This laboratory experiment involves using Stokes' Law to determine the viscosity and density of unknown fluids. Students will time the fall of spheres through fluid columns, then use the measurements to calculate viscosity based on Stokes' Law. They will also consider how sphere and cylinder diameters affect calculations. The goals are to understand fluid mechanics concepts like viscosity and Reynolds number, and apply Stokes' Law to characterize unknown fluids.
This presentation covers concepts such as surface tension, surface energy, liquid drops and bubbles, wetting, capillarity at the elementary school level. Comment down in a box for improvement.
Stoke's Law calculates rate of destabilization of an emulsion by equating gravitational force with the opposing hydrodynamic force. Stoke's Law can be used to predict emulsion stability.
This contains a basic idea about viscosity measurement devices and their principles. Working, principle, construction, and advantages of rotating viscometer are described here.
The forth lecture in the module Particle Technology, delivered to second year students who have already studied basic fluid mechanics.
Fluid flow in porous media covers the basic streamline and turbulent flow models for pressure drop as a function of flow rate within the media. The Modified Reynolds number determines the degree of turbulence in the fluid. The industrial processes of deep bed (sand) filtration and fluidisation are included.
Compressible flows in fluid mechanics in chemical engineeringUsman Shah
This slide will explain you the chemical engineering terms .Al about the basics of this slide are explain in it. The basics of fluid mechanics, heat transfer, chemical engineering thermodynamics, fluid motions, newtonian fluids, are explain in this process.
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.
nternational Journal of Engineering Research and Development is an international premier peer reviewed open access engineering and technology journal promoting the discovery, innovation, advancement and dissemination of basic and transitional knowledge in engineering, technology and related disciplines.
This presentation covers concepts such as surface tension, surface energy, liquid drops and bubbles, wetting, capillarity at the elementary school level. Comment down in a box for improvement.
Stoke's Law calculates rate of destabilization of an emulsion by equating gravitational force with the opposing hydrodynamic force. Stoke's Law can be used to predict emulsion stability.
This contains a basic idea about viscosity measurement devices and their principles. Working, principle, construction, and advantages of rotating viscometer are described here.
The forth lecture in the module Particle Technology, delivered to second year students who have already studied basic fluid mechanics.
Fluid flow in porous media covers the basic streamline and turbulent flow models for pressure drop as a function of flow rate within the media. The Modified Reynolds number determines the degree of turbulence in the fluid. The industrial processes of deep bed (sand) filtration and fluidisation are included.
Compressible flows in fluid mechanics in chemical engineeringUsman Shah
This slide will explain you the chemical engineering terms .Al about the basics of this slide are explain in it. The basics of fluid mechanics, heat transfer, chemical engineering thermodynamics, fluid motions, newtonian fluids, are explain in this process.
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.
nternational Journal of Engineering Research and Development is an international premier peer reviewed open access engineering and technology journal promoting the discovery, innovation, advancement and dissemination of basic and transitional knowledge in engineering, technology and related disciplines.
Physics ( human eye and the colourful world).Nikhil Dahiya
ppt on human eye and its structure. shows different parts of the eye . helps the student to learn about the eye more breifly.it is a science ppt which will be helpfull . teachers can also take it in the us for letting the students understand better .
Project for engineering and school students.
In this project, you can find everything related to the concept of viscosity :- Definition, Derivation, Units, Kinematic viscosity. Newton's law of viscosity, variation of viscosity with temperature, types of fluids are also included. If you find it helpful to you, give some feedback.
Thank You very much :)
Droplet thermal behavior study with light scattering techniqueAnurak Atthasit
THE 10TH INTERNATIONAL SYMPOSIUM ON FLOW VISUALIZATION
August 26 - 29, 2002, Kyoto, Japan
To present the results obtained from a basic experiment on droplet interaction in a dense linear droplet stream. The interaction of individual droplet with one another and with surrounding influences their transport characteristics.
A vibrating orifice generator produces a stream of monosized droplets. The experiments have been performed by using the electrostatic deviator to obtain the evolution of the main droplet characteristics in a wide range of the spacing parameter value Co (ratio between droplet spacing to droplet diameter). The basic experiment allows quantifying precisely the evolution of the drag coefficient and the droplet evaporation rate for different droplet spacings.
The problem of the relaxation of a cold package of critical or supercritical fluid in a hotter environment of the same fluid is studied. An asymptotic theory valid in the limit of small values of the parameter 𝜏=𝛾∞𝜖 , where 𝛾∞ is the ratio between the characteristic thermal diffusion time and the life time of the droplet and 𝜖 the ratio between the fluid densities at the hot and cold regions is developed. Recession laws which are different from the classical 𝑑2 law can be derived from the zeroth order approximation solution in subcritical case [6] as well in critical and supercritical ones. Except for the critical case, additional assumptions on the thermodynamical properties of the gas phase restore the classical 𝑑2 law. A numerical resolution of the problem for a Van der Waals gas in supercritical conditions is performed to check the validity of the results of the asymptotic analysis. It is found that a transition region generally separate the two regions of the fluid in the supercritical conditions. The behavior of this region is numerically analyzed.
An Investigation of effect of Temperature Difference and Initial Moisture Con...ijsrd.com
The study of natural convection involves analysis of surface geometry that is having fluid- saturated porous medium. Various temperature differences are considered between the two isolated walls, while the top wall considered being an adiabatic. CFD tool and mathematical analysis was studied and analyzed to carry out the research. By the help of study, it is analyzed that higher intensity rate of natural convection. The simulation of the various temperatures and initial moisture contents were carried out to determine the effect on the performance of the natural convection. It has been noticed that temperature over the porous medium is uniformly distributed due to conduction, which is little higher in the fluid region. It has been recorded that the high moisture contents at the higher temperature side wall than lower one.
COLLEGE
PHYSICS LAB REPORT
STUDENTS NAME
ANALYSIS OF A BUBBLE CHAMBER PICTURE
SUPERVISED BY:
19/05/2020
1. Introduction
A bubble chamber is a vessel filled with a superheated transparent liquid (most often liquid hydrogen) used to detect electrically charged particles moving through it. It was invented in 1952 by Donald A. Glaser, for which he was awarded the 1960 Nobel Prize in Physics.
A convenient way to study the properties of the fundamental subatomic particles is through observation of their bubble trails, or tracks, in a bubble chamber. Using measurements made directly on a bubble chamber photograph, we can often identify the particles from their tracks and calculate their masses and other properties. In a typical experiment, a beam of a particular type of particle is sent from an accelerator into a bubble chamber, which is a large liquid-filled vessel. To simplify the analysis of the data, the liquid used is often hydrogen, the simplest element. The use of liquid hydrogen, while it simplifies the analysis, complicates the experiment itself, since hydrogen, a gas at room temperature, liquefies only when cooled to -246◦C. For charged particles to leave tracks in passing through the chamber, the liquid must be in a “super-heated” state, in which the slightest disturbance causes boiling to occur. In practice, this is accomplished by expanding the vapor above the liquid with a piston a few thousandths of a second before the particles enter the chamber.
2. Methods
2.1 Materials needed:
1. student worksheet per student
2. Ruler
3. Scissors
4. Glue stick
5. Pocket calculator
2.2 Procedures
2.2.1 Calculation of the X Particle’s Mass.
Make measurements on each of the photographs. In particular, for each of the circled events measure these four quantities:
· `Σ - The length of the Σ track,
· θ - the angle between the Σ− and π− track,
· s - the sagitta of the π− track,
· `π - The chord length of the π− track.
Your values for the event should be close to those given in the sample input. Run the program using each set of measurements, and tabulate the computed X0 mass from each event. Compute an average of the calculated masses and find the average deviation, expressing your result as Mx ±∆Mx.
Compare your final result with some known neutral particles listed below and identify the X0 particle based on this comparison.
Particlemass (in MeV/c2)
π0 135
K0 498
n 940
Λ0 1116
Σ0 1192
Ξ0 1315
2.2.2 Determination of the Angle θ.
The angle θ between the π− and Σ− momentum vectors can be determined by drawing tangents to the π− and Σ− tracks at the point of the Σ− decay.
We can then measure the angle between the tangents using a protractor. We can show.
COLLEGE
PHYSICS LAB REPORT
STUDENTS NAME
ANALYSIS OF A BUBBLE CHAMBER PICTURE
SUPERVISED BY:
19/05/2020
1. Introduction
A bubble chamber is a vessel filled with a superheated transparent liquid (most often liquid hydrogen) used to detect electrically charged particles moving through it. It was invented in 1952 by Donald A. Glaser, for which he was awarded the 1960 Nobel Prize in Physics.
A convenient way to study the properties of the fundamental subatomic particles is through observation of their bubble trails, or tracks, in a bubble chamber. Using measurements made directly on a bubble chamber photograph, we can often identify the particles from their tracks and calculate their masses and other properties. In a typical experiment, a beam of a particular type of particle is sent from an accelerator into a bubble chamber, which is a large liquid-filled vessel. To simplify the analysis of the data, the liquid used is often hydrogen, the simplest element. The use of liquid hydrogen, while it simplifies the analysis, complicates the experiment itself, since hydrogen, a gas at room temperature, liquefies only when cooled to -246◦C. For charged particles to leave tracks in passing through the chamber, the liquid must be in a “super-heated” state, in which the slightest disturbance causes boiling to occur. In practice, this is accomplished by expanding the vapor above the liquid with a piston a few thousandths of a second before the particles enter the chamber.
2. Methods
2.1 Materials needed:
1. student worksheet per student
2. Ruler
3. Scissors
4. Glue stick
5. Pocket calculator
2.2 Procedures
2.2.1 Calculation of the X Particle’s Mass.
Make measurements on each of the photographs. In particular, for each of the circled events measure these four quantities:
· `Σ - The length of the Σ track,
· θ - the angle between the Σ− and π− track,
· s - the sagitta of the π− track,
· `π - The chord length of the π− track.
Your values for the event should be close to those given in the sample input. Run the program using each set of measurements, and tabulate the computed X0 mass from each event. Compute an average of the calculated masses and find the average deviation, expressing your result as Mx ±∆Mx.
Compare your final result with some known neutral particles listed below and identify the X0 particle based on this comparison.
Particlemass (in MeV/c2)
π0 135
K0 498
n 940
Λ0 1116
Σ0 1192
Ξ0 1315
2.2.2 Determination of the Angle θ.
The angle θ between the π− and Σ− momentum vectors can be determined by drawing tangents to the π− and Σ− tracks at the point of the Σ− decay.
We can then measure the angle between the tangents using a protractor. We can show.
COLLEGE
PHYSICS LAB REPORT
STUDENTS NAME
ANALYSIS OF A BUBBLE CHAMBER PICTURE
SUPERVISED BY:
19/05/2020
1. Introduction
A bubble chamber is a vessel filled with a superheated transparent liquid (most often liquid hydrogen) used to detect electrically charged particles moving through it. It was invented in 1952 by Donald A. Glaser, for which he was awarded the 1960 Nobel Prize in Physics.
A convenient way to study the properties of the fundamental subatomic particles is through observation of their bubble trails, or tracks, in a bubble chamber. Using measurements made directly on a bubble chamber photograph, we can often identify the particles from their tracks and calculate their masses and other properties. In a typical experiment, a beam of a particular type of particle is sent from an accelerator into a bubble chamber, which is a large liquid-filled vessel. To simplify the analysis of the data, the liquid used is often hydrogen, the simplest element. The use of liquid hydrogen, while it simplifies the analysis, complicates the experiment itself, since hydrogen, a gas at room temperature, liquefies only when cooled to -246◦C. For charged particles to leave tracks in passing through the chamber, the liquid must be in a “super-heated” state, in which the slightest disturbance causes boiling to occur. In practice, this is accomplished by expanding the vapor above the liquid with a piston a few thousandths of a second before the particles enter the chamber.
2. Methods
2.1 Materials needed:
1. student worksheet per student
2. Ruler
3. Scissors
4. Glue stick
5. Pocket calculator
2.2 Procedures
2.2.1 Calculation of the X Particle’s Mass.
Make measurements on each of the photographs. In particular, for each of the circled events measure these four quantities:
· `Σ - The length of the Σ track,
· θ - the angle between the Σ− and π− track,
· s - the sagitta of the π− track,
· `π - The chord length of the π− track.
Your values for the event should be close to those given in the sample input. Run the program using each set of measurements, and tabulate the computed X0 mass from each event. Compute an average of the calculated masses and find the average deviation, expressing your result as Mx ±∆Mx.
Compare your final result with some known neutral particles listed below and identify the X0 particle based on this comparison.
Particlemass (in MeV/c2)
π0 135
K0 498
n 940
Λ0 1116
Σ0 1192
Ξ0 1315
2.2.2 Determination of the Angle θ.
The angle θ between the π− and Σ− momentum vectors can be determined by drawing tangents to the π− and Σ− tracks at the point of the Σ− decay.
We can then measure the angle between the tangents using a protractor. We can show.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
- For advanced developers: master the skills to efficiently apply PowSyBl functionalities to your real-world scenarios.
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
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.
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
Elevating Tactical DDD Patterns Through Object CalisthenicsDorra BARTAGUIZ
After immersing yourself in the blue book and its red counterpart, attending DDD-focused conferences, and applying tactical patterns, you're left with a crucial question: How do I ensure my design is effective? Tactical patterns within Domain-Driven Design (DDD) serve as guiding principles for creating clear and manageable domain models. However, achieving success with these patterns requires additional guidance. Interestingly, we've observed that a set of constraints initially designed for training purposes remarkably aligns with effective pattern implementation, offering a more ‘mechanical’ approach. Let's explore together how Object Calisthenics can elevate the design of your tactical DDD patterns, offering concrete help for those venturing into DDD for the first time!
Generating a custom Ruby SDK for your web service or Rails API using Smithyg2nightmarescribd
Have you ever wanted a Ruby client API to communicate with your web service? Smithy is a protocol-agnostic language for defining services and SDKs. Smithy Ruby is an implementation of Smithy that generates a Ruby SDK using a Smithy model. In this talk, we will explore Smithy and Smithy Ruby to learn how to generate custom feature-rich SDKs that can communicate with any web service, such as a Rails JSON API.
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered QualityInflectra
In this insightful webinar, Inflectra explores how artificial intelligence (AI) is transforming software development and testing. Discover how AI-powered tools are revolutionizing every stage of the software development lifecycle (SDLC), from design and prototyping to testing, deployment, and monitoring.
Learn about:
• The Future of Testing: How AI is shifting testing towards verification, analysis, and higher-level skills, while reducing repetitive tasks.
• Test Automation: How AI-powered test case generation, optimization, and self-healing tests are making testing more efficient and effective.
• Visual Testing: Explore the emerging capabilities of AI in visual testing and how it's set to revolutionize UI verification.
• Inflectra's AI Solutions: See demonstrations of Inflectra's cutting-edge AI tools like the ChatGPT plugin and Azure Open AI platform, designed to streamline your testing process.
Whether you're a developer, tester, or QA professional, this webinar will give you valuable insights into how AI is shaping the future of software delivery.
Smart TV Buyer Insights Survey 2024 by 91mobiles.pdf91mobiles
91mobiles recently conducted a Smart TV Buyer Insights Survey in which we asked over 3,000 respondents about the TV they own, aspects they look at on a new TV, and their TV buying preferences.
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
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.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...
Viscosity & stokes’ law
1. Measurement Laboratory No. 3
EGR 101
Fluid Mechanics: Stokes’ Law and Viscosity
Measurement Laboratory
Investigation No. 3
Scott A. Shearer, Professor
Jeremy R. Hudson, Graduate Teaching Assistant
Biosystems and Agricultural Engineering
1. Introduction
This laboratory investigation involves determining the viscosity and mass density of
an unknown fluid using Stokes’ Law. Viscosity is a fluid property that provides an
indication of the resistance to shear within a fluid. Specifically, you will be using a
fluid column as a viscometer. To obtain the viscometer readings you will use a
stopwatch to determine the rate of drop of various spheres within the fluid. You will
determine both density and viscosity.
2. Learning Outcomes
On completion of this laboratory investigation students will:
• Appreciate the engineering science of 'fluid mechanics.'
• Understand the concept of fluid 'viscosity.'
• Understand the concept of dimensionless parameters, and most specifically
the determination of Reynold's Number.
• Be able to predict the settling time of spheres in a quiescent fluid.
• Be able to calculate the viscosity of an unknown fluid using Stokes' Law and
the terminal velocity of a sphere in this fluid.
• Be able to correct for the diameter effects of fluid container on the
determination of fluid viscosity using a 'falling ball' viscomter.
3. Definitions
Fluid – a substance that deforms continuously when subjected to a shear stress.
Viscosity – a fluid property that relates the shear stress in a fluid to the angular rate of
deformation.
Fluid Mechanics – the study of fluid properties.
Reynold’s Number – dimensionless parameter that represents the ratio of viscous to
inertial forces in a fluid.
1
2. Measurement Laboratory No. 3
EGR 101
4. Stokes’ Law
Figure 1: George Gabriel Stokes
George Gabriel Stokes, an Irish-born mathematician, worked most of his professional
life describing fluid properties. Perhaps his most significant accomplishment was the
work describing the motion of a sphere in a viscous fluid. This work lead to the
development of Stokes’ Law, a mathematical description of the force required to
move a sphere through a quiescent, viscous fluid at specific velocity. This law will
form the basis of this laboratory investigation.
Stokes' Law is written as,
Fd = 6pmVd
where Fd is the drag force of the fluid on a sphere, m is the fluid viscosity, V is the
velocity of the sphere relative to the fluid, and d is the diameter of the sphere. Using
this equation, along with other well-known principle of physics, we can write an
expression that describes the rate at which the sphere falls through a quiescent,
viscous fluid.
To be begin we must draw a free body diagram (FBD) of the sphere. That is we must
sketch the sphere and all of the internal and external forces acting on the sphere as it
is dropped into the fluid. Figure 2 shows a sketch of the entire system (sphere
dropping through a column of liquid). The FBD is the dashed cross-section that has
been removed and exploded in the left portion of this figure.
2
3. Measurement Laboratory No. 3
EGR 101
Fb
Fd
mg
Figure 2: Free-body diagram of a sphere in a quiescent fluid.
The FBD in this figure lists three forces acting on the sphere; Fb, F d, and mg. The
first two forces arise from the buoyancy effect of displacing the fluid in question, and
from the viscous drag of the fluid on the sphere, respectively. Both forces act
upwards -- buoyancy tending to 'float' the sphere (F b) and the drag force (F d)
resisting the acceleration of gravity. The only force acting downwards is the body
force resulting from gravitational attraction (mg). By summing forces in the vertical
direction we can write the following equation,
Fb + Fd = mg
The buoyancy force is simply the weight of displaced fluid. As you may recall from
earlier work in science and math, the volume of a sphere (vsphere) is written as,
4 3
v sphere = pr
3
Combining this volume with the mass density of the fluid, rfluid, we can now write the
buoyancy force as the product ,
4 3
Fb = mdf g = pr r fluid g
3
where g is the gravitational acceleration and r is the radius of the sphere. Combining
all of the previous relationships that describe the forces acting on the sphere in a fluid
we can write the following expression,
3
4. Measurement Laboratory No. 3
EGR 101
4 3
pr r fluid g + 6pmVd = mg
3
Rearranging and regrouping the terms from the above equation we arrive at the
following relationship,
2r 2 ( sphere - r fluid )
r g
V=
9m
While Stokes’ Law is straight forward, it is subject to some limitations. Specifically,
this relationship is valid only for ‘laminar’ flow. Laminar flow is defined as a
condition where fluid particles move along in smooth paths in lamina (fluid layers
gliding over one another). The alternate flow condition is termed ‘turbulent’ flow.
This latter condition is characterized by fluid particles that move in random in
irregular paths causing an exchange of momentum between particles.
Engineers utilize a dimensionless parameter known as the Reynold’s number to
distinguish between these two flow conditions. This number is a ratio between the
inertial and viscous forces within the fluid. Engineering students will learn more
about the origin of this parameter – the Buckingham Pi Theorem – in the final two
years of the curriculum. For now we will define the Reynold’s number as,
rVd
NR =
m
where NR is Reynold’s Number, rfluid is the mass density of the fluid, V is the velocity
of the fluids relative to the sphere, and d is the diameter of the sphere.
The application of the Reynold’s Number to fluids problems is to determine the
nature of the fluid flow conditions – laminar or turbulent. For the case where we
have a viscous and incompressible fluid flowing around a sphere, Stokes’ Law is
valid providing the Reynold’s Number has a value less than 1.0. When utilizing
Stokes’ Law, it is appropriate to verify the application of this law is appropriate.
5. Falling Ball Viscometers
The falling ball viscometer is based on Stokes’ Law, and is what we will use in this
laboratory investigation. This type of viscometer consists of a circular cylinder
containing the fluid and a smooth ball. The ball is placed in the fluid and the time that
it takes to fall the length of the cylinder is recorded. This time is then utilized to back
the viscosity out of the velocity relationship that we derived using Stokes’ Law and
summing forces. As the ball is dropped into the fluid it accelerates as a result of the
gravitational field until the ball reaches terminal velocity. Terminal velocity occurs
4
5. Measurement Laboratory No. 3
EGR 101
when the viscous and buoyancy forces equal the weight of the ball. At this point the
velocity of the ball is maximum, or terminal. To simplify our approach, we will allow
the ball to reach terminal velocity prior to making the time measurements.
6. Laboratory Procedures
Part I: Determine the viscosity of an unknown fluid
1) At your lab station you will find several different sizes of spheres of different
materials. The materials are brass, Teflon, and glass. For the first procedure you
need to use the largest of the Teflon spheres.
2) Using the micrometer determine the diameter of the largest Teflon sphere to the
nearest 0.001 inch. You must convert this measurement to SI units (Hint: 1.00 in.
equals 2.54 cm.) Next using the digital scales, find the mass of the Teflon sphere
to the nearest 0.01 g. You can now use these two numbers to determine the
density of the Teflon sphere (g/cm3).
3) Next you will need to measure the fall time of the sphere through the fluid in the
2000-mL graduated cylinder (to the nearest 0.01 s). To do this use the stopwatch
to measure the amount of time it takes for the sphere to fall from the 1600-mL
mark to the 400-mL mark.
4) Repeat steps for the remaining two Teflon spheres of that size.
5) Measure the distance using the ruler between the 1600-mL graduation line and the
400-mL graduation line.
6) Now using the time recorded from the stopwatch for each sphere dropped and the
distance measurement between the graduation lines, determine the velocity of
each sphere as it passed through the fluid (cm/s). You will need to use the steel
scale to determine the distance between the 400 and 1600 ml marks
7) Using Stokes’ Law provided in the lab manual, determine the viscosity (m) of the
fluid using the average velocity of the three spheres. A common unit of viscosity
is the Poise, or 1 g/cm.s.
8) Calculate the Reynold’s Number using the fluid and ball properties determined
above.
Part II: Predict the fall time of similar size spheres of differing materials:
1) Using the micrometer, determine the diameter of the largest glass and brass
spheres (nearest 0.001 in.). There should be three of each and these diameters
should be roughly the same as the diameters of the Teflon spheres used earlier.
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6. Measurement Laboratory No. 3
EGR 101
2) Next use the digital scales to determine the mass of each of the spheres (nearest
0.01 g). Using the mass and diameter measurements, calculate the density of the
glass and brass spheres (g/cm3).
3) Now using your calculated viscosity for the unknown fluid, use Stokes Law to
determine the velocity for the spheres (cm/s). Using the velocity and the distance
between the 1600-mL and the 400-mL graduation lines determine the fall time for
the spheres.
4) Next confirm your predicted fall times by timing each of the spheres falling
through the fluid.
Part III: Predict the fall time of differing size spheres of similar material
1) Determine the diameters of the remaining six glass spheres. And measure their
respective individual masses in the electronic scale. Use these measurements to
confirm the density of the glass spheres.
2) Now using your calculated viscosity for the unknown fluid, use Stokes Law to
determine the velocity for the spheres. Using the velocity and the distance
between the 1600-mL and the 400-mL graduation lines determine the fall time for
the spheres.
4) Next confirm your predicted fall times by timing each of the spheres falling through
the fluid.
Part IV: Determine an unknown fluid
1) For this procedure you will need the remaining six Teflon spheres and the smaller
fluid filled graduated cylinder.
2) As before measure the diameters and masses for each of the Teflon spheres and
confirm the density of Teflon.
3) Next determine the mass of the fluid in the graduated cylinder and the volume. The
mass of the graduated cylinder while empty will be provided in lab. Using the
volume and the mass of the fluid, calculate the density.
4) Now as before use the stop watch to measure the fall time between two graduation
lines on the graduated cylinder. Which lines you use are of your own choosing.
Repeat for all six of the spheres. Note: For small diameter fluid columns there is
an interaction between the fluid and the wall of the cylinder. For this reason you
must correct for the diameter interaction using the following relationship,
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7. Measurement Laboratory No. 3
EGR 101
3 5
È d Êdˆ Êdˆ ˘
m c = m Í1 - 2.104 + 2.09Á ˜ - 0.95Á ˜ ˙
Í
Î D Ë D¯ Ë D¯ ˙˚
where mc is the corrected viscosity, and D is the internal diameter of the cylinder.
5) Using Stokes Law determine the viscosity of the unknown fluid by using the
average velocities of each of the two different size spheres.
7. Concluding Questions
1) In Part I, Step 8, what is the value of the Reynold’s Number, and using this value is
Stokes’ Law valid? Why, or why not?
2) In Part II, Step 4, were there any difficulties in measuring the fall times of the brass
spheres? Would increasing the diameter of the brass sphere make the problem
worse or better?
3) In Part III, Step 4, how did your predicted fall times compare to measured fall
times? What were the possible sources of error if any that occurred?
4) Given your calculated density and viscosity of your unknown fluid in Part IV,
confirm your findings with the lab TA to identify your unknown fluid. Who did
your results compare to the data from the TA?
5) In the lab manual there is a formula listed for Stokes Law that contains a correction
factor relating the diameter of the sphere and the diameter of the graduated
cylinder. Measure the diameter of the graduated cylinder and determine the
corrected fall times for the two different size spheres in Part IV?
6) Was there a significant difference between the corrected values for fall times and
the non-corrected values? How much did the diameter of the graduated cylinder
influence the fall time of the sphere?
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