FLUID MECHANICS
MahmoodAjabbarHebah
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Mar 08, 2021
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About This Presentation
An experiment was effectively accomplished utilizing a virtual lab. As for the calculation part, the pipe diameters of 25mm and 15mm which were tested are compared. As it is noticed, as the velocity of the fluid flow increases, the head loss increases. Besides, the friction factor increases as the p...
Slide Content
1
ASIA PACIFIC UNIVERSITY OF
TECHNOLOGY & INNOVATION
EE0383.5-3-FLM
LAB REPORT FLUID MECHANICS
TITLE LAB REPORT FLUID MECHANICS
NAME & STUDENT ID
MAHMOOD ABDULJABBAR HEBAH
LECTURER LOW YEE SAN
ASIA PACIFIC UNIVERSITY OF
TECHNOLOGY & INNOVATION
EE0383.5-3-FLM
LAB REPORT FLUID MECHANICS
TITLE LAB REPORT FLUID MECHANICS
NAME & STUDENT ID
MAHMOOD ABDULJABBAR HEBAH
LECTURER LOW YEE SAN
2
ACKNOWLEDGEMENT
“The completion of this undertaking couldn’t have been possible without the
instruction and continues guidance from lecturer Mr. LOW YEE. His contribution is
sincerely appreciated and gratefully acknowledged. As well as my fellow classmates
their useful Participation.”
ACKNOWLEDGEMENT
“The completion of this undertaking couldn’t have been possible without the
instruction and continues guidance from lecturer Mr. LOW YEE. His contribution is
sincerely appreciated and gratefully acknowledged. As well as my fellow classmates
their useful Participation.”
3
Table of Contents
ABSTRACT........................................................................................................................... 5
Introduction ............................................................................................................................ 6
Theory .................................................................................................................................... 7
Friction loss in pipe................................................................................................................ 9
Objective .............................................................................................................................. 13
Procedures ............................................................................................................................ 13
Analysis & Results............................................................................................................... 15
Theoretical calculation ......................................................................................................... 18
Discussion ............................................................................................................................ 20
Conclusion ........................................................................................................................... 21
REFERENCES .................................................................................................................... 22
Table of Contents
ABSTRACT........................................................................................................................... 5
Introduction ............................................................................................................................ 6
Theory .................................................................................................................................... 7
Friction loss in pipe................................................................................................................ 9
Objective .............................................................................................................................. 13
Procedures ............................................................................................................................ 13
Analysis & Results............................................................................................................... 15
Theoretical calculation ......................................................................................................... 18
Discussion ............................................................................................................................ 20
Conclusion ........................................................................................................................... 21
REFERENCES .................................................................................................................... 22
4
List of Figures
Figure 1 Types of flow............................................................................................................... 6
Figure 2 Types of fittings........................................................................................................... 7
Figure 3 Internal surface of smooth and rough pipes ................................................................ 8
Figure 4 Flow shape ................................................................................................................... 8
Figure 5 Reynold number vs friction coefficient ..................................................................... 10
Figure 6 Figure 2 : Reynolds Number (Re) ............................................................................. 11
Figure 7 Sample of head loss ................................................................................................... 12
Figure 8 Head Loss. ................................................................................................................. 12
Figure 9 (K) Geometry Factor. ................................................................................................ 12
Figure 10 Connection Of The Pipe System ............................................................................. 13
Figure 11 Setting the Pipe Diameter ........................................................................................ 13
Figure 12 Turn on inlet valve................................................................................................... 13
Figure 13 Turn on inlet valve................................................................................................... 14
Figure 14 Change manometer knot fro isolate to airvent ........................................................ 14
Figure 15 Pipe Diameter and Friction Factor Graph ............................................................... 16
Figure 16 Head Loss ................................................................................................................ 16
Figure 17 Time taken to fill up 10cm tank .............................................................................. 16
Figure 18 Parameter and calculation by Virtual lab ................................................................ 17
Figure 19 Parameter and Calculation by Virtual Lab .............................................................. 19
List of Figures
Figure 1 Types of flow............................................................................................................... 6
Figure 2 Types of fittings........................................................................................................... 7
Figure 3 Internal surface of smooth and rough pipes ................................................................ 8
Figure 4 Flow shape ................................................................................................................... 8
Figure 5 Reynold number vs friction coefficient ..................................................................... 10
Figure 6 Figure 2 : Reynolds Number (Re) ............................................................................. 11
Figure 7 Sample of head loss ................................................................................................... 12
Figure 8 Head Loss. ................................................................................................................. 12
Figure 9 (K) Geometry Factor. ................................................................................................ 12
Figure 10 Connection Of The Pipe System ............................................................................. 13
Figure 11 Setting the Pipe Diameter ........................................................................................ 13
Figure 12 Turn on inlet valve................................................................................................... 13
Figure 13 Turn on inlet valve................................................................................................... 14
Figure 14 Change manometer knot fro isolate to airvent ........................................................ 14
Figure 15 Pipe Diameter and Friction Factor Graph ............................................................... 16
Figure 16 Head Loss ................................................................................................................ 16
Figure 17 Time taken to fill up 10cm tank .............................................................................. 16
Figure 18 Parameter and calculation by Virtual lab ................................................................ 17
Figure 19 Parameter and Calculation by Virtual Lab .............................................................. 19
5
ABSTRACT
“Begin with the results from 25 mm pipe clearly observed from 3 trials that one
of it are well off the head loss range compared to other trials. As shown in Table 1, for
the 2nd and 3rd trials the head loss is 135.45cm and friction factor 0.026 and the average
friction factor is 0.03. This might be human error or an instrumental error as this was
done by virtual lab. Next, friction factor remained within 0. 001 to 0. 011 in all the three
trials whereas the average was 0.01. Furthermore, as it comes to head loss the pipe had
3 different readings which was between 119.7 to 81.9 cm. End of the experiment, its
proven that Reynold number, Re is more than 4000 and friction factor esteem gives an
implying that the stream is hydraulically smooth. Experiment was effectively
accomplished utilizing virtual lab. As for the calculation part, pipe diameter of 25mm
and 15mm which were tested are compared. As it is noticed, as the velocity of the fluid
flow increases, the head loss increases. Besides, the friction factor increases as the pipe
diameter increases. In conclusion, using velocity which has related to flow rate to
compare the relationship with friction factor, which when the flow rate increase,
velocity of the fluid increase, the friction factor is decreases.”
ABSTRACT
“Begin with the results from 25 mm pipe clearly observed from 3 trials that one
of it are well off the head loss range compared to other trials. As shown in Table 1, for
the 2nd and 3rd trials the head loss is 135.45cm and friction factor 0.026 and the average
friction factor is 0.03. This might be human error or an instrumental error as this was
done by virtual lab. Next, friction factor remained within 0. 001 to 0. 011 in all the three
trials whereas the average was 0.01. Furthermore, as it comes to head loss the pipe had
3 different readings which was between 119.7 to 81.9 cm. End of the experiment, its
proven that Reynold number, Re is more than 4000 and friction factor esteem gives an
implying that the stream is hydraulically smooth. Experiment was effectively
accomplished utilizing virtual lab. As for the calculation part, pipe diameter of 25mm
and 15mm which were tested are compared. As it is noticed, as the velocity of the fluid
flow increases, the head loss increases. Besides, the friction factor increases as the pipe
diameter increases. In conclusion, using velocity which has related to flow rate to
compare the relationship with friction factor, which when the flow rate increase,
velocity of the fluid increase, the friction factor is decreases.”
6
Introduction
“As the significance of fluid mechanics is known in our every day lives. Since
it has boundless applications to automobiles, airplane, and spacecraft, for example,
microscopic biological system. Physical science which manages both fixed and moving
bodies affected by force is fluid mechanics. The consistent domain in fluid mechanics
doesn't hold explicit calculation as in various applications, with position and time the
density of liquid fluctuates. Moreover, mechanical and kinematics conduct of material
in the fluid mechanics is a bit determined mechanics because its displayed as a
consistent mass rather than discrete particles.”
“When fluid flow through pipes, pressure loss (friction) occurs in pipes stream
or passage of pipes. This is because of the impact of liquid consistency of pipes or duct
surface. There are two types of liquid stream turbulent flow and laminar flow.The flow
of water in very smoothly and noticeable is laminar flow whereas turbulent flow, where
the water flows spontaneously, causing it impossible to predict the flow surrounding it.
Turbulent flow can impact the pipes which cause vibration and it will lead in failure.
Furthermore, to identify the type of flow, Reynolds number must be known. Reynold
number predicts the stream design in various fluid flow circumstances, the following
mathematical expression shows if:”
“Turbulent Flow, Re > 4000”
“Transitional Flow, 2300 < Re < 4000”
“Laminar Flow, Re < 2300”
“Usually Re > 4000 for flow in most piping systems”
Figure 1 Types of flow
Introduction
“As the significance of fluid mechanics is known in our every day lives. Since
it has boundless applications to automobiles, airplane, and spacecraft, for example,
microscopic biological system. Physical science which manages both fixed and moving
bodies affected by force is fluid mechanics. The consistent domain in fluid mechanics
doesn't hold explicit calculation as in various applications, with position and time the
density of liquid fluctuates. Moreover, mechanical and kinematics conduct of material
in the fluid mechanics is a bit determined mechanics because its displayed as a
consistent mass rather than discrete particles.”
“When fluid flow through pipes, pressure loss (friction) occurs in pipes stream
or passage of pipes. This is because of the impact of liquid consistency of pipes or duct
surface. There are two types of liquid stream turbulent flow and laminar flow.The flow
of water in very smoothly and noticeable is laminar flow whereas turbulent flow, where
the water flows spontaneously, causing it impossible to predict the flow surrounding it.
Turbulent flow can impact the pipes which cause vibration and it will lead in failure.
Furthermore, to identify the type of flow, Reynolds number must be known. Reynold
number predicts the stream design in various fluid flow circumstances, the following
mathematical expression shows if:”
“Turbulent Flow, Re > 4000”
“Transitional Flow, 2300 < Re < 4000”
“Laminar Flow, Re < 2300”
“Usually Re > 4000 for flow in most piping systems”
Figure 1 Types of flow
7
Theory.
“When a gas or a liquid flow through a pipe, the flow of fluid through a pipe is
resisted by viscous shear stresses within the fluid and the turbulence that occurs along
the internal pipe wall. Due to this there will be a loss of pressure in the fluid, because
energy is required to overcome the viscous or frictional forces exerted by the walls of
the pipe on the moving fluid. In addition to the energy lost due to frictional forces, there
will be a loss in energy when the fluid flows through fittings, such as valves, elbows,
contractions and expansions. This loss in pressure is mainly due to the local flow
separation as it moves through such fittings. The pressure loss in pipe flows is
commonly referred to as head loss. The frictional losses are mainly caused in a straight
pipe, friction loss induced in fittings, such as bends, couplings, valves, or transitions in
hose or pipe accounts for minor losses. The frictional losses are referred to as major
losses (hf) while losses through fittings, etc, are called minor losses (hm). Together they
make up the total head losses (h) for pipe flows.”
Figure 2 Types of fittings
“In practice, loss in a pipe flow comes into picture in cases like calculation of
rate of flow in the pipes connecting two reservoirs at different levels or to calculate the
additional head required to double the rate of flow along an existing pipeline. These
pipe losses are dependent on number of factors like viscosity of the fluid, the size of
the internal pipe diameter, the internal roughness of the inner surface of the pipe, the
Theory.
“When a gas or a liquid flow through a pipe, the flow of fluid through a pipe is
resisted by viscous shear stresses within the fluid and the turbulence that occurs along
the internal pipe wall. Due to this there will be a loss of pressure in the fluid, because
energy is required to overcome the viscous or frictional forces exerted by the walls of
the pipe on the moving fluid. In addition to the energy lost due to frictional forces, there
will be a loss in energy when the fluid flows through fittings, such as valves, elbows,
contractions and expansions. This loss in pressure is mainly due to the local flow
separation as it moves through such fittings. The pressure loss in pipe flows is
commonly referred to as head loss. The frictional losses are mainly caused in a straight
pipe, friction loss induced in fittings, such as bends, couplings, valves, or transitions in
hose or pipe accounts for minor losses. The frictional losses are referred to as major
losses (hf) while losses through fittings, etc, are called minor losses (hm). Together they
make up the total head losses (h) for pipe flows.”
Figure 2 Types of fittings
“In practice, loss in a pipe flow comes into picture in cases like calculation of
rate of flow in the pipes connecting two reservoirs at different levels or to calculate the
additional head required to double the rate of flow along an existing pipeline. These
pipe losses are dependent on number of factors like viscosity of the fluid, the size of
the internal pipe diameter, the internal roughness of the inner surface of the pipe, the
8
change in elevation between the ends of the pipe, material of the pipe and the length of
the pipe along which the fluid travels.”
“Pipes with smooth surface does not account for larger friction loss, whereas
pipes with less smooth walls such as concrete, cast iron and steel fluid requires large
energy to overcome the friction induced in a pipe due to the viscosity of liquid. Rougher
the inner wall of the pipe, more will be the pressure loss due to friction.”
Figure 3 Internal surface of smooth and rough pipes
Figure 4 Flow shape
(Source: Haung et al 2013)
change in elevation between the ends of the pipe, material of the pipe and the length of
the pipe along which the fluid travels.”
“Pipes with smooth surface does not account for larger friction loss, whereas
pipes with less smooth walls such as concrete, cast iron and steel fluid requires large
energy to overcome the friction induced in a pipe due to the viscosity of liquid. Rougher
the inner wall of the pipe, more will be the pressure loss due to friction.”
Figure 3 Internal surface of smooth and rough pipes
Figure 4 Flow shape
(Source: Haung et al 2013)
9
Friction loss in pipe
“The friction loss in a uniform, straight sections of pipe, known as "major loss",
is caused by the effects of viscosity, the movement of fluid molecules against each other
or against the (possibly rough) wall of the pipe. Here, it is greatly affected by whether
the flow is laminar or turbulent. Laminar Flow: It occurs when the fluid flows in parallel
layers without adjacent mixing between the layers. In this type of flow there are neither
eddies nor cross currents, with fast flow over the centre part of the pipe and no
movement near the pipe surface. The roughness of the pipe surface influences neither
the fluid flow nor the friction loss. For laminar flow Reynoldsâ €™s number (Re) <
2100.”
“Turbulent Flow, it occurs when the liquid is moving fast with mixing between
layers. The speed of the fluid at a point continuously undergoes changes in both
magnitude and direction. For turbulent flow Reynolds's number 2100 < Re < 4000”
“Transitional flow: is a mixture of laminar and turbulent flow, with turbulence
flow in the centre of the pipe and laminar flow near the edges of the pipe. Each of these
flows behaves in different manners in terms of their frictional energy loss while flowing
and have different equations that predict their behaviour. For transitional flow
Reynolds's number Re > 4000.”
“It is useful to characterize that roughness as the ratio of the roughness height k
to the pipe diameter D, the relative roughness. Three sub-domains pertain to turbulent
flow:”
“In the smooth pipe domain, friction loss is relatively insensitive to
roughness.”
“In the rough pipe domain, friction loss is dominated by the relative
roughness and is insensitive to Reynolds number.”
“In the transition domain, friction loss is sensitive to both.”
“The Darcy Equation is a theoretical equation that predicts the frictional energy
loss in a pipe based on the velocity of the fluid and the resistance due to friction. It is
used almost exclusively to calculate head loss due to friction in turbulent flow.”
Friction loss in pipe
“The friction loss in a uniform, straight sections of pipe, known as "major loss",
is caused by the effects of viscosity, the movement of fluid molecules against each other
or against the (possibly rough) wall of the pipe. Here, it is greatly affected by whether
the flow is laminar or turbulent. Laminar Flow: It occurs when the fluid flows in parallel
layers without adjacent mixing between the layers. In this type of flow there are neither
eddies nor cross currents, with fast flow over the centre part of the pipe and no
movement near the pipe surface. The roughness of the pipe surface influences neither
the fluid flow nor the friction loss. For laminar flow Reynoldsâ €™s number (Re) <
2100.”
“Turbulent Flow, it occurs when the liquid is moving fast with mixing between
layers. The speed of the fluid at a point continuously undergoes changes in both
magnitude and direction. For turbulent flow Reynolds's number 2100 < Re < 4000”
“Transitional flow: is a mixture of laminar and turbulent flow, with turbulence
flow in the centre of the pipe and laminar flow near the edges of the pipe. Each of these
flows behaves in different manners in terms of their frictional energy loss while flowing
and have different equations that predict their behaviour. For transitional flow
Reynolds's number Re > 4000.”
“It is useful to characterize that roughness as the ratio of the roughness height k
to the pipe diameter D, the relative roughness. Three sub-domains pertain to turbulent
flow:”
“In the smooth pipe domain, friction loss is relatively insensitive to
roughness.”
“In the rough pipe domain, friction loss is dominated by the relative
roughness and is insensitive to Reynolds number.”
“In the transition domain, friction loss is sensitive to both.”
“The Darcy Equation is a theoretical equation that predicts the frictional energy
loss in a pipe based on the velocity of the fluid and the resistance due to friction. It is
used almost exclusively to calculate head loss due to friction in turbulent flow.”
10
“Where:”
“hf = Friction head loss”
“f = Darcy resistance factor”
“L = Length of the pipe”
“D = Pipe diameter”
“v = Mean velocity”
“g = acceleration due to gravity”
“In turbulent flow, the friction factor, f depends upon the Reynolds number and
on the relative roughness of the pipe, k/D, where, k is the roughness parameter and D
is the inner diameter of the pipe. When k is very small compared to the pipe diameter
D i.e., k/D > 0, f depends only on Re. When k/D is a significant value, at low Re, the
flow can be considered as in smooth regime (no effect of roughness). As Re increases,
the flow becomes transitionally rough, called as transition regime in which the friction
factor rises above the smooth value and is a function of both k and Re and Re increases
more and more the flow eventually reaches a fully rough regime in which f is
independent of Re. For design purposes, the frictional characteristics of round pipes,
both smooth and rough are summarized by the friction factor chart, which is a log-log
of fanning friction factor vs Re which is based on Moody's chart.”
Figure 5 Reynold number vs friction coefficient
“Where:”
“hf = Friction head loss”
“f = Darcy resistance factor”
“L = Length of the pipe”
“D = Pipe diameter”
“v = Mean velocity”
“g = acceleration due to gravity”
“In turbulent flow, the friction factor, f depends upon the Reynolds number and
on the relative roughness of the pipe, k/D, where, k is the roughness parameter and D
is the inner diameter of the pipe. When k is very small compared to the pipe diameter
D i.e., k/D > 0, f depends only on Re. When k/D is a significant value, at low Re, the
flow can be considered as in smooth regime (no effect of roughness). As Re increases,
the flow becomes transitionally rough, called as transition regime in which the friction
factor rises above the smooth value and is a function of both k and Re and Re increases
more and more the flow eventually reaches a fully rough regime in which f is
independent of Re. For design purposes, the frictional characteristics of round pipes,
both smooth and rough are summarized by the friction factor chart, which is a log-log
of fanning friction factor vs Re which is based on Moody's chart.”
Figure 5 Reynold number vs friction coefficient
11
“V = Flow Velocity”
“D = Length of the fluid”
“ρ = Fluid density (
??????�
�
2
)”
“μ = Dynamic viscosity (Pa s)”
“V = Kinematic viscosity
�
2
�
=
??????
�
”
Figure 6 Figure 2 : Reynolds Number (Re)
“Friction losses in pipes consider as a complex system geometry in the flow
capacity and the fluid properties of the system. By looking into the mathematical
equation of the square of the flow rate proportional to the head loss. This expression
will lead to the Darcy equation which will allow us to understand many things for the
loss due to friction in pipes. The Darcy equation as shown:”
“APL major loss = Friction pressure loss in fluid flow (Pa(N/m2), psf (lb/ft2).”
“ƒ = Darcy Weisbach friction coefficient”
“L = Length oƒ pipe (m)”
“ρ = Velocity ƒluid (m /s)”
“D = Hydraulic diameter (m, ƒt)”
“V = Fluid density ( kg/m3)”
“V = Flow Velocity”
“D = Length of the fluid”
“ρ = Fluid density (
??????�
�
2
)”
“μ = Dynamic viscosity (Pa s)”
“V = Kinematic viscosity
�
2
�
=
??????
�
”
Figure 6 Figure 2 : Reynolds Number (Re)
“Friction losses in pipes consider as a complex system geometry in the flow
capacity and the fluid properties of the system. By looking into the mathematical
equation of the square of the flow rate proportional to the head loss. This expression
will lead to the Darcy equation which will allow us to understand many things for the
loss due to friction in pipes. The Darcy equation as shown:”
“APL major loss = Friction pressure loss in fluid flow (Pa(N/m2), psf (lb/ft2).”
“ƒ = Darcy Weisbach friction coefficient”
“L = Length oƒ pipe (m)”
“ρ = Velocity ƒluid (m /s)”
“D = Hydraulic diameter (m, ƒt)”
“V = Fluid density ( kg/m3)”
12
Figure 7 Sample of head loss
“Using this following equation head loss can be identified:”
“Shows fluid statics AP = pgh”
“Thus, h =
??????�
�
, Head Loss= f
??????
??????
??????????????????�
2
2�
”
“One of most broad connections in fluid mechanics is the connection between
pressure loss and head loss and its significant for turbulent or laminar streams, round
or non - circular channels, rough or smooth surface pipes.”
Figure 8 Head Loss.
“Therefore, in laminar flow, relationship between the speed and head loss is
relative as opposed to speed square. Friction factor is in this way contrarily relative to
speed.”
Figure 9 (K) Geometry Factor.
Figure 7 Sample of head loss
“Using this following equation head loss can be identified:”
“Shows fluid statics AP = pgh”
“Thus, h =
??????�
�
, Head Loss= f
??????
??????
??????????????????�
2
2�
”
“One of most broad connections in fluid mechanics is the connection between
pressure loss and head loss and its significant for turbulent or laminar streams, round
or non - circular channels, rough or smooth surface pipes.”
Figure 8 Head Loss.
“Therefore, in laminar flow, relationship between the speed and head loss is
relative as opposed to speed square. Friction factor is in this way contrarily relative to
speed.”
Figure 9 (K) Geometry Factor.
13
Objective
“To determine the friction in the pipe of various diameters.”
Procedures
“A virtual laboratory was utilized for this experiment.”
“As shown in figure 6, five pipes available, and each pipes has an alternate
diameter associated with a stopwatch, differential manometer, an assortment tank,
and scale.”
Figure 10 Connection Of The Pipe System
1.“The 25mm diameter pipe has been chosen for the 1st trial as shown below:”
Figure 11 Setting the Pipe Diameter
2.“All pipes are turned off whereas chosen diameter of pipe is turned on which is 25mm
demonstrated down:”
Figure 12 Turn on inlet valve
Objective
“To determine the friction in the pipe of various diameters.”
Procedures
“A virtual laboratory was utilized for this experiment.”
“As shown in figure 6, five pipes available, and each pipes has an alternate
diameter associated with a stopwatch, differential manometer, an assortment tank,
and scale.”
Figure 10 Connection Of The Pipe System
1.“The 25mm diameter pipe has been chosen for the 1st trial as shown below:”
Figure 11 Setting the Pipe Diameter
2.“All pipes are turned off whereas chosen diameter of pipe is turned on which is 25mm
demonstrated down:”
Figure 12 Turn on inlet valve
14
3.“To flow the water through 25mm chosen pipe, the main inlet valve turned on.”
Figure 13 Turn on inlet valve
4.“When its steady flow in the pipe, change the knot to read the exact position. Turn on
the leeave estimation of collection tank to permit watar streaming in the pipe to
persistently stream outside which shown in figure below:”
Figure 14 Change manometer knot fro isolate to airvent
5.“Manometer perusing has been recorded.”
6.“This been rehashed for 3 trials, at that point followed by different measurements of
the pipe.”
3.“To flow the water through 25mm chosen pipe, the main inlet valve turned on.”
Figure 13 Turn on inlet valve
4.“When its steady flow in the pipe, change the knot to read the exact position. Turn on
the leeave estimation of collection tank to permit watar streaming in the pipe to
persistently stream outside which shown in figure below:”
Figure 14 Change manometer knot fro isolate to airvent
5.“Manometer perusing has been recorded.”
6.“This been rehashed for 3 trials, at that point followed by different measurements of
the pipe.”
15
Analysis & Results
“The experiment conducted in total of 15 times. To get the average values, three
separated trials performed for each of the five pipes. Table 1shows the values of all
trials obtain from the virtual lab.”
“Table 1: Results from 3 Trials”
“As it shows that friction factor decreases, when the diameter of the pipe
decreases. Therefore, chart underneath shows connection between friction factor and
diameter of the pipe.”
Analysis & Results
“The experiment conducted in total of 15 times. To get the average values, three
separated trials performed for each of the five pipes. Table 1shows the values of all
trials obtain from the virtual lab.”
“Table 1: Results from 3 Trials”
“As it shows that friction factor decreases, when the diameter of the pipe
decreases. Therefore, chart underneath shows connection between friction factor and
diameter of the pipe.”
16
Figure 15 Pipe Diameter and Friction Factor Graph
“Manometer displays the readings in trial 2, once set pipes diameter.”
Figure 16 Head Loss
“Head loss was determined by appling following formula since the left limb
reading (LL) is 24.25cm and right limb reading (RL) is 34cm of the manometer.”
“Head Loss (H) = 12.6(left limb — right limb)”
“Head Loss (H) = 12.6 (24.25 – 34)”
“Head Loss (H) = 12.6( -9.75 cm)”
“Head Loss (H) = - 122.85cm”
“Since there is no negative (-) head loss,”
“Head Loss (H) = 122.85cm”
“Time is noted when the exit valve is closed and shown below time taken to fill 10cm tank:”
Figure 17 Time taken to fill up 10cm tank
Figure 15 Pipe Diameter and Friction Factor Graph
“Manometer displays the readings in trial 2, once set pipes diameter.”
Figure 16 Head Loss
“Head loss was determined by appling following formula since the left limb
reading (LL) is 24.25cm and right limb reading (RL) is 34cm of the manometer.”
“Head Loss (H) = 12.6(left limb — right limb)”
“Head Loss (H) = 12.6 (24.25 – 34)”
“Head Loss (H) = 12.6( -9.75 cm)”
“Head Loss (H) = - 122.85cm”
“Since there is no negative (-) head loss,”
“Head Loss (H) = 122.85cm”
“Time is noted when the exit valve is closed and shown below time taken to fill 10cm tank:”
Figure 17 Time taken to fill up 10cm tank
17
Figure 18 Parameter and calculation by Virtual lab
“To calculate Qact (cm3/sec):”
“Qact (cm3/sec) =
??????��?????? �� �ℎ� �??????�?????? ×ℎ
�
”
“Qact (cm3/sec) =
3500 ×10
25.5
= 1372.549 (cm
3
/sec)”
“To calculate velocity:”
“Velocity (cm / sec) =
Qact
??????
”
“When the area of pipe is:”
“A = =
��
2
4
”
“Therefore,”
“Velocity (cm / sec) =
Qact
??????
”
“Velocity (cm / sec) =
1372.549
?????? × 2.5
2
4
= 279.66 (cm/sec)”
“Calculated Analytical Friction Factor using Darcy equation:”
“Friction Factor (f) =
2gd
??????
2
×
H
??????
”
“Friction Factor (f) =
×9.81×25×10
−2
279.662×10
−2
×
2× 122.85×10
−2
3
= Friction Factor (f) = 0.0257”
Figure 18 Parameter and calculation by Virtual lab
“To calculate Qact (cm3/sec):”
“Qact (cm3/sec) =
??????��?????? �� �ℎ� �??????�?????? ×ℎ
�
”
“Qact (cm3/sec) =
3500 ×10
25.5
= 1372.549 (cm
3
/sec)”
“To calculate velocity:”
“Velocity (cm / sec) =
Qact
??????
”
“When the area of pipe is:”
“A = =
��
2
4
”
“Therefore,”
“Velocity (cm / sec) =
Qact
??????
”
“Velocity (cm / sec) =
1372.549
?????? × 2.5
2
4
= 279.66 (cm/sec)”
“Calculated Analytical Friction Factor using Darcy equation:”
“Friction Factor (f) =
2gd
??????
2
×
H
??????
”
“Friction Factor (f) =
×9.81×25×10
−2
279.662×10
−2
×
2× 122.85×10
−2
3
= Friction Factor (f) = 0.0257”
18
Theoretical calculation
“To obtain the average friction factor by the three trials conducted during the
experiment. Accordingly, 1 trial was taken for calculation and 2 diameters will be
calculated for the pipe.”
“Firstly, the values are set in simulation for diameter 25mm and pipe
length,3m. Thus,”
“Reynold Number (Re) =
�VL
??????
”
“Velocity of water (ρ) = 1000”
“Valocity (V) = 279.66 (cm/sec)”
“μ. = (8.9 × 10
−4
)”
“Length (L) which is pipe diameter = 25 mm”
“Thus,”
“Reynold Number (Re) =
1000×279.6610
−2
×2510
−3
8.910
−4
”
“Reynold Number, Re = 78. 556 K”
“To figure friction factor, as demonstrated below Darcy equation used. Thus, the
roughness material (s) to be 0.045mm supposed.”
“ƒ = 0.0255.”
“Consequently, head loss determined as follows:”
“HL = 121.978 cm”
“Percentage of error formula shown below. Simulated values and calculated values are
compared. Table 2:”
“ERROR % =
Simulated Value — Calculated Value
Calculated Value
× 100”
Theoretical calculation
“To obtain the average friction factor by the three trials conducted during the
experiment. Accordingly, 1 trial was taken for calculation and 2 diameters will be
calculated for the pipe.”
“Firstly, the values are set in simulation for diameter 25mm and pipe
length,3m. Thus,”
“Reynold Number (Re) =
�VL
??????
”
“Velocity of water (ρ) = 1000”
“Valocity (V) = 279.66 (cm/sec)”
“μ. = (8.9 × 10
−4
)”
“Length (L) which is pipe diameter = 25 mm”
“Thus,”
“Reynold Number (Re) =
1000×279.6610
−2
×2510
−3
8.910
−4
”
“Reynold Number, Re = 78. 556 K”
“To figure friction factor, as demonstrated below Darcy equation used. Thus, the
roughness material (s) to be 0.045mm supposed.”
“ƒ = 0.0255.”
“Consequently, head loss determined as follows:”
“HL = 121.978 cm”
“Percentage of error formula shown below. Simulated values and calculated values are
compared. Table 2:”
“ERROR % =
Simulated Value — Calculated Value
Calculated Value
× 100”
19
“Next, the diameter of pipe is set to 15mm and length same as 3m.”
Figure 19 Parameter and Calculation by Virtual Lab
“Thus,”
“Reynold Number (Re) =
�VL
??????
”
“Reynold Number (Re) =
1000×360.2908×10
−2
×15×10
−3
8.9×10
−4
”
“Reynold Number, Re = 60.723 K”
“To figure friction factor, Darcy equation is utilized as demonstrated below.”
“Thus, the roughness material (s) 0.0001mm supposed.”
“f = 0 .01”
“Head loss determined:”
“HL = 132.32 cm”
“Next, the diameter of pipe is set to 15mm and length same as 3m.”
Figure 19 Parameter and Calculation by Virtual Lab
“Thus,”
“Reynold Number (Re) =
�VL
??????
”
“Reynold Number (Re) =
1000×360.2908×10
−2
×15×10
−3
8.9×10
−4
”
“Reynold Number, Re = 60.723 K”
“To figure friction factor, Darcy equation is utilized as demonstrated below.”
“Thus, the roughness material (s) 0.0001mm supposed.”
“f = 0 .01”
“Head loss determined:”
“HL = 132.32 cm”
20
Discussion
“Based on the result of the experiment, there are many things that can be
discussed regards to the data observed. Beginning to explain about the experiment
conducted through the virtual lab, there are 5 pipes with various diameters to set for
water flow. In this experiment, each pipe has performed 3 trials to get an average
friction factor. The relationship between the head loss and the velocity has been shown
in figure 9, which when the flow rate increases, the velocity of the fluid increase, the
head loss increases. The friction factor is proportional to the pipe diameter. Which
velocity is related to the flow rate from the equation:”
Q =
V
�
“Where,”
“Q = Flow rate”
“V = Velocity”
“T = Time.”
“Begin with the results from 25 mm pipe clearly observed from 3 trials that one
of it are well off the head loss range compared to other trials. As shown in Table 1, for
the 2nd and 3rd trials the head loss is 135.45cm and friction factor 0.026 and the average
friction factor is 0.03. This might be human error or an instrumental error as this was
done by virtual lab.”
“Next, friction factor remained within 0. 001 to 0. 011 in all the three trials
whereas the average was 0.01. Furthermore, as it comes to head loss the pipe had 3
different readings which was between 119.7 to 81.9 cm. End of the experiment, its
proven that Reynold number, Re is more than 4000 and friction factor esteem gives an
implying that the stream is hydraulically smooth. This can be effectively seen by
observing Moody's chart below:”
Discussion
“Based on the result of the experiment, there are many things that can be
discussed regards to the data observed. Beginning to explain about the experiment
conducted through the virtual lab, there are 5 pipes with various diameters to set for
water flow. In this experiment, each pipe has performed 3 trials to get an average
friction factor. The relationship between the head loss and the velocity has been shown
in figure 9, which when the flow rate increases, the velocity of the fluid increase, the
head loss increases. The friction factor is proportional to the pipe diameter. Which
velocity is related to the flow rate from the equation:”
Q =
V
�
“Where,”
“Q = Flow rate”
“V = Velocity”
“T = Time.”
“Begin with the results from 25 mm pipe clearly observed from 3 trials that one
of it are well off the head loss range compared to other trials. As shown in Table 1, for
the 2nd and 3rd trials the head loss is 135.45cm and friction factor 0.026 and the average
friction factor is 0.03. This might be human error or an instrumental error as this was
done by virtual lab.”
“Next, friction factor remained within 0. 001 to 0. 011 in all the three trials
whereas the average was 0.01. Furthermore, as it comes to head loss the pipe had 3
different readings which was between 119.7 to 81.9 cm. End of the experiment, its
proven that Reynold number, Re is more than 4000 and friction factor esteem gives an
implying that the stream is hydraulically smooth. This can be effectively seen by
observing Moody's chart below:”
21
Conclusion
“Experiment was effectively accomplished utilizing virtual lab. As for the
calculation part, pipe diameter of 25mm and 15mm which were tested are compared.
As it is noticed, as the velocity of the fluid flow increases, the head loss increases.
Besides, the friction factor increases as the pipe diameter increases. In conclusion, using
velocity which has related to flow rate to compare the relationship with friction factor,
which when the flow rate increase, velocity of the fluid increase, the friction factor is
decreases.”
Conclusion
“Experiment was effectively accomplished utilizing virtual lab. As for the
calculation part, pipe diameter of 25mm and 15mm which were tested are compared.
As it is noticed, as the velocity of the fluid flow increases, the head loss increases.
Besides, the friction factor increases as the pipe diameter increases. In conclusion, using
velocity which has related to flow rate to compare the relationship with friction factor,
which when the flow rate increase, velocity of the fluid increase, the friction factor is
decreases.”
22
REFERENCES
P.N Modi and S.M.Seth, “Hydraulics and Fluid Mechanics�,
Standard Book House, Delhi, 2010.
Miller, R. W., Flow Measurement Engineering Handbook, Second Edition,
McGraw-Hill, 1989.
Madan Mohan Das, Fluid Mechanics and Turbo Machines, PHI Learning
Pvt. Ltd, 2008.
REFERENCES
P.N Modi and S.M.Seth, “Hydraulics and Fluid Mechanics�,
Standard Book House, Delhi, 2010.
Miller, R. W., Flow Measurement Engineering Handbook, Second Edition,
McGraw-Hill, 1989.
Madan Mohan Das, Fluid Mechanics and Turbo Machines, PHI Learning
Pvt. Ltd, 2008.
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