Hydraulics Unit 43: Fluid Mechanics and Pipeline Design

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Unit 43 Hydraulics

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Table of Contents
Introduction......................................................................................................................................3
LO1 Deep Analysis Of Water Internal Friction And The Pipeline.................................................4
1-A Selection Of A Pipeline And The Materials Used For Adjusting The Friction And
Viscosity Problems......................................................................................................................4
1-B Laminar And The Turbulent Flow......................................................................................5
1-B Absolute And The Kinetic Coefficient Of Viscosity..........................................................5
1-C Froude And Reynolds Numbers.........................................................................................0
1-D Transformation Of Laminar And Turbulent Flow..............................................................0
1-E Calculation Of Froude And Reynolds Number...................................................................1
Commenting About The Type Of Flow...................................................................................3
LO2 Calculation Of Fluid Forces At Repose Or In-Wave..............................................................5
2-A Pipeline Average Flow Velocity........................................................................................5
2-B Calculation Of Hydraulic Radius.........................................................................................6
1) Hydraulic Radius Of Pipe....................................................................................................6
2) Hydraulic Radius Of Rectangular Chanel...........................................................................7
Effect Of Cross-Sectional Shape On Hydraulic Radius..........................................................8
Conclusion...............................................................................................................................9
2-C Open Channel Flow Velocity And Total Delivery Rate.....................................................9
Practical Solutions In Notch Weirs........................................................................................10
LO3 Circulation Of Fluids Inside Suitably Sized Pipelines..........................................................11
3-A Deepness Of Water Flowing In An Open Horizontal Channel........................................11
3-B Constant Width Of A Water Channel With Same Depth..................................................12
3-C Calculation Of Pressure Loss Using Darcy Weisbach Pressure Equation........................12
3-D Calculation Of Head Loss And Delivery Rate Using Darcy Weisbach Equation.............13

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3-E Head Loss Calculation...................................................................................................13
3-F Head Loss When Level Of Upper Reservoir Went Down By 5m................................14
3-G Effect Of Varying DW Friction Factor On Head Loss And Delivery Rate.................15
3-H Justifying Results For The Orifice And Jet Experiment...................................................17
LO4 Computing Hydrostatic Pressure For Substructures Of Given Context................................20
4-A Calculation Of Force On Rectangular Cassion Depth.......................................................20
4-B Calculation Of Force On Circular Cassion Depth.............................................................20
Comparing With Rectangular Cassion Force............................................................................21
References......................................................................................................................................22
List of Figures
Figure 1: Laminar Flow...................................................................................................................5
Figure 2: Turbulent Flow.................................................................................................................5
Figure 3 Transition in flows of a pipeline.......................................................................................1
Figure 4 Pipeline for velocity flow calculation...............................................................................5
Figure 5 Water head graph with velocity........................................................................................6
Figure 6: Two Channel Cross Section.............................................................................................8
Figure 7: Open channel water flow in a pipeline...........................................................................11
List of Tables
Table 1 Difference table of Froude and Reynolds numbers............................................................0
Table 2 Rectangular weir results...................................................................................................10
Table 3 V-notch weir results..........................................................................................................10
Table 4: Comparison Sheet of Experimental vs Calculated Data..................................................18

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Introduction
I have analyzed learning outcomes of this report as per given scenario. This reports highlights the
deep analysis of water internal friction within the pipeline discussing the viscosity and friction
measures related to it. The Froude and Reynolds numbers are also being analyzed and computed
according to the given conditions. I have also analyzed the calculations of fluid forces both static
and in-wave. It was also practically seen that how to fit fluids in different sized pipes.

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LO1 Deep Analysis Of Water Internal Friction And The Pipeline
1-A Selection Of A Pipeline And The Materials Used For Adjusting The
Friction And Viscosity Problems
Viscosity of water
As we know that in liquids molecular forces are greater than in gases, they exert a strong force of
attraction on each other. We can easily find the type of pipeline if we know the viscosity. We
have to add some more shear resistance in a pipeline if the viscosity at any point increases. When
the viscosity increases, there occurs a less pressure and an abundant increase in the consumption
of the power.
Friction
If there are friction problems inside a pipeline it can reduce the efficiency of pipe and its
throughput. It demands much more repair which will increase the cost of system. As the losses in
friction affects the performance of a pipeline and loss in it will definitely cause bad flow rate and
pressure inside the pipeline.
Things that causes friction in a pipeline
 Valves
 Bends
 Fittings
 Expansion joints
Friction between the water and pipeline must be consider because it can affect our system in
future. Diameter of the pipeline must be greater than we calculated in starting when we are using
the metal piping system, because of the only friction problem we have.

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1-B Laminar And The Turbulent Flow
Laminar flow
Flow will be laminar whenever the
streamlines are parallel. Streamlines are the
supposed lines which would have no
perpendicular surface. As we are taking the
flow in parallel surfaces, we will take in
account that the flow consists of some
laminar lines that are parallel.
Figure 1: Laminar Flow
Turbulent flow
Flow will be turbulent whenever there exists
a breakage of stream lines and the fluids at a
pint get mixed, a very high velocity will
reach at that point. This happens because of
the loss in energy and the fluid heat up.
Figure 2: Turbulent Flow
1-B Absolute And The Kinetic Coefficient Of Viscosity
Absolute coefficient of viscosity
When we calculate the internal resistance we
take in account the concept of absolute
viscosity. When there exists a movement of
one horizontal plane with regard to another
one which requires a specific tangential
force per unit area with a unit velocity, we
will refer it as the absolute coefficient of
viscosity (Alomair, 2016).
It is given as
Units are kg/ms and Ns/m^2
Kinetic coefficient of viscosity
When we calculate the ratio of absolute
coefficient of velocity to density, it will be
referred as kinetic coefficient of viscosity.
Keep in mind that it includes no other forces
(Yang, 2016).
It is given as
Its unit is (m^2/s)

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1-C Froude And Reynolds Numbers
Table 1 Difference table of Froude and Reynolds numbers
Froude numbers Reynolds numbers
It is the relationship between the inertial
forces and the gravity.
It is the relationship between inertial and the
frictional forces (Erturk, 2018).
Smaller FORCE Larger flow
Laminar flow Turbulent flow
F= f turbulent
f gravitational
= U
gy
1
2
U= mean velocity
Y= Horizontal depth
R= f turbulent
f viscous
=Uy
v
U= mean velocity
Y= Horizontal depth
1-D Transformation Of Laminar And Turbulent Flow
During the laminar flow
Whenever the fluid flow increases there exists a transition in laminar flow. Transition occur at
moderate speed. At higher speed there exists a turbulent flow. There would be laminar flow at
slow speed.
Consider a Reynolds experiment.
He performed the experiment in (1842-1912). He considered a glass tube and then inserted a dye
in it. He observed that during the small speed flow was laminar but little lighter because of the
dye, when the speed of the flow was increased, a transition in the flow occurred and a blast
occurred, When the speed was further increased he saw that the whole pipe was filled with dye
making the flow blurred (Tsompanas, 2018).

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Figure 3 Transition in flows of a pipeline
1-E Calculation Of Froude And Reynolds Number
Solution:
Given Data
Width of the open channel=2 m
flow rate of the water =v =5 m s−1
Viscosity =μ=8.9 ×10−4 Pa
Density of water=ρ=1000 kg m−3
To Find
Calculaiton of Froude number=Fr =?
Calculation of Reynolds Number =Re=?
Calculaiton of Type of fluid ( laminar∨turbulent )=?
Formulas to be used
Froude number=Fr = V
(gD)1 /2
Here,
D=diamter
V =velocity
g=gravitaional accelaration
Reynolds Number =Re= ρ× V × D
μ
Here,
ρ=density

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V =velocity
D=diameter
μ=viscosity
Calculation of Froude number
Froude number=Fr = V
( gD)1 /2
For D=0.5m.
Here V=5, g= 9.8 and D=0.5. So, by substituting the values of D, g and V in the above equation
we get:
Froude number=Fr = 5
(9.8 ×0.5)1 /2
Fr= 5
( 4.9)1/ 2
Fr= 5
2.2135
Fr=2.258
Hence the value of Froude no. for diameter 0.5m is 2.258
For D=2.
Here V=5, g= 9.8 and D=2By substituting the values of D, g and V in the above equation we get:
Froude number=Fr = 5
(9.8 ×2)1/ 2
Fr= 5
(19.6)1 /2
Fr= 5
4.427
Fr=1.057
Hence the value of Froude no. for diameter 2m is 1.057
Calculation of Reynolds Number
Reynolds Number =Re= ρ× V × D
μ

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For D=0.5m.
Here V=5, ρ=1000 , μ=8.9× 10−4and D=0.5. So, by substituting the values of D, μ ,V and ρ in
the above equation we get:
Re= ρ ×V × D
μ
Re= 1000 ×5 ×0.5
8.9× 10− 4
Re= 1000 ×5 ×0.5
0.00089
Re= 2500
0.00089
Re=2808988.7
Hence the value of Reynolds no. for diameter 0.5m is 2808988.7
For D=2m.
Here V=5, ρ=1000 , μ=8.9× 10−4and D=2. So, by substituting the values of D, μ ,V and ρ in the
above equation we get:
Re= ρ ×V × D
μ
Re= 1000 ×5 ×2
8.9× 10−4
Re= 1000 ×5 ×2
0.00089
Re= 10000
0.00089
Re=11235955.05
Hence the value of Reynolds no. for diameter 2m is 11235955.05
Commenting About The Type Of Flow
As we know that the type of flow depends of the Reynolds number. The relation between the
type of flow and Reynolds number is given as follows:
Re >2000 →the type of flow would be Laminar
Re <2000 →the type of flow would be Turbulnet

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So, If Reynolds number is greater than 2000 then the flow in the tube would be laminar and if it
is less than 2000 then it would be turbulent.
In 1st case Reynolds no. for diameter 0.5m is 2808988.7 which is greater than 2000 so it is
laminar. In 2nd Case of Reynolds no. for diameter 2m is 11235955.05 which is greater than 2000
so it is laminar.

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LO2 Calculation Of Fluid Forces At Repose Or In-Wave
2-A Pipeline Average Flow Velocity
Bernoulli’s equation
P+ 1
2 ρ v2 + ρgh=c
Calculation of Velocity flow rate in terms of Bernoulli’s equation:
Let’s suppose that the pipeline has constant hydraulic pressure.
Figure 4 Pipeline for velocity flow calculation
Supposition:
h 1=h2
v 2=0
Given:
ΔP=P 2−P 1
Δh=h 2−h 1
g=Gravity
c=coefficient used on thebasis of a fluid∧units
Calculation:
P 1+0.5 ρV 12=P 2
V 1=(2∗(P2−P1)/ ρ)1/ 2
¿( 2∗(P 2−P1)/ ρ)1 /2
Using the criteria ΔP=P 2−P 1 , Δh=h 2−h 1, Bernoulli equation can be expressed in terms of
average flow velocity of fluid flowing in a pipeline.
V 1=c∗(2 g∗Δh)1/ 2