SCHOOL OF ENGINEERING
DIPLOMA IN MECHANICAL ENGINEERING
PRACTICAL LAB 1 REPORT
EXPERIMENT 1: LOSSES IN PIPING SYSTEMS
APRIL 2024 SESSION
Course Code
Course Title
Learning
Assessed
:
:
:
EGR 2183
Fluid Mechanics
CLO 3 - Perform Fluid Mechanics experiments according to
Standard Operating Procedures
Group Name
Team Member
:
:
1
2
3
Group 2
*Submission
Date/Test Date
:
Lecturer
Total Mark
:
:
Feedback
:
Name
ASSESSMENT
Instructor’s Signature :
Matric No.
Table of Contents
1.0
Introduction ........................................................................................................................ 3
1.1
Introduction of Internal Flow of Piping ..............................................................................3
1.2
Type of Fluid Flow ..........................................................................................................3
1.3
The Entrance Region .......................................................................................................4
1.4
Losses of Flow in Pipes....................................................................................................5
2.0 Objectives................................................................................................................................. 6
3.0 Theoretical Background ......................................................................................................... 6
4.0 Methodology ............................................................................................................................ 7
5.0 Results ...................................................................................................................................... 8
6.0 Discussion................................................................................................................................11
6.1 The head loss in the fluid between the 3/8” vs 1/2" PVC pipe. ............................................. 11
6.2 The effects of volume flow rate on the head loss, 𝒉𝑳 in a fluid. ............................................ 12
6.3 Experimental vs. Theoretical head loss, 𝒉𝑳 in the fluid. ...................................................... 13
6.4 Factors that caused Percentage Error and Solution ............................................................ 13
7.0 Conclusion ............................................................................................................................. 14
8.0 References .............................................................................................................................. 15
9.0 Appendix-A ...................................................................................................................... 16
10.0 Appendix-B..................................................................................................................... 18
1.0 Introduction
1.1 Introduction of Internal Flow of Piping
Liquid or gas flow through pipes or ducts is commonly used in heating and cooling
applications and fluid distribution networks. The fluid in such applications is usually forced to
flow by a fan or pump through a flow section. There is friction which directly related to the
pressure drop and head loss during flow through pipes and ducts. Pressure drop is used to
determine the pumping power requirement. (Yunus A.Cengel and John M.Cimbala, 2014)
Figure 1: Pipes (Ubuy, 2012)
Figure 2: Duct (librarykeeda, 2020)
A typical piping system involves pipes of different diameters connected to each
other by various fittings or elbows to routes the fluid, valves to control the flow rate, and
pumps to pressurize the fluid. (Yunus A.Cengel and John M.Cimbala, 2014)
Figure 3: Valve (RS, 1937)
Figure 4: Pump (KOKENT, 1990)
1.2 Type of Fluid Flow
Fluid flow in three possible regimes:
a) Turbulent Flow
A dynamic and chaotic type of fluid flow
characterized by irregular motion and the
formation of eddied, vortices, and fluctuations
in velocity and pressure. It occurs at high
velocities, low viscosity, and in the presence of
disturbances or obstacles, playing a significant
role in many natural and engineered systems.
(BYJU'S, 2011)
Figure 5: Turbulent Flow
(physics world , 2017)
b) Laminar Flow
Figure 6: Laminar Flow
(Mad Laboratory, 2008)
A smooth and orderly type of fluid flow
characterized by parallel layers of fluid
particles moving without significant mixing. In
laminar flow, the particles move in a
predictable manner, following well-defined
streamlines. It occurs at low velocities, high
viscosities, and in the absence of obstructions,
creating an organized and predictable flow
pattern. (BYJU'S, 2011)
c) Transitional Flow
A type of fluid flow that occurs between
laminar and turbulent flow regimes. It
exhibits a mixture of laminar and turbulent
characteristics, with the flow pattern
oscillating between the two states. It is
influenced by factors such as flow velocity,
fluid viscosity, and pipe roughness, making it
a transitional phase in fluid behavior
analysis. (BYJU'S, 2011)
Figure 7: Transitional Flow
(Google , 2024)
1.3 The Entrance Region
The region of flow in which the effects of the viscous shearing forces caused by fluid
viscosity are felt is called the velocity boundary layer or just the boundary layer. The
hypothetical boundary surface divides the flow in a pipe into two regions:


Boundary layer region,
The viscous effects and the velocity changes are significant
Irrotational flow region.
The frictional effects are negligible and the velocity remains essentially
constant in the radial direction
Figure 8: Development of The Velocity
Boundary Layer in a Pipe
The thickness of this boundary layer increases in the flow direction until the boundary layer
reaches the pipe center and thus fills the entire pipe, as shown in Figure 8, and the velocity
becomes fully developed a little farther downstream. The region from the pipe inlet to the
point at which the velocity profile is fully developed is called the hydrodynamic entrance
region, and the length of this region is called the hydrodynamic entry length. Flow in the
entrance region is called hydrodynamically developing flow since this is the region where
the velocity profile develops. The region beyond the entrance region in which the velocity
profile is fully developed and remain unchanged is called the hydrodynamically fully
developed region. The flow is said to be fully developed when the normalized temperature
profile remains unchanged as well.
Source: (Yunus A.Cengel and John M.Cimbala, 2014)
1.4 Losses of Flow in Pipes
There are two types of losses which could happen during the flow in pipes:


Major Losses
The major losses of energy are due to friction effect between the moving fluid and the
walls of pipe.
Minor Losses
The losses due to disturbances in flow pattern or due to change in velocity are called
as minor losses. These losses may occur because of the sudden change in the area of
flow and the direction of flow. These losses are less as compare to major losses. The
minor loss of the energy includes the following cases:
i.
Loss of energy because of sudden enlargement
ii.
Loss of energy because of sudden contraction
iii.
Loss of energy at the entrance of a pipe
iv.
Loss of energy at the exit of a pipe
v.
Loss of energy because of bend
vi.
Loss of energy in various pipe fittings
vii.
Loss of energy because of obstruction
Source: (ROHINI COLLEGE OF ENGINEERING & TECHNOLOGY , 2007)
2.0 Objectives



Measure and analyse friction or pressure loss (differential pressure) across various pipes, fittings,
and valves in a piping system.
Determine the discharge coefficient for flow measuring devices.
Investigate the relationship between flow rate, pipe diameter, and head loss in the turbulent
region, and compare theoretical values with experimental results to assess accuracy and identify
potential sources of error.
3.0 Theoretical Background
There are several equations that might be used in this experiment.

The head loss for pipe flow problems, ℎ = 𝑓
, where
f is friction factor,
L is length of pipe,
D is diameter of pipe,
V is velocity of fluid flow,
g is gravitational acceleration.

Friction loss for laminar flow, 𝑓 =
, where
Re is the Reynold’s Number.

Friction loss for turbulent loss,
= −1.8 log[
ɛ / D is the relative roughness.

Minor head loss, ℎ = 𝐾
, where
KL is the resistance coefficient.
/
.
.
+
.
] , where
4.0 Methodology
Preparation:
1. Connect the hydraulic bench to the piping loss apparatus.
2.Adjust valves to control flow.
3.Purge air bubbles from the system.
4.Ensure the apparatus is ready for the experiment.
Experiment Procedure:
1.Open the flow control valve to allow water to flow through the desired pipeline.
2.Adjust water flow rate using the pressure control valve.
3.Measure and record the flow rate using a water meter and stopwatch.
4.Open corresponding pressure taps to measure pressure loss across pipes or
fittings/valves.
5.Record the pressure readings using a differential pressure gauge.
6.Repeat the experiment at different flow rates and for different pressure tapings
as specified in the experimental data sheet.
7.Record the flow rates and pressure readings for each experimental condition.
5.0 Results
Room Temperature: 25° c
Table 1: Experimental data with respect to different diameter of pipe.
Type
Volume,
V
(𝐿)
Time,
t
(s)
Flow
Rate, Q
(L/s)
ℎ
(actual)
(m)
𝑣
(m/s)
Re
[-]
f
(pipe)
[-]
𝐾
(valve
or
fitting)
[-]
ℎ
(theory)
(m)
Percentage
Difference
(%)
0.7963
Differential
gauge
pressure
difference,
∆𝑃
(kPa)
7
PVC
1/2”
(ID=17mm,
L=1.25m)
47.78
60
0.7136
3.5082
66935
0.01984
-
0.9153
22.0365
39.71
60
0.6618
6
0.6116
2.9157
55630
0.02060
-
0.6564
6.8251
31.38
60
0.5230
4
0.4077
2.3042
43963
0.02165
-
0.4308
5.3621
PVC
3/8”
(ID=13.9m
m,
L=1.25m)
47.78
60
0.7963
15
1.5291
5.2474
81863
0.01919
-
2.3996
36.2769
39.71
60
0.6618
11
1.1213
4.3611
68035
0.01972
-
1.7190
34.7702
31.38
60
0.5230
7
0.7136
3.4465
53766
0.02084
-
1.1346
37.1093
Globe
Valve
3/4”
(ID=20.9m
m)
47.78
60
0.7963
50
5.0968
2.3211
54446
-
15.00
4.1189
23.7417
39.71
60
0.6618
31
3.1600
1.9290
45248
-
15.00
2.8448
11.0798
31.38
60
0.5230
16
1.6309
1.5245
35760
-
15.00
1.7768
8.2114
90deg
Elbow
3/4”
(ID=20.9m
m)
47.78
60
0.7963
1
0.1019
2.3211
54446
-
1.75
0.4805
78.7929
39.71
60
0.6618
1
0.1019
1.9290
45248
-
1.75
0.3319
69.2979
31.38
60
0.5230
0
0
1.5245
35760
-
1.75
0.2073
100
Graph of Volume flow rate against Head Loss in the 1/2" PVC Pipe
1.0000
0.9153
0.9000
Head Loss,hL (m)
0.8000
0.6564
0.7000
0.7136
0.6000
0.5000
0.6116
0.4308
0.4000
0.3000
0.4077
0.2000
0.1000
0.0000
0.5000
0.5500
0.6000
0.6500
0.7000
Volume Flow Rate,Q (L/s)
Theoretical
0.7500
0.8000
0.8500
Experimental
Figure 9: Graph of volume flow rate against head loss in the 1/2” PVC pipe.
Graph of Volume flow rate against Head Loss in the 3/8" PVC Pipe
3.0000
2.3996
Head Loss,hL (m)
2.5000
2.0000
1.719
1.5291
1.5000
1.1346
1.0000
1.1213
0.7136
0.5000
0.0000
0.5000
0.5500
0.6000
0.6500
0.7000
0.7500
0.8000
Volume Flow Rate,Q (L/s)
Experimental
Theoretical
Figure 10: Graph of Volume flow rate against head loss in the 3/8” PVC pipe.
0.8500
Graph of Volume flow rate against Head Loss in the 3/4" Globe Valve
6.0000
5.0968
Head Loss,hL (m)
5.0000
4.0000
3.16
4.1189
3.0000
1.7768
2.8448
2.0000
1.6309
1.0000
0.0000
0.5000
0.5500
0.6000
0.6500
0.7000
0.7500
0.8000
0.8500
Volume Flow Rate,Q (L/s)
Theoretical
Experimental
Figure 11: Graph of Volume flow against head loss in the 3/4" Globe Valve.
Graph of Volume flow rate against Head Loss in the 3/4" 90 deg Elbow
0.6000
0.4805
Head Loss,hL (m)
0.5000
0.4000
0.3319
0.3000
0.2073
0.2000
0.1019
0.1019
0.1000
0
0.0000
0.5000
0.5500
0.6000
0.6500
0.7000
0.7500
0.8000
Volume Flow Rate,Q (L/s)
Theoretical
Experimental
Figure 12: Graph of Volume flow against head loss in the 3/4" 90deg Elbow.
0.8500
6.0 Discussion
6.1 The head loss in the fluid within the 3/8” vs 1/2" PVC pipe.
As shown in the Figures 9 and 10, when comparing both graphs, the peak value of the
experimental Head Loss,ℎ in the 1/2" Pipe pipe (Inner Diameter of 17 × 10 𝑚) with the value
of 0.7136m is significantly lower than that of the 3/8” PVC pipe (Inner Diameter of 13.9 × 10 𝑚 )
with the value of 1.5291m. This difference is attributed to the head loss being affected by the
viscosity of the dynamic fluid (water), and the wall shear stress of the PVC pipe (Yunus A.Cengel
and John M.Cimbala, 2014). It is important to note that both Reynold number of the 1/2" and the
3/8” exceed the critical value of 4000, indicating that the flow of the fluid (horizontally) within
these PVC pipes is turbulent. Overall, there are two main factors that can be easily manipulated
and closely related to each other, that affected the value of head loss in this experiment: Darcy
friction factor, f and Diameter of the pipe, D.
a. Darcy Friction Factor, f:
According to the Colebrook equation, the co-relationship between the friction factor, f and the ratio
of the roughness to the pipe’s internal diameter, , and the Reynold number, Re can be determined
for a turbulent flow. This equation is stated as below:
1
6.9
𝜀
≅ −1.8log [
+(
). ]
𝑅𝑒
3.7𝐷
𝑓
From a mathematical analysis perspective, the Darcy Friction Factor, f is inversely proportional to
both the ratio of the mean height of the roughness of the pipe to the pipe diameter, , and the
Reynold Number, Re. At large Reynold Number, the friction factor, f is a minimum for a smooth
pipe and increases with its roughness. This indicates that as the diameter decrease, the ratio of
roughness to diameter will decrease, and the friction factor will increase for a turbulent flow (Yunus
A.Cengel and John M. Cimbala, 2014). (This can refer to the Appendix-B item No.1). Moreover,
according to the Darcy-Weisbach equation, the Head Loss, ℎ , is directly proportional to the
friction factor, f. Thereof, the high value of friction factor, induced by the pipe’s rough internal
surface and high Reynolds number, will increase the wall shear force in the pipe, in which the shear
stress’ direction is opposite to the fluid. Over a certain area in contact, this high resistance factor
resulting in a greater shear force exerted by the fluid against the inner wall of the PVC pipe
(𝑆ℎ𝑒𝑎𝑟 𝑓𝑜𝑟𝑐𝑒, 𝑉 = 𝜏𝐴). This indicates that more energy losses due to the shear force (also can be
refer as friction) as it moves along the pipe. Overall, the head loss is greater in 3/8” PVC pipe.
b. Diameter of the Pipe, D:
In this experiment, in which the fluid’s properties are remain constant, the 3/8” PVC pipe with a
smaller diameter (13.9mm) indeed have a higher ratio of the mean height of roughness to the pipe
diameter ( ), which in turn causes a relatively higher value of friction factor (f), and thus inducing
a higher value of head loss, ℎ in the flowing fluid within the PVC pipeline. The comparison
between 3/8” and 1/2" PVC pipes are stated as below:


3/8” PVC pipe: smaller diameter, D means higher velocity for a specific flow rate, Q,
leading to more friction and higher head loss, ℎ .
1/2” PVC pipe: larger diameter, D allows for slower velocity for a specific flow rate, Q,
resulting in less friction and lower head loss, ℎ .
Technically, the increases/decreases in head loss in a fluid can be influenced by several
factors such as volume flow rate, pipe length, and pipe diameter. For PVC pipes, as the diameter
decreases, the head loss, ℎ increases due to a reduction in the cross-sectional area through which
the fluid can flow. This means that for the same flow rate, the fluid will move faster in a smaller
diameter pipe and resulting in higher friction and thus greater head loss.
6.2 The effects of volume flow rate on the head loss, 𝒉𝑳 in a fluid.
Figure 9 presents both the experimental and theoretical values related to specific volume
flow rates under control. Our observations indicate that the head loss, ℎ , increases with the rising
volume flow rate of the fluid within the pipe’s internal region. This suggests that higher flow rates
contribute to an increase in the fluid’s head loss. According to the Poiseuille’s law:
𝑄=𝑉
𝐴 =
∆
where Q is volume flow rate, 𝜇 is dynamic coefficient of viscosity of the fluid, and D is the Inner
diameter of the pipe.
Given that the diameter of the 3/8” PVC pipe and the dynamic coefficient of viscosity
remain constant, the variation in volume flow rate, Q corresponds to a change in the average
velocity of the fluid per unit of time (second). This alteration in average velocity can be attributed
to the adjusted power of the water pump. Due to the fact that the shear force impact, 𝜏, that is
induced by the viscosity of the fluid, acting on the inner wall of the pipe, is always opposite in
direction of the flow of the fluid. This force is the result of the fluid’s viscosity, which creates
internal friction as the fluid layers move relative to each other. This shear force is responsible for
the “drag force” that opposes the motion of the fluid, leading to the pressure drops in pipe flow and
thus inducing the head loss in the fluid. Overall, the high average velocity of the dynamic fluid
within the PVC pipe will induces a high-volume flow rate, which in turn increases the head loss,
ℎ of the fluid. Moreover, the volume flow rate, Q, is directly proportional to the quartic of inner
diameter of the PVC pipe. This is because the increase in head loss with higher flow rates is a result
of the greater frictional forces acting against the horizontal movement of the fluid, which are indeed
more pronounced at higher velocities (Yunus A.Cengel and John M.Cimbala, 2014). When the
diameter of the PVC pipe increases, the volume flow rate increases, thereby inducing a greater
value of head loss, ℎ in the fluid. These changing variables are monitored and systematically
represented in the graphical illustrations inside Figures 9, and 10.
6.3 Experimental vs. Theoretical head loss, 𝒉𝑳 in the fluid.
The experimental and theoretical values of head loss, ℎ in the fluid are presented in Table
1. These data are monitored and controlled by specific volume flow rate of the fluid within the
pipeline.
At a flow rate of 0.7963 L/s, the head loss percentage difference for various type of
pipe/fitting/valve are recorded as follows: 22.0365% for a 1/2" PVC pipe, 36.2769% for a 3/8”
PVC pipe, 23.7417% for a Globe valve, and a significant 78.7929% for a 3/4" 90-degree elbow
fitting. When the flow rate decreases to 0.6618 L/s, the percentage differences adjust
to 6.8251% for the 1/2" PVC pipe, 34.7702% for the 3/8” PVC pipe, 11.0798% for the Globe valve,
and 69.2979% for the elbow fitting. At an even slower rate of 0.5230 L/s, the differences
are 5.3621% for the 1/2" PVC pipe, 37.1093% for the 3/8” PVC pipe, 8.2114% for the Globe
Valve, and a complete deviation of 100% for the elbow fitting. Across the various flow rates tested,
the 3/4" 90-degree elbow fitting consistently exhibits the highest deviation between experimental
and theoretical head loss, ℎ values.
6.4 Factors that caused Percentage Error and Solution
There are several factors that can caused the experimental values deviates from the
theoretical head loss in the fluid such as inconsistency data displayed by the flow rate indicator,
inaccurately data displayed by the pressure gauge meter, turbulent flow, and partial closed valve in
the fluid system.
1. Inconsistency data displayed by the flow rate indicator.
The inconsistency data displayed by the flow rate indicator will result in an unreliable
measurement of the flow rate of the fluid within the PVC pipeline. It also increases the
toughness for us to calculate the flow rate for the fluid accurately. As a result, it will lead to
significant deviations between the experimental and theoretical head loss, ℎ values.
2. Inaccurately data displayed by the pressure gauge meter.
The inaccurately date displayed by the pressure gauge meter resulted from the presence of the
air inside the branch connection pipe to the pressure gauge meter. This will result in
inaccurately data generated by the pressure gauge meter. Consequently, the experimental head
loss will deviate from the theoretical one.
3. Turbulent flow.
The disorderly and rapid fluctuations of swirling region inside the turbulent flow can causes
significant fluctuations in the values of velocity, temperature, and pressure (Yunus A.Cengel
and John M. Cimbala, 2014). This is because the instantaneous velocity component is the sum
of average velocity of the fluid and a fluctuating component velocity. Consequently, it results
in the total amount of shear stress in a turbulent flow is the sum of two different component
shear stresses: shear stress in laminar flow and shear stress in turbulent flow. As a result, any
random eddy motion of the turbulent flow will cause unexpected changes in pressure, and the
velocity of the flow. This will affect the accuracy of the data being collected. (Yunus A.Cengel
and John M. Cimbala, 2014)
4. Partial closed valve in the fluid system.
The partial closed valve will significantly increase head loss within the fluid system. This
occurs when the turbulent eddies that are produced in the valve and continue downstream.
These eddies led to some mechanical energy consumption, due to the energy is dissipated into
heat in the downstream pipe flow. This phenomenon explained the huge pressure difference
observed in global valve. (Yunus A.Cengel and John M. Cimbala, 2014) Eventually, it will
affect the experimental head loss values.
5. Solutions:
To minimize these experimental errors, the experiment should be conducted in a more careful
way. Firstly, the average volume flow rate of the fluid should be considered and multiply with
the calibration factor that is set by the manufacturer. Apart from that, the air from the connection
branch pipe should be removed entirely to avoid inaccuracy/sensitivity of the pressure meter.
Besides, the volume flow rate should be adjusted carefully to minimize the eddies motion in
the turbulent flow. Lastly, ensure that the valve closed completely to avoid turbulent eddies
being produced below the valve and the downstream within the pipeline.
7.0 Conclusion
In conclusion, this experiment proven that the diameter of the pipeline, volume flow rate of the
fluid does contribute to reduction/increment of the head loss in the fluid system. When the properties of the
fluid such as temperature and density remain constant, the head loss in the fluid changes correspond to the
specific volume flow rate, Reynold number, viscosity of the fluid, and friction factor. It is important to note
that the flow can be classified into laminar and turbulent. For our experiment, the flow in all types of the
components is said to be turbulent as the Reynold number exceeds 4000. Therefore, it is expected that the
friction factor is high when the flow is in a smaller diameter pipe. This results in high average velocity of
the flow and eventually increases eddies motion in turbulent flow. These random fluctuations indeed caused
unexpected rise in head loss in the fluid. Therefore, 3/8” PVC pipe has the second highest deviation between
the experimental and theoretical head loss values. However, in the case of highest deviation between
experimental and theoretical head loss in the 90-degree elbow fitting, the pressure drops inaccurately due
to the flow separation, which it can be improved by reducing the change of direction instead of sharp turn.
Overall, this experiment fulfils the expectation of the theoretical value as the percentage difference capped
at the ranged of 5.3621% to 37.1093% for the horizontal flowing fluid within the PVC pipeline.
8.0 References
BYJU'S, 2011. Types of Fluid Flow. [Online]
Available at: https://byjus.com/gate/types-of-fluid-flow/
[Accessed 3 May 2024].
Google , 2024. transitional flow. [Online]
Available at:
https://www.google.com/search?q=transitional+flow&sca_esv=46dfe222c76fb569&sca_upv=1&udm=2
&biw=786&bih=658&ei=q6Q0Zp3IEqaOseMP7f6hEA&ved=0ahUKEwjdyZutjPGFAxUmR2wGHW1_
CAIQ4dUDCBA&uact=5&oq=transitional+flow&gs_lp=Egxnd3Mtd2l6LXNlcnAiEXRyYW5zaXRpb25
hbCBmbG9
[Accessed 3 May 2024].
KOKENT, 1990. PEDROLLO PUMP ENERGY SAVE 22000W 1000~6000L/MIN 35~15M F100/160A.
[Online]
Available at: https://www.kokent.com.my/product/pedrollo-pump-energy-save-22000w-10006000lmin3515m-f100160a/
[Accessed 3 May 2024].
librarykeeda, 2020. What is ducting/Types of ducting/ thickness of GI duct sheet/How to calculate the area
of ducting?. [Online]
Available at: https://www.librarykeeda.com/2020/07/what-is-ductingtypes-of-ducting.html
[Accessed 3 May 2024].
Mad Laboratory, 2008. Laminar Flow Leapfrog Fountain. [Online]
Available at: https://madlaboratory.wordpress.com/2008/05/23/laminar-flow-leapfrog-fountain/
[Accessed 3 May 2024].
physics world , 2017. Is turbulent flow universal after all?. [Online]
Available at: https://physicsworld.com/a/is-turbulent-flow-universal-after-all/
[Accessed 3 May 2024].
physicsworld, 2017. Is turbulent flow universal after all?. [Online]
Available at: https://physicsworld.com/a/is-turbulent-flow-universal-after-all/
[Accessed 3 May 2024].
ROHINI COLLEGE OF ENGINEERING & TECHNOLOGY , 2007. 4.5 MAJOR AND MINOR LOSSES
OF FLOW IN PIPES , Tamil Nadu, India: ROHINI COLLEGE OF ENGINEERING & TECHNOLOGY .
RS, 1937. RS PRO Stainless Steel Full Bore, 2 Way, Ball Valve, BSPP 2in. [Online]
Available at: https://my.rs-online.com/web/p/ball-valves/7644278
[Accessed 3 May 2024].
Ubuy, 2012. White PVC Pipe - Custom Length - 1.5 Inch Sch40. [Online]
Available at: https://www.ubuy.com.my/en/product/FEOKONK-pvc-pipe-sch40-1-1-2-inch-1-5-whitecustom-length-1ft
[Accessed 3 May 2024].
Yunus A.Cengel and John M. Cimbala, 2014. Chapter 8.5 Turbulent flow in pipes. In: Fluid MechanicsFundamentals and Application Third Edition. New York,US: McGraw-Hill, p. 362.
Yunus A.Cengel and John M. Cimbala, 2014. Chapter 8.5- Turbulent Flow in Pipes. In: Fluid MechanicsFundamentals and Application Third Edition. New York,US: McGraw-Hill, p. 368.
Yunus A.Cengel and John M. Cimbala, 2014. Chapter 8.6 Minor Losses. In: Fluid MechanicsFundamentals and Application Third Edition. New York,US: McGraw-Hill, pp. 374-375.
Yunus A.Cengel and John M.Cimbala, 2014. Chapter 8.1 Introduction. In: Fluid MechanicsFundamentals and Application Third Edition. New York, US: McGraw-Hill, p. 362.
Yunus A.Cengel and John M.Cimbala, 2014. Chapter 8.3 The Entrance Region. In: Fluid Mechanics Fundamentals and Application Third Edition. New York, US: McGraw- Hill, p. 362.
Yunus A.Cengel and John M.Cimbala, 2014. Chapter 8.4 Laminar Flow in Pipes- Pressure Drop and Head
Loss. In: Fluid Mechanics-Fundamentals and Applications Third Edition. New York,US: McGraw-Hill,
pp. 355-356.
9.0 Appendix-A
a. Volume Flow Rate, Q:
For 1/2" PVC Pipe, 𝑄 =
𝑄=
47.78
60
𝑄 = 0.7963 𝐿/𝑠
b. Experimental Head Loss (actual),𝒉𝑳 :
ℎ =
𝜌𝑔
∆𝑃
For 1/2” PVC pipe, the change in pressure is 7kPa.
ℎ =
(1000)(9.81)
7000
ℎ = 0.7136𝑚
c. Average velocity of the flow, 𝒗𝒂𝒗𝒈 :
𝑄 =𝐴 ×𝑣
For 1/2" PVC pipe, its cross-sectional area, 𝐴 needs to be determined first.
𝐴 =
𝜋𝐷
4
𝐴 =
𝜋(17 × 10 )
4
𝐴 = 2.2698 × 10 𝑚
𝑣
=
𝑄
𝐴
Do note that the unit of Q needs to be in cubic meter. (0.001 factor)
0.7136(0.001)
2.2698 × 10
𝑣
=
𝑣
= 3.5082𝑚/𝑠
d. Reynold Number, Re:
𝑅𝑒 =
𝜌𝑣
𝐷
𝜇
Where 𝜌 is density, D is Inner diameter of pipe, and 𝜇 is he dynamic coefficient of viscosity.
For 1/2" PVC pipe, at which the average velocity, 𝑣
𝑅𝑒 =
is 3.5082m/s:
(1000)(3.5082)(17 × 10 )
(0.891 × 10 )
𝑅𝑒 = 66935
e. Darcy Friction Factor, f:
For 1/2" PVC pipe, the Reynold Number exceeds 4000, the flow is turbulent. In addition, roughness, 𝜀 of
the PVC is equal to 0.0015mm.
1
6.9
𝜀
≅ −1.8log [
+(
). ]
𝑅𝑒
3.7𝐷
𝑓
1
6.9
0.0015 × 10
≅ −1.8log [
+(
) . ]
66935
(3.7)(17 × 10 )
𝑓
𝑓 = 0.01984
f.
Theoretical Head Loss (theory),𝒉𝑳 :
For 1/2" PVC pipe:
ℎ =𝑓
𝐿𝑣
𝐷 2𝑔
ℎ =(0.01984) (
.
×
.
)( (
.
)
)
ℎ = 0.9153𝑚
g. Percentage Difference, 𝜹 (%):
𝛿=
𝑣 −𝑣
𝑣
× 100%
where 𝑣 is experimental value and 𝑣 is theoretical value.
For 1/2" PVC pipe,
𝛿=
0.7136 − 0.9153
× 100%
0.9153
𝛿 = 22.0365%
10.0 Appendix-B
1.