This document summarizes an experiment analyzing potential flow theory for fluid flowing around a cylinder. Potential flow theory assumes an inviscid fluid and cannot account for drag. The experiment measured pressure coefficients around a cylinder in a wind tunnel and compared the results to potential flow theory. As expected, the experimental results showed drag due to viscosity that the theory could not capture. The boundary layer separation point varied with Reynolds number, supporting that viscosity affects the flow behavior.
Fluid Mechanics Chapter 4. Differential relations for a fluid flowAddisu Dagne Zegeye
Introduction, Acceleration field, Conservation of mass equation, Linear momentum equation, Energy equation, Boundary condition, Stream function, Vorticity and Irrotationality
Fluid Mechanics Chapter 4. Differential relations for a fluid flowAddisu Dagne Zegeye
Introduction, Acceleration field, Conservation of mass equation, Linear momentum equation, Energy equation, Boundary condition, Stream function, Vorticity and Irrotationality
Dimensional analysis Similarity laws Model laws R A Shah
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Forces on Fluid
Dimensionless Numbers
Model laws
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Dimension less numbers in applied fluid mechanicstirath prajapati
In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned. It is also known as a bare number or pure number or a quantity of dimension one[1] and the corresponding unit of measurement in the SI is one (or 1) unit[2][3] and it is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Examples of quantities, to which dimensions are regularly assigned, are length, time, and speed, which are measured in dimensional units, such as meter , second and meter per second. This is considered to aid intuitive understanding. However, especially in mathematical physics, it is often more convenient to drop the assignment of explicit dimensions and express the quantities without dimensions, e.g., addressing the speed of light simply by the dimensionless number 1.
Dimensional analysis Similarity laws Model laws R A Shah
Rayleigh's method- Theory and Examples
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Model and Similitude
Forces on Fluid
Dimensionless Numbers
Model laws
Distorted models
Dimension less numbers in applied fluid mechanicstirath prajapati
In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned. It is also known as a bare number or pure number or a quantity of dimension one[1] and the corresponding unit of measurement in the SI is one (or 1) unit[2][3] and it is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Examples of quantities, to which dimensions are regularly assigned, are length, time, and speed, which are measured in dimensional units, such as meter , second and meter per second. This is considered to aid intuitive understanding. However, especially in mathematical physics, it is often more convenient to drop the assignment of explicit dimensions and express the quantities without dimensions, e.g., addressing the speed of light simply by the dimensionless number 1.
Prezentacija o iskustvu sa stručnog usavršavanja financiranog iz Programa za cjeloživotno učenje. Prezentirana je tema sustavnog vođenja iz pozicije CARNeta.
El 80% de tus clientes están respresentados por un buyer persona con patrones comunes. ¿Los conoces? Tu organización debe tener claro quién es su buyer persona y el momento que están preparados para la venta. Todo tiene que estar alineado y en coherencia con la misión y visión de tu organización.
lab 4 requermenrt.pdf
MECH202 – Fluid Mechanics – 2015 Lab 4
Fluid Friction Loss
Introduction
In this experiment you will investigate the relationship between head loss due to fluid friction and
velocity for flow of water through both smooth and rough pipes. To do this you will:
1) Express the mathematical relationship between head loss and flow velocity
2) Compare measured and calculated head losses
3) Estimate unknown pipe roughness
Background
When a fluid is flowing through a pipe, it experiences some resistance due to shear stresses, which
converts some of its energy into unwanted heat. Energy loss through friction is referred to as “head
loss due to friction” and is a function of the; pipe length, pipe diameter, mean flow velocity,
properties of the fluid and roughness of the pipe (the later only being a factor for turbulent flows),
but is independent of pressure under with which the water flows. Mathematically, for a turbulent
flow, this can be expressed as:
hL=f
L
D
V
2
2 g
(Eq.1)
where
hL = Head loss due to friction (m)
f = Friction factor
L = Length of pipe (m)
V = Average flow velocity (m/s)
g = Gravitational acceleration (m/s^2)
Friction head losses in straight pipes of different sizes can be investigated over a wide range of
Reynolds' numbers to cover the laminar, transitional, and turbulent flow regimes in smooth pipes. A
further test pipe is artificially roughened and, at the higher Reynolds' numbers, shows a clear
departure from typical smooth bore pipe characteristics.
Experiment 4: Fluid Friction Loss
The head loss and flow velocity can also be expressed as:
1) hL∝V −whe n flow islaminar
2) hL∝V
n
−whe n flow isturbulent
where hL is the head loss due to friction and V is the fluid velocity. These two types of flow are
seperated by a trasition phase where no definite relationship between hL and V exist. Graphs
of hL −V and log (hL) − log (V ) are shown in Figure 1,
Figure 1. Relationship between hL ( expressed by h) and V ( expressed by u ) ;
as well as log (hL) and log ( V )
Experiment 4: Fluid Friction Loss
Experimental Apparatus
In Figure 2, the fluid friction apparatus is shown on the right while the Hydraulic bench that
supplies the water to the fluid friction apparatus is shown on the left. The flow rate that the
hydraulic bench provides can be measured by measuring the time required to collect a known
volume.
Figure 2. Experimental Apparatus
Experimental Procedure
1) Prime the pipe network with water by running the system until no air appears to be discharging
from the fluid friction apparatus.
2) Open and close the appropriate valves to obtain water flow through the required test pipe, the four
lowest pipes of the fluid friction apparatus will be used for this experiment. From the bottom to the
top, these are; the rough pipe with large diameter and then smooth pipes with three successively
smaller diameters.
3) Measure head loss ...
Cfd Simulation and Experimentalverification of Air Flow through Heated PipeIOSR Journals
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Numerical Study of Forced Convection in a Rectangular Channel
Original Research Article
Journal of Chemistry and Materials Research Vol. 1 (1), 2014, 7–11
Salim Gareh
Numerical Investigation of Mixed Convective Flow inside a Straight Pipe and B...iosrjce
The present study deals with a numerical investigation of steady laminar and turbulent mixed
convection heat transfer in a horizontal pipe and bend pipe using air as the working fluid.The thermal boundary
condition chosen is that of uniform temperature at the outer wall. Computations were performed to investigate
the effect of inlet Rayleigh number and Reynolds number in the velocity and temperature profile at inside of the
pipe. The secondary flow is more intense in the upper part of the cross-section. It increases throughout the
cross-section until its intensity reaches a maximum, and then it becomes weak at far downstream. For the
horizontal pipe the value of the L/D ratio becomes more than 10 the secondary flow effects are neutralized and
the velocity profile almost become constant throughout.
Effect of Geometry on Variation of Heat Flux and Drag for Launch Vehicle -- Z...Abhishek Jain
Above Research Paper can be downloaded from www.zeusnumerix.com
The research paper aims at studying the variation of the geometry of the launch vehicle nose and its effect on heat flux. CFDExpert software is first validated on NASA's hyperballistic model and then used on proposed geometries. Various nose radius and blending shapes are studied for effect on drag and heat flux. Cone ogive shape is found to decrease heat flux with an insignificant increase in drag. Authors Abhishek Jain (Zeus Numerix), Rohan Kedar and Prof V Kalamkar (SPCOE).
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The effect of finite volume fraction of suspended particulate matter on axially symmetrical jet mixing of incompressible dusty fluid has been considered. Here we are assuming the velocity and temperature in the jet to differ only slightly from that of surrounding stream, a perturbation method has been employed to linearize the equation those have been solved by using Laplace Transformation technique. Numerical computations have been made to find the solutions of the longitudinal perturbed fluid velocity and longitudinal perturbed particle velocity.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
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Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
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Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
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• Compatible with MAFI CCR system
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• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
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My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
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1. 1
Abstract
During this experiment, we will analyze one of
the first applications of the potential flow
theory, the cylindrical test in a tunnel wind.
Throughout this report, we will determine the
differences between the theory and the practical
results getting to describe them by the
information obtained from the pressure
coefficients, because is by the pressure
coefficients that a difference will be noted due
to a fundamental assumption made during the
development of the potential theory, that is to
consider an non-viscous fluid. Also due to this
assumption, we will get to discover the
Alembert´s Paradox that states the non-
presence of drag in the theory but strongly
contradicted by the experimental results.
The realization of this experiment and
report will provide us the sufficient material to
study and comprehend the correlation between
the theoretical and practical results that any
person will get if they commit to study
aerodynamics.
Introduction
Potential Flow Theory
The experiment of a fluid flowing and
surrounding a cylinder can be mathematically
explained by the superposition of a doublet and
uniform flow, presented in the Potential Flow
Theory.
In the figure 1, it can be appreciated
how the superposition of those kinds of flow
create the flow around a cylinder.
Fig. 1. - Superposition of the types of flow uniform and
doublet to create flow around a cylinder.
According to the next chart, the equations that
describes the potential fluid are [1]
:
Chart 1. - Stream functions and potential functions for
elementary flow.
Ψ = Ψuniform flow + Ψdoublet =
U r sinθ – B/r sinθ (1)
Φ = Φuniform flow + Φdoublet =
U r cosθ + B/r cosθ (2)
PRESSION DISTRIBUTION AROUND A CILINDER AND
COMPARISON WITH POTENTIAL FLOW THEORY
Rodríguez Cárdenas Jesús Guillermo, Martínez Ruiz Pablo Elías, Cisneros Moreno Víctor
José.
Potential Flow Theory: Theory that says that the flow does not loose energy when passes
through the surface of a body.
Doublet: Type of flow that in conjunction with uniform flow creates de flow around a cylinder.
2. Jesús Guillermo Rodríguez Cárdenas, Pablo Elías Martínez Ruiz, Victor José Cisneros Moreno
2
The flow line that is on the stagnation point
always have the value of zero confirming the
condition of 𝑟 = √𝐵/𝑈 as a constant. Due to
the fact that the velocity is tangential to the
streamlines, the velocity Vr being
perpendicular to a circle of radius 𝑟 = 𝑅 =
√𝐵/𝑈 equals zero, it means that the circle can
be considerate as a streamline of the flow.
Replacing 𝑅2
𝑈 instead of B and deriving dΨ/dr
and dΦ/dr the functions of the streamline
velocity components are obtained:
According to the condition of R=r, Vr
will be zero, thus:
So with 𝜃 = 0 𝑜𝑟 𝜋 evaluation the velocity will
be null, corroborating that the stagnation points
can be evaluated and resembles with the
information of the experimental test.
Pressure distribution over circular cylinder
Being the velocity function of 𝜃 the local
pressures will be too. Applying Bernoulli’s
equation the local pressure distribution can be
found as shown in the next equation:
During wind tunnel experiments, the
pressure coefficient can be understood as a
dimensionless value that will be changing
among a body in concordance with static and
dynamic pressure in the point of analysis, that is
why Cp is:
While the experiment occurs, a small
hole will be changing its position, measuring
local static pressure at a given angle of the
cylinder, this data can be taken as Cp values if
they are obtained with the previous equation.
Starting again with Bernoulli’s equation
the next simplification can be made, taking any
point for its calculation:
Substituting and simplifying the
equation (3) in (4), we finally obtain:
Making a comparison between the
theoretical results of the potential theory and the
experimental test, we must suppose that they
will be very similar, but the consideration of an
inviscid fluid will affect in a great way the
results giving the property of drag due to a
viscous flow, property that in the theoretical
calculations will not appear. The non-
resemblance of this property is called the
Alembert´s paradox.
Variation by Reynolds
As we said in the last paragraph, the results will
vary between the theory and the experiment due
to the fundamental assumption of a non-viscous
fluid. Therefore, is good to make a prediction of
what we will be obtaining during this
experiment. For an angle between 0º and 180º
the results will change according to the value of
the Reynolds where the differentiation between
subcritical, critical and supercritical Reynolds
numbers is important for the values that will be
expected.
Therefore, since the air particles in the
boundary layer have been already slowed down
by the viscosity encounters an adverse gradient
of pressure, the boundary separation will occur,
nevertheless, not all the separations will occur
in the same place or time, notice that the
(3)
(4)
(5)
(6)
(7)
(8)
(9)
3. 3
PRESSION DISTRIBUTION AROUND A CILINDER AND
COMPARISON WITH POTENTIAL FLOW THEORY
separation will occur when the air particle
cannot overcome an adverse pressure gradient.
That is why the velocity and turbulence of the
particle have an important place in this
situation, and the only way to measure a value
of turbulence is by the Reynolds, therefore is by
this number that the boundary separation will
vary according to next statement: at higher
Reynolds, the detachment will occur in greater
values of θ [1]
.
To support this statements and results
we can see the chart above, which shows the
report made by Achenbach and Schlichting in
1968.
Fig. 2. - Theoretical pressure distribution around a
circular cylinder, compared with data for a subcritical
Reynolds and supercritical Reynolds numbers.
Fig. 3. - Location of the separation points on a circular
cylinder as a function of the Reynolds number.
Experiment Description
This experiment was realized in a medium
capacity wind tunnel with a test area of
approximately 50cmx50cm where the cylinder
tested had a diameter of 10 cm approximately.
The items required to proceed with the
experiment where:
Cylinder with one static pressure intake
with the dimensions previously mentioned.
Digital manometer
Pitot tubes approximately 20 cm away from
the cylinder.
Protactor from 0 to 360 degrees.
For a better perception in the next image we
will describe the components and procedure to
follow for a correct development of the
experiment.
Fig. 4. - Photo of the wind tunnel with the cylinder in
position of test.
Fig. 5. - Protactor and pitot´s tube location.
CYLINDER
PROTACTOR
PITOT´S TUBE
4. Jesús Guillermo Rodríguez Cárdenas, Pablo Elías Martínez Ruiz, Victor José Cisneros Moreno
4
Fig. 6. - Making a measurement and lecture with the
Digital manometer.
Procedure
1.-Estimate the wind tunnel velocity
2.-Turn the cylinder in order to accommodate
the pressure intake facing the wind
3.-Measure the pressure intake of θ 2 by 2
grades starting from zero. Where we have the
maximum pressure differential that corresponds
to the θ of stagnation.
4. - Find the Cp in this point, which must be 1.
5.-Measure the pressure differential and
calculate the Cp for θ from stagnation point to
180.
6.-For a Cp=0 the hoses must be inverted.
7.-Register every variation for all the θ solicited.
Results and discussions
The values of atmospheric pressure (P), air
temperature (T) and dynamic pressure (q) were
measured in the laboratory.
P=92400Pa
T=299.65K
q=205.8Pa
Based on values of P and T, density (𝜌) and
velocity (𝑉) were calculated:
𝜌 =
𝑃
𝑅𝑇
(10)
𝜌 = 1.0755
𝑘𝑔
𝑚3
𝑉 = √
2𝑞
𝜌
(11)
𝑉 = 19.5624
𝑚
𝑠
After that, kinematic viscosity (𝜇) and Reynolds
number (𝑅𝑒) were calculated:
𝜇 = (
𝑇
𝑇0
)
𝑛
𝜇0 (12)
𝜇 = 0.00003282
𝑘𝑔
𝑚𝑠
The reference distance used for the
calculation of 𝑅𝑒 usually is the diameter of the
cylinder (D), but because it was not measured,
an approximation was made, so the reference
distance used was 10 cm.
𝑅𝑒 =
𝜌𝑉𝐷
𝜇
(13)
𝑅𝑒 = 64105.4754
Below are two tables, one with the
results of pressure coefficient (Cp) using the
experimental data and another with the results
of Cp using the potential flow theory.
The experimental values were calculated
with the following equation:
𝐶𝑝 =
𝑃𝑠0−𝑃𝑠 𝜃
𝑃𝑑0
(14)
For the case of the potential flow theory,
another one was used:
𝐶𝑝 = 1 − 4𝑠𝑒𝑛2
(𝜃) (15)
MANOMETER
6. Jesús Guillermo Rodríguez Cárdenas, Pablo Elías Martínez Ruiz, Victor José Cisneros Moreno
6
174 -1,26530612 0,956295199
176 -1,26579203 0,980536136
178 -1,26870748 0,9951281
180 -1,2585034 1
Graphic 1.-Comparison between values of CP from
experimental data and potential flow theory.
To finalize, the solution of the integral to
calculate de drag coefficient (Cd) was solved,
proving that in an inviscid there is no drag.
𝐶𝑑 = 2 [∫ 𝐶𝑝𝑑(𝑠𝑒𝑛𝜃) −
𝜋
2
0
∫ 𝐶𝑝𝑑(𝑠𝑒𝑛𝜃)
𝜋
𝜋
2
]
𝐶𝑑 = 2 {[−𝐶𝑝(𝑐𝑜𝑠𝜃)]0
𝜋
2
+ [𝐶𝑝(𝑐𝑜𝑠𝜃)] 𝜋
2
𝜋
}
𝐶𝑑 = 2 {𝐶𝑝 [− cos (
𝜋
2
) + 𝑐𝑜𝑠(0) + 𝑐𝑜𝑠(𝜋) − cos (
𝜋
2
)]}
𝐶𝑑 = 2𝐶𝑝[cos(0) + cos(𝜋)]
𝐶𝑑 = 2𝐶𝑝(1 − 1)
𝐶𝑑 = 0
Therefore, the drag obtained by the
integral equals zero, which can be explained by
the potential flow theory, assuming that an
inviscid flow is used. However, analyzing the
graphic obtained by using the experimental data
and the graphic obtained from potential flow
theory, can be observed that exists a significant
difference between both. The experimental
results don`t reach values of Cp below -1.3 and
once they pass from positive to negative they
keep being negative and the results from
potential flow theory reach a value of -3, they
become negative but return to the positive side
and are symmetrical. These differences are due
to viscosity, because an inviscid flow does not
experiments separation but a viscous one
separates when flowing through the surface of
an object, so, when it passes through the surface
of the cylinder, the Cp does not reach lower
values because once the flow separates, the
pressure stops decreasing. In addition, the Cp
does not return to being positive because the
flow already separated keeps approximately the
pressure that it had when the separation
occurred, that’s why in the graphic we can see
that after certain point the Cp becomes cuasi-
stable.
Conclusion
As told before, the difference between an
inviscid flow (potential flow theory) and a
viscous flow is something worth of attention.
The study of an inviscid flow helps us realize
how a flow under certain circumstances will
behave, which is easier than analyzing the
problem counting with viscosity, and after
understanding his behavior that way, viscosity
can be added to the equation. Once we start
approaching the problem without ignoring
viscosity, drag appears, and everything gets a
little more difficult to explain. Making
comparisons between viscous and inviscid flow
helps to identify which things can make the
flow act different. For example, from the
comparison made between the graphics showed
before, can be deduced that when the flow never
separates the Cp changes in a symmetrical way
and goes down and up again, but in the case
where drag is not cero after the flow separates
the Cp stabilizes. Also, when comparing the
graphic from experimental data showed above
with graphics at higher Re becomes almost
obvious that at higher Re the separation of the
flow delays, causing the Cp to have a different
behavior along the surface of the cylinder.
References
[1] John J. Bertin and Russell M. Cummings. Aerodynamics
for Engineers. 5th edition, Pearson, 2009.
-3,5
-3
-2,5
-2
-1,5
-1
-0,5
0
0,5
1
1,5
0 50 100 150 200
CP
Teta (°)
CP Vs Teta
Potential flow
theory
Experimental
Data
Table 1.-Data from the calculation of Cp X θ
7. 7
PRESSION DISTRIBUTION AROUND A CILINDER AND
COMPARISON WITH POTENTIAL FLOW THEORY
[2] Barnes W. Mccormick. Aerodynamics, Aeronautics and
Flight Mechanics. 1st edition, John Wiley & Sons, Inc.
1995.
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