This document provides an overview of fluid mechanics concepts across 14 lessons. It begins with an introduction that defines a fluid, discusses fluid properties and the governing equations. Subsequent lessons cover topics like fluid statics, kinematics, dynamics, the energy equation, and its applications. Later lessons address viscous flow, pipe flows, open channels, and pumps/turbines. The introduction provides historical context, defines density, pressure, compressibility, viscosity, and cavitation. It also introduces the concept of modeling fluids as a continuum using differential volumes and governing equations.
This paper presents the study of the dynamics and control of an axial variable structure satellite (asymmetric platform and an axisymmetric rotor). Inertia moments of the rotor change slowly over time. The dynamics of the satellite is described by using ordinary differential equations with Serret-Andoyer canonical variables. For undisturbed motion, the stationary solutions are found, and their stability is studied. The control law is obtained for the satellite with variable structure on the basis of the stationary solutions. By means of computer numerical simulations, we have shown that the motion of the satellite controlled by founded internal torque is stable.
D. Mladenov - On Integrable Systems in CosmologySEENET-MTP
Lecture by Prof. Dr. Dimitar Mladenov (Theoretical Physics Department, Faculty of Physics, Sofia University, Bulgaria) on December 7, 2011 at the Faculty of Science and Mathematics, Nis, Serbia.
This paper presents the study of the dynamics and control of an axial variable structure satellite (asymmetric platform and an axisymmetric rotor). Inertia moments of the rotor change slowly over time. The dynamics of the satellite is described by using ordinary differential equations with Serret-Andoyer canonical variables. For undisturbed motion, the stationary solutions are found, and their stability is studied. The control law is obtained for the satellite with variable structure on the basis of the stationary solutions. By means of computer numerical simulations, we have shown that the motion of the satellite controlled by founded internal torque is stable.
D. Mladenov - On Integrable Systems in CosmologySEENET-MTP
Lecture by Prof. Dr. Dimitar Mladenov (Theoretical Physics Department, Faculty of Physics, Sofia University, Bulgaria) on December 7, 2011 at the Faculty of Science and Mathematics, Nis, Serbia.
Lecture by prof. dr Neven Bilic from the Ruđer Bošković Institute (Zagreb, Croatia) at the Faculty of Science and Mathematics (Niš, Serbia) on October 29, 2014.
The visit took place in the frame of the ICTP – SEENET-MTP project PRJ-09 “Cosmology and Strings”.
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Lecture by prof. dr Neven Bilic from the Ruđer Bošković Institute (Zagreb, Croatia) at the Faculty of Science and Mathematics (Niš, Serbia) on October 29, 2014.
The visit took place in the frame of the ICTP – SEENET-MTP project PRJ-09 “Cosmology and Strings”.
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solution of introductoin to fluid mechanics and machines(Prof. Som and Prof. ...pankaj dumka
This book is pioneer in the field of fluid mechanics. Each student of mechanical engineering must buy it as it builds your concepts well and its problems can come in ESE of GATE exams because of its good difficulty level. Some students find it difficult to solve it so I am providing you my notes on its solutions .
chapter 4(Conservaion equations and Analysis of Finite Control Volumes) of second edition.
HYDAC axial piston pumps for open circuit in swash plate design are available in the pressure ranges medium and high, and feature a specific displacement flow of 10 cm³/rotation to 560 cm³/rotation.
Further discriminatory signature of inflationLaila A
These are the slides of the talk I gave on discriminating between models of inflation using space based gravitational wave detectors, at KEK in Tskuba University, Japan.
Passively Flapping Dynamics of a Flexible Foil Immersed in the Wake of a Cyli...ijceronline
Passive dynamics of flexible body in the von Kármán vortex is complicated and has not yet been well understood. In this work we numerically studied the passive flapping motion of an inverted flexible foil pinned in the wake of a rigid circular cylinder by an robust fluid structure interaction framework. The non-dimensional parameters are Reynolds number and distance between the cylinder and pinned-point of the foil. Simulation results show that the flexible foil can extract energy from the vortex street and be induced to vibrate periodically. It is revealed that the foil's motion patterns can be divided into two categories: inverted flapping and forward flapping, which depended on the cylinder-foil distance. Both the cylinder and foil experiences a drag reduction, the foil can even obtain thrust in inverted flapping mode. Compared with a single one in the same uniform flow, the foil's flapping frequency here is smaller but its amplitude is greater. This work would help us to elucidate the energy-saving mechanism of fish swimming and inspire the promising applications in marine engineering
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
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Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
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Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
In today's fast-changing business world, Companies that adapt and embrace new ideas often need help to keep up with the competition. However, fostering a culture of innovation takes much work. It takes vision, leadership and willingness to take risks in the right proportion. Sachin Dev Duggal, co-founder of Builder.ai, has perfected the art of this balance, creating a company culture where creativity and growth are nurtured at each stage.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
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Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
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The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
Unsubscribed: Combat Subscription Fatigue With a Membership Mentality by Head...
Lesson 1
1. FLUID MECHANICS
Department of Nuclear Engineering and Fluid Mechanics
University College of Engineering
University of Basque Country (EHU/UPV)
Vitoria-Gasteiz
Instructor: Iñigo Errasti Arrieta
2. CONTENTS
LESSON 1. INTRODUCTION
LESSON 2. FLUID STATICS
LESSON 3. FLUID KINEMATICS
LESSON 4. FLUID DYNAMICS
LESSON 5. THE ENERGY EQUATION
LESSON 6. APPLICATIONS OF BERNOULLI EQUATION
LESSON 7. LINEAR MOMENTUM THEOREM
LESSON 8. DIMENSIONAL ANALYSIS AND SIMILITUDE
LESSON 9. INCOMPRESSIBLE VISCOUS FLOW
LESSON 10. ENERGY LOSSES IN PIPES
LESSON 11. STEADY-STATE FLOW IN PIPES
LESSON 12. TRANSIENT REGIMES IN PIPES
LESSON 13. FLOW THROUGH OPEN CHANNELS
LESSON 14. PUMPS AND TURBINES
3. LESSON 1. INTRODUCTION TO FLUID MECHANICS
1. Field of application of Fluid Mechanics
2. Brief history of Fluid Mechanics
3. Fluid as a continuum. Fluid definition
4. Dimensions and Units
5. Operators
6. Physical properties of fluids
4. 1. Field of application of Fluid Mechanics
“Fluid Mechanics”, definition
Physical phenomena in nature
Engineering
Other aspects in common life
Main branches:
• Statics
• Kinematics
• Dynamics
• Aerodynamics
• Computational Fluid Dynamics (CFD)
5. 1. Field of application of Fluid Mechanics
Weather & climate
Vehicles
Environment
6. 1. Field of application of Fluid Mechanics
Physiology and medicine
Sports & Recreation
7. 2. Brief history of Fluid Mechanics
Archimedes
Mariotte, Torricelli, Pascal, Castelli
Newton, Bernoulli, Euler, D’Alembert
Chezy, Navier, Coriolis, Darcy
Pouiseuille, Hagen, Reynolds, Stokes
Froude, Francis, Pelton, Herschel
Thomson, Kelvin, Rayleigh, Lamb
Prandtl, von Karman, Blasius
Taylor, Kolmogorov, Nikuradse
8. 2. Brief history of Fluid Mechanics
Archimedes Newton Leibniz Bernoulli Euler
(287-212 BC) (1642-1727) (1646-1716) (1667-1748) (1707-1783)
Navier Stokes Reynolds Prandtl Taylor Kolmogorov
(1785-1836) (1819-1903) (1842-1912) (1875-1953) (1886-1975) (1903-1987)
9. 3. Fluid as a continuum. Definition of fluid
Definition of fluid
Comparison to solid
States of matter (liquid and gas)
Modelling the fluid as a continuum
10. 3. Fluid as a continuum. Definition of fluid
Comparison to solid
Time t0 Time t1 Time t2
- Deformation of solid: F
r
F
Ф1 r
F
Ф2 = Ф1 r
F
invariable with time τ=
Solid Solid Solid
A
τ : Shear stress
Time t0 Time t1 Time t2
F: Shear force
- Deformation of fluid:
r Ф2 > Ф1 r A: Contact area
r Ф1
F continuous with time
F F
Fluid Fluid Fluid
Figure 1.1. Deformation of solids and fluids
Figure 1.2b. Molecules are at relatively fixed positions in a solid. Figure 1.2a. Unlike a liquid, a gas does not
Groups of molecules move about each other in the liquid phase. form a free surface and it expands to fill the
Molecules move around at random in the gas phase (Cengel-Cimbala) entire available space (Cengel-Cimbala)
11. 3. Fluid as a continuum. Definition of fluid
The model of the continuum
- Differential volume range for analysing the fluid as a continuum
- Definition of the density in a fluid as a continuum
Figure 1.3. Differential volume in a fluid Figure 1.4. Density calculated in function of
region with varying density (from White) the differential volume (from White)
δm
ρ = lim
δV →δV * δ 0V
12. 4. Dimensions and Units
Dimensions, magnitudes and units
Primary dimensions
Secondary dimensions
SI and English systems
Conversion ratios
Some SI units: English units:
mass: kg pound-mass (lbm)
length: meter foot (ft)
time: second second (s)
force: newton pound-force (lbf)
work: joule British thermal unit (btu)
13. 4. Units
Prefixes, dimensions and unity conversion factors
Table 1.1. Prefixes
Table 1.2. Units in the SI and US system
Table 1.3. Unity conversion factors
14. 5. Operators
• Gradient of a scalar function f:
r r ∂f ( x, y, z ) r ∂f ( x, y, z ) r ∂f ( x, y, z ) r
gradf ( x, y, z ) = ∇f = i+ j+ k
∂x ∂y ∂z
r
• Divergence of a vector function f :
r r r ∂f x ( x, y , z ) ∂f y ( x, y, z ) ∂f z ( x, y, z )
divf ( x, y, z ) = ∇f = + +
∂x ∂y ∂z
r
• Curl of a vector function f :
r r r
i j k
r r r r ∂ ∂ ∂
cu rlf ( x, y, z ) = ∇xf =
∂x ∂y ∂z
f x ( x, y , z ) f y ( x, y , z ) f z ( x, y , z )
15. 6. Physical properties of fluids
1. Density, specific weight and specific gravity
2. Pressure
3. Ideal gas equation of state
4. Compressibility
5. Viscosity
6. Vapour pressure. Saturation pressure. Cavitation
7. Surface tension and capillary effect
16. 6.1. Density and specific weight
Density (definition, dimensions, units)
Specific weight (definition, dimensions, units)
Relative density or specific gravity (definition)
17. 6.1. Density, specific weight and specific gravity
• Density (definition)
m dm
ρ= ρ= dV
V dV dm
Mass per unit volume (kg/m3) V
Figure 1.5a. Concept of density of a fluid
1
• Specific volume (definition) Vs =
ρ
• Specific weight (definition) γ = ρg
ρ
SG =
• Specific gravity or relative density (definition)
ρH O 2
18. 6.1. Density, specific weight and specific gravity
Figure 1.5b. Approximate physical properties of common liquids at atmospheric pressure
19. 6.2. Pressure
Definition (2 forms)
Dimensions. Units
Pressure level with different references
20. 6.2. Pressure. Units
• Definition (2 forms)
Atmosphere Ratio of normal force (Fn)
to area at a point
Fn
A
Fn
P=
A
Figure 1.6. Pressure in plane A
r
dA ΔFn dFn
r P = lim =
dFn ΔA→0 ΔA dA
1 Pa= 1 Nw m-2
A 1 baria = 1 dyne cm-2
V
1 atm = 760 mmHg=1.013 x 105 Pa = 10.33 mwc
Figure 1.7. General concept of pressure = 2116 lbf ft-2
1 psi = 6895 Pa
21. 6.2. Pressure
• Pressure references
Absolute pressure (pabs): pressure relative to
absolute zero, absolute vacuum, p = 0 Pa.
pabs > patm ; pgauge > 0
(overpressure) Gauge pressure (pgauge): pressure relative to
the local atmospheric pressure.
pabs = patm ; pgauge = 0
pabs = p gage + patm
pabs < patm ; pgauge < 0
• Example 1:
(vacuum, suction)
A gage pressure of 50 kPa recorded in a location
where the atmospheric pressure is 100 kPa is
pabs = 0 expressed as either
p= 50 kPa gage or p=150 kPa abs
• Example 2:
Figure 1.8. Pressure references
22. 6.3. Ideal gas equation of state
• Definition of the equation of state
• Equation of state for an ideal gas
pV = nRT R = 8.314 J / Kmol K Universal gas constant
• Other forms of the equation of state
⎡R⎤
p = ρR * T R* = ⎢ ⎥
⎣M ⎦
(J/kg K) M: molecular weight (Kg/Kmol) of the gas
p = γR ' T ⎡ R ⎤
R' = ⎢ ⎥
⎣ Mg ⎦
(m/K)
23. 6.4. Compressibility and elasticity
Parameters:
dp
E =−
• Bulk modulus of elasticity E: (dV / V ) 1
E=
(dV / V ) α
• Compressibility α: α=−
dp
F
A
p=F/A ; V
Increase in F
(p + dp) ; (V + dV)
V Negative value (decrease)
Figure 1.9. Decrease in volume by an increase in pressure
24. 6.4. Compressibility and elasticity
Table 1.4 Values of bulk modulus of elasticity for some liquids
Liquid E (GPa)
Water 2,07
Ethanol 1,21
Benzene 1,03
Carbon tetrachloride 1,10
Mercury 26,20
Ideal gases: E = kp
Newton's formula for speed of sound c2 =
dp E
=
(Newton – Laplace equation): dρ ρ
25. 6.5. Viscosity
1. Viscosity: Dynamic and kinematic
2. Newton’s law of viscosity
3. Rheological diagram
4. Dependence on pressure and temperature
5. Viscometers
26. 6.5. Viscosity
Definition
Physical phenomena causing viscosity:
• Intermolecular cohesion:
r
r U2
U
r 2 τ
U1 r
U1
Figure 1.10. Influence of intermolecular cohesion on viscosity
● Collisional exchange of momentum:
r r
U2 U2
τ
r
U1 r
U1
Figure 1.11. Influence of momentum exchange on viscosity
27. 6.5. Newton’s law of viscosity
• Velocity profile, shear stress, deformation:
τ τ
y U + dU U + dU
ds
dθ
dV dy
dV dV
U U
μ: Dynamic viscosity
τ τ
U=0
τ F: Shear force
Time (t) Time (t + dt) A: Contact area
Figure 1.2 Deformation of a fluid element
F dθ dU
● Shear stress: τ= ● Deformation rate: =
dt dy
A
dθ dU dθ dU
• Newton’s law of viscosity: τ=μ =μ F = μA = μA
dt dy dt dy
• Inviscid flow hypothesis (ideal fluid)
μ =0 τ =0
28. 6.5. Rheological diagram
Newtonian fluid dθ dU μ: Dynamic viscosity
τ=μ =μ
Pseudo plastic fluid dt dy
Dilatant fluid
Ideal plastic
Ideal fluid
Elastic solid
Ideal plastic (Bingham) Dilatant τ = k ( gradU ) , n > 1
n
τ (N/m2) r 1
gradU = (τ − τ 0 )
μ
Newtonian
Plastic
Elastic Pseudo plastic τ = k ( gradU )n , n < 1
solid
Ideal fluid
dθ dU −1
= (s )
dt dy
Figure 1.13 Rheological diagram
29. 6.5. Dynamic and kinematic viscosity. Unities
Dynamic viscosity (absolute viscosity)
dθ dU
• Newton’s law of viscosity: τ=μ =μ
dt dy
SI system: : 1 Pa s = 1 Poiseuille = 1 Nw m-2s
CGS system: 1 poise = 1 dyne cm-2s
Kinematic viscosity: μ
ν=
ρ
SI system: : 1 m2s-1
CGS system: 1 cm2s-1 = 1 stoke
30. 6.5. Dependence on pressure and temperature
Effect of temperature
μ (Pa·s) μ↓ as T↑ ν↓ decreases when T↑
- Liquid:
ρ ≈ Cte (incompressible)
Gas
- Gas: μ ↑ con T↑
ν↑↑ increases when T↑
Liquid ρ ↓ con T↑ ( p = γR’T )
T (K) Sutherland correlation for viscosity of gases
Figure 1.14 Dynamic viscosity of gases and liquids as a function of temperature
Effect of pressure
μ ≈ Cte μ ≈ Cte (∆p not excessive)
- Liquid: ν ≈ Cte - Gas: ν↓ decreases when p↑
ρ ≈ Cte (incompressible) ρ ↑ as p↑
31. 6.5. Dependence on pressure and temperature
(Figures 1.15, 1.16 from White)
32. 6.5. Viscometers
a) b)
Engler viscometer
Redwood viscometer
Brookfield viscometer
Falling sphere viscometer
c) d)
Figures 1.17 Schematic of a) Engler, b) Redwood, c) Brookfield and d) falling sphere-type viscometers
33. 6.6. Vapour pressure and saturation pressure
Reviewing the concepts of vapour pressure and saturation pressure
Figure 1.18. Phase diagram
34. 6.6. Vapour pressure and saturation pressure
Cavitation:
Process of formation of the vapour of liquid when it is subjected to reduced
pressure at constant ambient temperature
Gaseous and vaporous cavitation
Cavitation number:
p − p sat p↓ , T p↑, T
Ca = p, T boiling implosion
1
ρU 2
2
p < psat (T) p > psat (T)
Figure 1.19. Schematic of the cavitation process
35. 6.6. Vapour pressure and saturation pressure
Figure 1.20. Consequence of cavitation damage on Figure 1.21. Consequence of cavitation damage
an impeller of a pump on an impeller of a pump. Detail
Figure 1.22. Consequence of cavitation damage on Figure 1.23. Consequence of cavitation damage on
an impeller of a pump. Profile view an impeller of a pump. Profile view
36. 6.7. Surface tension and capillary effect
Surface tension
Figure 1.24. Forces acting on a liquid at the
surface and deep inside (Cengel-Cimbala).
F
σ=
l
Capillary rise
2σ
h= cos φ
ρgR Figure 1.25. Capillary rise and fall of water
and mercury in a small diameter glass tube
(Cengel-Cimbala).
Figure 1.26. Forces acting on a liquid column that has risen in a tube.