This document provides an overview of fluid statics and pressure measurements. It begins with defining key fluid properties like viscosity and continuum hypothesis. It then discusses pressure at a point using Pascal's law and basic equations for pressure fields. The hydrostatic condition of zero acceleration is examined, leading to equations for pressure variation in incompressible and compressible fluids. Standard atmospheric models and various pressure measurement techniques like manometers, barometers, and mechanical devices are also summarized. Example problems are provided to demonstrate applications of the fluid statics concepts.
In fluid Mechanics course pressure measurement with different devices is much important. In this slides we will learn different pressure measuring devices.
1. Introduction to Kinematics
2. Methods of Describing Fluid Motion
a). Lagrangian Method
b). Eulerian Method
3. Flow Patterns
- Stream Line
- Path Line
- Streak Line
- Streak Tube
4. Classification of Fluid Flow
a). Steady and Unsteady Flow
b). Uniform and Non-Uniform Flow
c). Laminar and Turbulent Flow
d). Rotational and Irrotational Flow
e). Compressible and Incompressible Flow
f). Ideal and Real Flow
g). One, Two and Three Dimensional Flow
5. Rate of Flow (Discharge) and Continuity Equation
6. Continuity Equation in Three Dimensions
7. Velocity and Acceleration
8. Stream and Velocity Potential Functions
In fluid Mechanics course pressure measurement with different devices is much important. In this slides we will learn different pressure measuring devices.
1. Introduction to Kinematics
2. Methods of Describing Fluid Motion
a). Lagrangian Method
b). Eulerian Method
3. Flow Patterns
- Stream Line
- Path Line
- Streak Line
- Streak Tube
4. Classification of Fluid Flow
a). Steady and Unsteady Flow
b). Uniform and Non-Uniform Flow
c). Laminar and Turbulent Flow
d). Rotational and Irrotational Flow
e). Compressible and Incompressible Flow
f). Ideal and Real Flow
g). One, Two and Three Dimensional Flow
5. Rate of Flow (Discharge) and Continuity Equation
6. Continuity Equation in Three Dimensions
7. Velocity and Acceleration
8. Stream and Velocity Potential Functions
A fluid is a state of matter in which its molecules move freely and do not bear a constant relationship in space to other molecules.
In physics, fluid flow has all kinds of aspects: steady or unsteady, compressible or incompressible, viscous or non-viscous, and rotational or irrotational to name a few. Some of these characteristics reflect properties of the liquid itself, and others focus on how the fluid is moving.
Fluids are :-
Liquid : blood, i.v. infusions)
Gas : O2 , N2O)
Vapour (transition from liquid to gas) : N2O (under compression in cylinder), volatile inhalational agents (halothane, isoflurane, etc)
Sublimate (transition from solid to gas bypassing liquid state) : Dry ice (solid CO2), iodine
PLEASE NOTE THIS IS PART-1
By Referring or said Learning This Presentation You Can Clear Your Basics Fundamental Doubts about Fluid Mechanics. In this Presentation You Will Learn about Fluid Pressure, Pressure at Point, Pascal's Law, Types Of Pressure and Pressure Measurements.
Fluid mechanics is a science in study the fluid of liquids and gases in the cases of silence and movement and the forces acting on them can be divided materials found in nature into two branches.
Fluid Mechanics-Shear stress ,Shear stress distribution,Velocity profile,Flow Of Viscous Fluid Through The circular pipe ,Velocity profile for turbulent flow Boundary layer buildup in pipe,Velocity Distributions
Topics:
1. Introduction to Fluid Dynamics
2. Surface and Body Forces
3. Equations of Motion
- Reynold’s Equation
- Navier-Stokes Equation
- Euler’s Equation
- Bernoulli’s Equation
- Bernoulli’s Equation for Real Fluid
4. Applications of Bernoulli’s Equation
5. The Momentum Equation
6. Application of Momentum Equations
- Force exerted by flowing fluid on pipe bend
- Force exerted by the nozzle on the water
7. Measurement of Flow Rate
a). Venturimeter
b). Orifice Meter
c). Pitot Tube
8. Measurement of Flow Rate in Open Channels
a) Notches
b) Weirs
A fluid is a state of matter in which its molecules move freely and do not bear a constant relationship in space to other molecules.
In physics, fluid flow has all kinds of aspects: steady or unsteady, compressible or incompressible, viscous or non-viscous, and rotational or irrotational to name a few. Some of these characteristics reflect properties of the liquid itself, and others focus on how the fluid is moving.
Fluids are :-
Liquid : blood, i.v. infusions)
Gas : O2 , N2O)
Vapour (transition from liquid to gas) : N2O (under compression in cylinder), volatile inhalational agents (halothane, isoflurane, etc)
Sublimate (transition from solid to gas bypassing liquid state) : Dry ice (solid CO2), iodine
PLEASE NOTE THIS IS PART-1
By Referring or said Learning This Presentation You Can Clear Your Basics Fundamental Doubts about Fluid Mechanics. In this Presentation You Will Learn about Fluid Pressure, Pressure at Point, Pascal's Law, Types Of Pressure and Pressure Measurements.
Fluid mechanics is a science in study the fluid of liquids and gases in the cases of silence and movement and the forces acting on them can be divided materials found in nature into two branches.
Fluid Mechanics-Shear stress ,Shear stress distribution,Velocity profile,Flow Of Viscous Fluid Through The circular pipe ,Velocity profile for turbulent flow Boundary layer buildup in pipe,Velocity Distributions
Topics:
1. Introduction to Fluid Dynamics
2. Surface and Body Forces
3. Equations of Motion
- Reynold’s Equation
- Navier-Stokes Equation
- Euler’s Equation
- Bernoulli’s Equation
- Bernoulli’s Equation for Real Fluid
4. Applications of Bernoulli’s Equation
5. The Momentum Equation
6. Application of Momentum Equations
- Force exerted by flowing fluid on pipe bend
- Force exerted by the nozzle on the water
7. Measurement of Flow Rate
a). Venturimeter
b). Orifice Meter
c). Pitot Tube
8. Measurement of Flow Rate in Open Channels
a) Notches
b) Weirs
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 3(Kinematics of Fluid) of second edition.
FLUID FLOW
A fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases.
“Fluid flow may be defined as the flow of substances that do not permanently resist distortion”
The subject of fluid flow can be divided into-
fluid statics
fluid dynamics
Pressure and Pressure head is one of the major branch in Fluid Mechanics Engineering. It includes Pascal's and Hydro static law, which are the basic of Fluid Mechanics.
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
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.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
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.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
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.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
Vaccine management system project report documentation..pdf
fluid-mechanics
1. CUFE 201: FLUID MECHANICS
LECTURE 1: FLUID STATICS (SECTION A)
MARCH 2015
E. Mungofa
Fuels and Energy Engineering
2. OUTLINE
Overview
Continuum Hypothesis
Fluid properties
Pressure at a Point
Basic Equations for the Pressure Field
Hydrostatic Condition
Standard Atmosphere
Manometry and Pressure Measurements
Example Problems
3. FLUID MECHANICS OVERVIEW
Gas Liquids Statics Dynamics
Air, He, Ar,
N2, etc.
Water, Oils,
Alcohols,
etc.
0=∑ iF
Viscous/Inviscid
Steady/Unsteady
Compressible/
Incompressible
0>∑ iF
Laminar/
Turbulent
, Flows
Compressibility Viscosity
Vapor
Pressure
Density
Pressure
Buoyancy
Stability
Surface
Tension
Fluid Mechanics
Turbo Pumps
4. CONTINUUM HYPOTHESIS
We ignore the fact that it contains of billions of
individual molecules(atoms) in small region.
Treat fluid as varying continuously from one point to
next
Fluid : any substance that deforms continuously when
subjected to shear stress, no matter how small is the
force
5. FLUID PROPERTIES
Viscosity : property of a fluid that a fluid offer
resistance to shear stresses
It arises from intermolecular cohesion and transfer of
intermolecular momentum.
6. FLUID PROPERTIES
Viscosity : property of a fluid that a fluid offer
resistance to shear stresses
It arises from intermolecular cohesion and transfer of
intermolecular momentum.
8. FLUID STATICS
By definition, the fluid is at rest.
Or, no there is no relative motion between adjacent
particles.
No shearing forces is placed on the fluid.
There are only pressure forces, and no shear.
Results in relatively “simple” analysis
Generally look for the pressure variation in the fluid
Applications: Floating or submerged bodies, water dams
and gates, liquid storage tanks, etc.
9. PRESSURE AT A POINT: PASCAL’S LAW
How does the pressure at a point vary with orientation of the plane passing
through the point?
Pressure is the normal force per unit area at a
given point acting on a given plane within a
fluid mass of interest.Blaise Pascal (1623-1662)
p is average pressure in the x, y, and z direction.
Ps is the average pressure on the surface
θ is the plane inclination
δ is the length is each coordinate direction, x, y, z
δs is the length of the plane
γ is the specific weight
Wedged Shaped Fluid
Mass
F.B.D.
Pressure Forces
Gravity Force
V = (1/2δyδz)*δx
10. Pressure at a Point: Pascal’s Law
For simplicity in our Free Body Diagram, the x-pressure forces
cancel and do not need to be shown. Thus to arrive at our solution
we balance only the the y and z forces:
Pressure Force
in the y-direction
on the y-face
Pressure Force
on the plane in
the y-direction
Rigid body
motion in the y-
direction
Pressure Force
in the z-direction
on the z-face
Pressure Force
in the plane in
the z-direction
Weight of the
Wedge
Rigid body
motion in the z-
direction
Now, we can simplify each equation in each direction, noting that δy and δz can
be rewritten in terms of δs:
11. Pressure at a Point: Pascal’s Law
Substituting and rewriting the equations of motion, we obtain:
Math
Now, noting that we are really interested at point only, we let δy and
δz go to zero:
Pascal’s Law: the pressure at a point in a fluid at rest, or in motion, is
independent of the direction as long as there are no shearing stresses
present.
12. Pressure at a Point: Pascal’s Law
p1δxδs
psδxδsp2δxδs
ps = p1 = p2
Note: In dynamic system subject to shear, the normal stress representing
the pressure in the fluid is not necessarily the same in all directions. In
such a case the pressure is taken as the average of the three directions.
13. Pressure Field Equations
How does the pressure vary in a fluid or from point to point when no
shear stresses are present?
Consider a Small Fluid Element
Surface Forces
Body Forces
Taylor Series
V = δyδzδx
For simplicity the x-direction surface forces are not shown
p is pressure
γ is specific weight
14. Pressure Field Equations
Looking at the resultant surface forces in the y-direction:
Similarly, looking at the resultant surface forces in the x and z-direction, we
obtain:
Expressing these results in vector form:
15. Pressure Field Equations
Now, we note by definition, the “del” operator or gradient is the
following :
Then,
Now, rewriting the surface force equation, we obtain the following:
Now, we return the body forces, and we will only consider weight:
16. Pressure Field Equations
Use Newton’s Second Law to Sum the Forces for a Fluid
Element:
δm is the mass of the fluid element, and a is acceleration.
Then summing the surface forces and the body forces:
δm
“Most General Form”
for No Shear
17. Hydrostatic Condition: a = 0
0
Writing out the individual vector components:
This leads to the conclusion that for liquids or gases at rest, the
Pressure gradient in the vertical direction at any point in fluid
depends only on the specific weight of the fluid at that point. The
pressure does not depend on x or y.
Hydrostatic Equation
18. Hydrostatic Condition: Physical Implications
•Pressure changes with elevation
•Pressure does not change in the horizontal x-y plane
•The pressure gradient in the vertical direction is negative
•The pressure decreases as we move upward in a fluid at rest
•Pressure in a liquid does not change due to the shape of the container
•Specific Weight γ does not have to be constant in a fluid at rest
•Air and other gases will likely have a varying γ
•Thus, fluids could be incompressible or compressible statically
19. Hydrostatic Condition: Incompressible Fluids
The specific weight changes either through ρ, density or g, gravity. The
change in g is negligible, and for liquids ρ does not vary appreciable, thus most
liquids will be considered incompressible.
Starting with the Hydrostatic Equation:
We can immediately integrate since γ is a constant:
where the subscripts 1 and 2 refer two different vertical levels as in the
schematic.
20. Hydrostatic Condition: Incompressible Fluids
As in the schematic, noting the definition of h = z2 –z1:
h is known as the pressure head. The type of pressure distribution is known
as a hydrostatic distribution. The pressure must increase with depth to hold
up the fluid above it, and h is the depth measured from the location of p2.
Linear Variation with Depth
The equation for the pressure head is the following:
Physically, it is the height of the column of fluid of a specific weight, needed
to give the pressure difference p1 – p2.
21. Hydrostatic Condition: Incompressible Fluids
If we are working exclusively with a liquid, then there is a free surface
at the liquid-gas interface. For most applications, the pressure exerted
at the surface is atmospheric pressure, po. Then the equation is
written as follows:
The Pressure in a homogenous, incompressible fluid at rest depends on
the depth of the fluid relative to some reference and is not influenced by
the shape of the container.
p = po
p = p1
p = p2
Lines of constant Pressure
For p2 = p = γh + po
h1
For p1 = p = γh1 + po
22. Hydrostatic Application: Transmission of Fluid Pressure
•Mechanical advantage can be gained with equality of pressures
•A small force applied at the small piston is used to develop a large force at the
large piston.
• This is the principle between hydraulic jacks, lifts, presses, and hydraulic controls
•Mechanical force is applied through jacks action or compressed air for example
1
1
2
2 F
A
A
F =
23. Hydrostatic Condition: Compressible Fluids
Gases such as air, oxygen and nitrogen are thought of as compressible, so
we must consider the variation of density in the hydrostatic equation:
Note: γ = ρg and not a constant, then g
dz
dp
ρ−=
By the Ideal gas law: Thus,
RT
p
=ρ
R is the Gas Constant
T is the temperature
ρ is the density
Then,
For Isothermal Conditions, T is constant, To:
25. Hydrostatic Condition: U.S. Standard Atmosphere
Idealized Representation of the Mid-Latitude Atmosphere
Linear Variation, T = Ta - βz
Isothermal, T = To
Standard Atmosphere is used in
the design of aircraft, missiles
and spacecraft.
Stratosphere:
Troposphere:
26. Hydrostatic Condition: U.S. Standard Atmosphere
Starting from,
Now, for the Troposphere, Temperature is not constant:
Substitute for temperature and Integrate:
β is known as the lapse rate, 0.00650 K/m, and Ta is the temperature at
sea level, 288.15 K.
pa is the pressure at sea level, 101.33 kPa, R is the gas constant, 286.9
J/kg.K
28. Measurement of Pressure
Absolute Pressure: Pressure measured relative to a perfect vacuum
Gage Pressure: Pressure measured relative to local atmospheric pressure
•A gage pressure of zero corresponds to a pressure that is at local
atmospheric pressure.
•Absolute pressure is always positive
•Gage pressure can be either negative or positive
•Negative gage pressure is known as a vacuum or suction
• Standard units of Pressure are psi, psia, kPa, kPa (absolute)
•Pressure could also be measured in terms of the height of a fluid in a column
•Units in terms of fluid column height are mm Hg, inches of Hg, inches of
H20,etc
Example: Local Atmospheric Pressure is 14.7 psi, and I measure a 20 psia (“a” is for absolute). What is
the gage pressure?
The gage pressure is 20 psia – 14.7 psi = 5.3 psi
If I measure 10 psia, then the gage pressure is -4.7 psi, or is a “vacuum”.
30. Measurement of Pressure: Barometers
Evangelista Torricelli
(1608-1647)
The first mercury barometer was constructed in 1643-1644 by Torricelli. He
showed that the height of mercury in a column was 1/14 that of a water barometer,
due to the fact that mercury is 14 times more dense that water. He also noticed
that level of mercury varied from day to day due to weather changes, and that at
the top of the column there is a vacuum.
Animation of Experiment:
Torricelli’s Sketch Schematic:
Note, often pvapor is very small,
0.0000231 psia at 68° F, and
patm is 14.7 psi, thus:
31. Measurement of Pressure: Manometry
Manometry is a standard technique for measuring pressure using liquid
columns in vertical or include tubes. The devices used in this manner are
known as manometers.
The operation of three types of manometers will be discussed today:
1) The Piezometer Tube
2) The U-Tube Manometer
3) The Inclined Tube Manometer
The fundamental equation for manometers since they involve columns of
fluid at rest is the following:
h is positive moving downward, and negative moving upward, that is pressure
in columns of fluid decrease with gains in height, and increase with gain in
depth.
32. Measurement of Pressure: Piezometer Tube
pA (abs)
Moving from left to right:
Closed End “Container”
pA(abs) - γ1h1 = po
po
Move Up the
Tube
Rearranging: 11hpp oA γ=−
Gage Pressure
Then in terms of gage pressure, the equation for a Piezometer Tube:
Disadvantages:
1)The pressure in the container has to
be greater than atmospheric pressure.
2) Pressure must be relatively small to
maintain a small column of fluid.
3) The measurement of pressure must
be of a liquid.
Note: pA = p1 because they are at the same level
33. Measurement of Pressure: U-Tube Manometer
Closed End
“Container”
pA
Since, one end is open we can work entirely in gage pressure:
Moving from left to right: pA + γ1h1 = 0- γ2h2
Then the equation for the pressure in the container is the following:
If the fluid in the container is a gas, then the fluid 1 terms can be ignored:
Note: in the same fluid we can
“jump” across from 2 to 3 as
they are at the sam level, and
thus must have the same
pressure.
The fluid in the U-tube is known
as the gage fluid. The gage fluid
type depends on the application,
i.e. pressures attained, and
whether the fluid measured is a
gas or liquid.
34. Measurement of Pressure: U-Tube Manometer
Measuring a Pressure Differential
pA
pB
Closed End
“Container”
Closed End
“Container”
Moving from left to right: pA + γ1h1 - γ2h2 = pB
- γ3h3
Then the equation for the pressure difference in the container is the following:
Final notes:
1)Common gage fluids are Hg and
Water, some oils, and must be
immiscible.
2)Temp. must be considered in very
accurate measurements, as the gage
fluid properties can change.
3) Capillarity can play a role, but in
many cases each meniscus will cancel.
35. Measurement of Pressure: Inclined-Tube Manometer
This type of manometer is used to measure small pressure changes.
pA
pB
Moving from left to right: pA + γ1h1 - γ2h2 = pB
- γ3h3
h2
θ
θ
h2
l2
2
2
sin
l
h
=θ θsin22 lh =
Substituting for h2:
Rearranging to Obtain the Difference:
If the pressure difference is between gases:
Thus, for the length of the tube we can measure a greater pressure differential.