve was closed and globe valve was
opened such that the water only flows through the blue
6. Experimental Results:
line. Experimental data was processed in MATLAB. The
results are shown below:
Step 8: Pressure measuring transducer was detached from
the Tap 19 and Tap 20 and connected it to Tap 17 and
Tap 18.
Step 9: Steps 3 through 7 were repeated.
Steps 10: To measure the water temperature use a digital
thermometer. Use this value for the calculation of density
and viscosity.
 Figure 8: showing the graph between friction factor and Reynold
Figure 12: showing the graph between minor loss coefficient and
number for pipeA at different flow rates.
Reynold number for expansion fitting at different flow rates.

Figure 9: showing curve fit of the data shown in fig.8

From fig.8, it can be seen that as Reynold number

increases, friction factor decreases. Figure 13: Graph between average minor loss coefficient for different
bends and R/D ratio

Figure 10: showing the graph between friction factor and Reynold
number for pipeL at different flow rates.

Figure 14: showing curve fit of the data shown in fig.13

Figure 11: showing curve fit of the data shown in fig.10

From fig.11 it can be seen that it can be seen that as

Reynold number increases, friction factor decreases. Figure 15: showing the graph between minor loss coefficient and
Reynold number for contraction fitting at different flow rates.
 determined using flow rate, total pressure head,
acceleration due to gravity, and pump efficiency

Figure 16:showing graph between minor loss coefficient of valveD

and Reynold number calculated at different flow rates

Figure 17: showing graph between minor loss coefficient of valveK

and Reynold number calculated at different flow rates

7. Comments:
 The loss associated with the straight section of
pipe is called major loss. The loss associated with
the elbows, valves, etc. is called minor loss.
 The equation valid for determining change in
pressure in pipe system is
𝑃2 − 𝑃1 𝑉12 − 𝑉22
+ = ℎ𝑙 + ℎ𝑚 𝐸𝑞. (2.18)
𝜌 2𝑔
Equation (2.18) is valid for steady, incompressible
flow.
 Friction factor decreases with an increase in
Reynold Number. This is because at high Reynold
number, inertial forces dominate friction forces.
 As pipe diameter increases, Reynold number
decreases. So, friction factor increases.
 Minor loss coefficient for expansion fitting
increases with increase in Reynold number.
 Minor loss coefficient for contraction fitting
increases with increase in Reynold number.
 Minor loss coefficient decreases with increasing
R/D ratio.
 Minor loss coefficient of valve increases with
increase in Reynold Number.
 To size the pump at the required flow rate, a
certain total differential head must be generated by
the pump. Total differential head is determined
from Equation (2.7). After that pump power is